From 78e09ff7611a5868cecf09bcbb43935c320f3c37 Mon Sep 17 00:00:00 2001 From: Daniel Lakens Date: Fri, 28 Jun 2024 09:29:19 +0200 Subject: [PATCH] 1.5.1 --- 17-replication.qmd | 16 +++++++++----- changelog.qmd | 2 +- .../figure-html/fig-fig131-1.png | Bin 0 -> 12977 bytes .../figure-html/fig-fig132-1.png | Bin 0 -> 10467 bytes .../figure-html/fig-fig134-1.png | Bin 0 -> 14795 bytes .../figure-html/fig-fig136-1.png | Bin 0 -> 17882 bytes .../figure-html/fig-fig137-1.png | Bin 0 -> 15734 bytes .../figure-html/fig-fig138-1.png | Bin 0 -> 14667 bytes .../figure-html/fig-paradox-1.png | Bin 0 -> 13617 bytes .../figure-html/fig-pdft-1.png | Bin 0 -> 12135 bytes .../figure-html/fig-pdistr1-1.png | Bin 0 -> 14245 bytes .../figure-html/fig-pdistr2-1.png | Bin 0 -> 14455 bytes .../figure-html/fig-tdist-1.png | Bin 0 -> 13031 bytes docs/01-pvalue_files/figure-html/q1-1.png | Bin 0 -> 12781 bytes .../figure-html/unnamed-chunk-3-1.png | Bin 0 -> 23856 bytes docs/17-replication.html | 20 ++++++++++++++---- ...Improving-Your-Statistical-Inferences.epub | Bin 17660421 -> 17661510 bytes .../Improving-Your-Statistical-Inferences.pdf | Bin 18007247 -> 18010960 bytes docs/changelog.html | 6 +++--- docs/search.json | 6 +++--- 20 files changed, 34 insertions(+), 16 deletions(-) create mode 100644 docs/01-pvalue_files/figure-html/fig-fig131-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-fig132-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-fig134-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-fig136-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-fig137-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-fig138-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-paradox-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-pdft-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-pdistr1-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-pdistr2-1.png create mode 100644 docs/01-pvalue_files/figure-html/fig-tdist-1.png create mode 100644 docs/01-pvalue_files/figure-html/q1-1.png create mode 100644 docs/01-pvalue_files/figure-html/unnamed-chunk-3-1.png diff --git a/17-replication.qmd b/17-replication.qmd index 8c49b012..2662de2f 100644 --- a/17-replication.qmd +++ b/17-replication.qmd @@ -18,13 +18,13 @@ At the same time, the authors of the replication project acknowledged that a sin >After this intensive effort to reproduce a sample of published psychological findings, how many of the effects have we established are true? Zero. And how many of the effects have we established are false? Zero. Is this a limitation of the project design? No. It is the reality of doing science, even if it is not appreciated in daily practice. Humans desire certainty, and science infrequently provides it. As much as we might wish it to be otherwise, a single study almost never provides definitive resolution for or against an effect and its explanation. The original studies examined here offered tentative evidence; the replications we conducted offered additional, confirmatory evidence. In some cases, the replications increase confidence in the reliability of the original results; in other cases, the replications suggest that more investigation is needed to establish the validity of the original findings. Scientific progress is a cumulative process of uncertainty reduction that can only succeed if science itself remains the greatest skeptic of its explanatory claims. -A replication study is an experiment where the methods and procedures in a previous study are repeated by collecting new data. Typically, the term **direct replication study** is used when the methods and measures are as similar to the earlier study as possible. In a **conceptual replication study** a researcher intentionally introduces differences with the original study, either because they aim to systematically explore the impact of this change, or because they are not able to use the same methods and procedures. It is important to distinguish replication, where new data is collected, from **reproducibility**, where the same data is used to reproduce the reported results. In reproducibility checks the goal is to examine the presence of errors in the analysis files. Confusingly, the large-scale collaborative research project where 100 studies in psychology were replicated, and which is often considered an important contributor to the **replication crisis**, was called the Reproducibility Project: Psychology [@opensciencecollaboration_estimating_2015]. It should have been called the Replication Project: Psychology. Our apologies. +A replication study is an experiment where the methods and procedures in a previous study are repeated by collecting new data. Typically, the term **direct replication study** is used when the methods and measures are as similar to the earlier study as possible. In a **conceptual replication study** a researcher intentionally introduces differences with the original study with the aim to test the generalization of the effect, either because they aim to systematically explore the impact of this change, or because they are not able to use the same methods and procedures. It is important to distinguish replication, where new data is collected, from **reproducibility**, where the same data is used to reproduce the reported results. In reproducibility checks the goal is to examine the presence of errors in the analysis files. Confusingly, the large-scale collaborative research project where 100 studies in psychology were replicated, and which is often considered an important contributor to the **replication crisis**, was called the Reproducibility Project: Psychology [@opensciencecollaboration_estimating_2015]. It should have been called the Replication Project: Psychology. Our apologies. The goal of direct replication studies is first of all to identify Type 1 or Type 2 errors in the literature. In any original study with an alpha of 5% and a statistical power of 80% there is a probability of making an erroneous claim. Direct replication studies (especially those with low error rates) have the goal to identify these errors in the scientific literature, which is an important part of having a reliable knowledge base. It is especially important given that the scientific literature is biased, which increases the probability that a published claim is a Type 1 error. Schmidt [-@schmidt_shall_2009] also notes that claims can be erroneous because they were based on fraudulent data. Although direct replication studies can not identify fraud, they can point out erroneous claims due to fraud. The second important goal of direct replications is to identify factors in the study that were deemed irrelevant, but were crucial in generating the observed data [@tunc_falsificationist_2023]. For example, researchers might discover that an original and replication study yielded different results because the experimenter in one study treated the participants in a much more friendly manner than the experimenter in the other study. Such details are typically not reported in the method section, as they are deemed irrelevant, but direct replication studies might identify such factors. This highlights how replication studies are never identical in the social sciences. They are designed to be similar in all ways that a researcher thinks will matter. But not all factors deemed irrelevant will by irrelevant (and vice versa). -The goal of conceptual replication studies is to examine the generalizability of effects [@sidman_tactics_1960]. Researchers intentionally vary factors in the experiment to examine if this leads to variability in the results. Sometimes this variability is theoretically predicted, and sometimes researchers simply want to see what will happen. I would define a direct replication as a study where a researcher has the goal to not introduce variability compared to the original study, while in a conceptual replication variability is introduced intentionally. This distinction means that it is possible that what one researcher aims to be a direct replication is seen by a peer as a conceptual replication. For example, if a researcher sees no reason why an effect tested in Germany would not be identical in The Netherlands, they will consider it a direct replication. A peer might believe there are theoretically relevant differences between the two countries that make this a conceptual replication, as they would interpret the study as intentionally introducing variability by not keeping an important factor constant. The only way to clarify which factors are deemed theoretically relevant is to write a **constraints on generalizability** statement in the discussion where researchers specify which contexts they theoretically expect the effect to replicate in, and where variability in the results would not be considered problematic for their original claim [@simons_constraints_2017]. +The goal of conceptual replication studies is to examine the generalizability of effects [@sidman_tactics_1960]. Researchers intentionally vary factors in the experiment to examine if this leads to variability in the results. Sometimes this variability is theoretically predicted, and sometimes researchers simply want to see what will happen. I would define a direct replication as a study where a researcher has the goal to not introduce variability in the effect size compared to the original study, while in a conceptual replication variability is introduced intentionally with the goal to test the generalizability of the effect. This distinction means that it is possible that what one researcher aims to be a direct replication is seen by a peer as a conceptual replication. For example, if a researcher sees no reason why an effect tested in Germany would not be identical in The Netherlands, they will consider it a direct replication. A peer might believe there are theoretically relevant differences between the two countries that make this a conceptual replication, as they would interpret the study as intentionally introducing variability by not keeping an important factor constant. The only way to clarify which factors are deemed theoretically relevant is to write a **constraints on generalizability** statement in the discussion where researchers specify which contexts they theoretically expect the effect to replicate in, and where variability in the results would not be considered problematic for their original claim [@simons_constraints_2017]. It should be clear that the goals of replication studies are rather modest. At the same time, they are essential for a well-functioning empirical science. They provide a tool to identify false positive or false negative results, and can reveal variability across contexts that might falsify theoretical predictions, or lead to the generation of new theories. Being able to systematically replicate and extend a basic effect is one of the most important ways in which scientists develop and test theories. Although there are other approaches to generating reliable knowledge, such as **triangulation** where the same theory is tested in different but complementary ways, in practice the vast majority of scientifically established claims are based on replicable effects. @@ -140,9 +140,15 @@ Although a statistical difference between effect sizes is one coherent approach Let's take a step back, and consider which statistical test best reflects the question 'did this study replicate'. On the one hand it seems reasonable to consider an effect 'not replicated' if there is a statistically significant difference between the effect sizes. However, this can mean that a non-significant effect in the replication studies leads to a 'replication' just because the effect size estimate is not statistically smaller than the original effect size. On the other hand, it seems reasonable to consider an effect replicated if it is statistically significant in the replication study. These two approaches can lead to a conflict, however. Some statistically significant effects are statistically smaller than the original study. Should these be considered 'replicated' or not? We might want to combine both statistical tests, and consider a study a replication if the effect is both statistically different from 0 (i.e., *p* < .05 in a traditional significance test), and the difference in effect sizes is not statistically different from 0 (i.e., *p* > .05 for a test of heterogeneity in a meta-analysis of both effect sizes). We can perform both tests, and only consider a finding replicated if both conditions are met. Logically, a finding should then be considered as a non-replication if the opposite is true (i.e., *p* > .05 for significance test of the replication study, and *p* < .05 for the test of heterogeneity). -However, due to the low power of the test for a difference between the effect sizes in the original and replication study, it is not easy to meet the bar of an informative result. In practice, many replication studies that do not yield a statistically significant result will also not show a statistically significant difference as part of the test of heterogeneity. In a preprint (that we never bothered to resubmit after we received positive reviews) Richard Morey and I [@morey_why_2016] summarized this problem in our title "Why most of psychology is statistically unfalsifiable". If we want to have an informative test for replication following the criteria outlined above, most tests will be uninformative, and lead to inconclusive results. +However, due to the low power of the test for a difference between the effect sizes in the original and replication study, it is not easy to meet the bar of an informative result. In practice, many replication studies that do not yield a statistically significant result will also not show a statistically significant difference as part of the test of heterogeneity. In a preprint (that we never bothered to resubmit after we received positive reviews) Richard Morey and I [@morey_why_2016] summarized this problem in our title "Why most of psychology is statistically unfalsifiable". If we want to have an informative test for replication following the criteria outlined above, most tests will be uninformative, and lead to inconclusive results. -As we can never increase the sample size of original studies, and we also can not do science if we can not conclude claims in the literature can not be replicated, we will need to be pragmatic and develop alternative statistical procedures to claim an effect can not be replicated. As the large uncertainty in the original effect sizes are the main cause of the problem, a logical solution is to move to statistical approaches where this uncertainty is not part of the test. An intuitive approach would be to test if the effect size in the replication study is statistically smaller than the effect in the original study. In the example above we would test whether the 95% confidence interval around the effect size in the replication study excludes the effect in the original study (i.e., 0.6, or 0.592 when converted to Hedges'*g*). In essence this is a two-sided test against the original effect size. This is the equivalent of changing a independent *t*-test where two groups are compared to a one-sample *t*-test where the 95% confidence interval in one group is compared against the observed mean in the other group, ignoring uncertainty in this other group. We do not accept this approach when we compare two means, and we should not accept this approach when we compare two standardized mean differences from an original and replication study. The problem is that this test will too easily reject the null-hypothesis that the two effects are equal, because it ignores the variability in one of the two effect sizes. +This problem becomes even bigger if we admit that we often consider some effects too small to matter. @anderson_there_2016 mention an additional approach to analyzing replication studies where we do not just test the difference in effect sizes between an original and replication study, but combine this with an equivalence test to examine if the difference - if any - is too small to matter. With very large sample sizes tiny differences between studies can become statistically significant, which would result in the conclusion that a study did not replicate, even if the difference is considered too small to matter. + +Anderson also point out the importance of incorporating a [smallest effect size of interest](#sec-sesoi) when interpreting whether a replication study yields a null effect. For example, @mccarthy_registered_2018 replicated a hostility priming study originally reported to have an effect size of *d* = 3.01. In a multi-lab replication they observed an effect very close to zero: *d* = 0.06, 95% CI = [0.01, 0.12]. This effect was statistically different from the original, but statistically significant. McCarthy and colleagues argue this effect, even if significant, is too small to matter, and conclude "Our results suggest that the procedures we used in this replication study are unlikely to produce an assimilative priming effect that researchers could practically and routinely detect. Indeed, to detect priming effects as small as the 0.08-scale-unit difference we observed (which works out to approximately d = 0.06, 95% CI = [0.01, 0.12]), a study would need 4,362 participants in each priming condition to have 80% power with an alpha set to .05." + +Should we consider the replication study with *d* = 0.06 a successful replication, just because the effect is significant in a very large sample? As explained in the chapter on [equivalence testing](#sec-equivalencetesting), effects very close to zero are often considered equivalent to the absence of an effect because the effect is practically insignificant, theoretically smaller than expected, or impossible to reliably investigate given the resources that researchers have available. As @mccarthy_registered_2018 argue, the very small effect they observed is no longer practically feasible to study, and psychologists would therefore consider such effects equivalent to a null result. It is recommended to specify a smallest effect of interest in replication studies, where possible together with the original author (see the example by @morey_preregistered_2021 below) and evaluate replication studies with an equivalence test against the smallest effect size of interest. + +As noted above, although ideally we directly test the difference between effect sizes, the uncertainty in the original effect size estimate when sample sizes are small can make lead to a test with very low power. As we can never increase the sample size of original studies, and we also can not do science if we can not conclude claims in the literature can not be replicated, we will need to be pragmatic and develop alternative statistical procedures to claim an effect can not be replicated. As the large uncertainty in the original effect sizes are the main cause of the problem, a logical solution is to move to statistical approaches where this uncertainty is not part of the test. An intuitive approach would be to test if the effect size in the replication study is statistically smaller than the effect in the original study. In the example above we would test whether the 95% confidence interval around the effect size in the replication study excludes the effect in the original study (i.e., 0.6, or 0.592 when converted to Hedges'*g*). In essence this is a two-sided test against the original effect size. This is the equivalent of changing a independent *t*-test where two groups are compared to a one-sample *t*-test where the 95% confidence interval in one group is compared against the observed mean in the other group, ignoring uncertainty in this other group. We do not accept this approach when we compare two means, and we should not accept this approach when we compare two standardized mean differences from an original and replication study. The problem is that this test will too easily reject the null-hypothesis that the two effects are equal, because it ignores the variability in one of the two effect sizes. An alternative approach is to test against a more conservative effect size, and consider an original finding not replicated if this conservative effect size can be rejected. In practice researchers are primarily interested in the question whether the effect size in the replication study is statistically smaller that the effect size in the original study. This questions is answered by an *inferiority test*, which is statistically significant if the 90% confidence interval around the effect size in the replication study does not contain the conservative effect size estimate. One implementation of an inferiority test is the *small telescopes* approach [@simonsohn_small_2015]. In the small telescopes approach a test is performed against the effect the original study had 33% power to detect. In the example in @fig-rep-1 the original study had 33% power to detect and effect of *d* = 0.4. @@ -158,7 +164,7 @@ pwr::pwr.t.test( The 95% confidence interval of the replication study shows effects larger than 0.277 can be rejected, so a 90% confidence interval would be able to reject even smaller effect sizes. Therefore, the small telescopes approach would allow researchers to conclude that the original effect could not be replicated. The small telescopes is popular especially when replicating small original studies, as the smaller the sample size, the larger the effect size the study had 33% power to detect, and this the easier it is to reject in a replication study. This is the opposite of what happens if we want to test the two effect sizes against each other, where smaller original studies reduce the power of the test. -A fair point of criticism of the small telescopes approach is that the convention to test against an effect the original study had 33% power to detect is completely arbitrary. Ideally researchers would specify the *smallest effect size of interest* and perform an inferiority test against the smallest effect that would actually matter. Specifying a smallest effect size of interest is difficult, however. In some cases researchers involved in the original study might specify the smallest effect they care about. For example, in a multi-lab replication study of the action-sentence compatibility effect the researchers who published the original study stated that they considered an effect of 50 milliseconds or less theoretically negligible [@morey_preregistered_2021]. The large sample size allowed the authors to conclusively reject the presence of effects as large or larger than were considered theoretically negligible. +A fair point of criticism of the small telescopes approach is that the convention to test against an effect the original study had 33% power to detect is completely arbitrary. Ideally researchers would specify the *smallest effect size of interest* and perform an inferiority test against the smallest effect that would actually matter. Specifying a smallest effect size of interest is difficult, however. In some cases researchers involved in the original study might specify the smallest effect they care about. For example, in a multi-lab replication study of the action-sentence compatibility effect the researchers who published the original study stated that they considered an effect of 50 milliseconds or less theoretically negligible [@morey_preregistered_2021]. The large sample size allowed the authors to conclusively reject the presence of effects as large or larger than were considered theoretically negligible. Another approach is to set the smallest effect size of interest based on theoretical predictions. Alternatively, researchers might set the smallest effect size of interest to be larger than the [crud factor](#sec-crud), which is the effect size in a literature due to theoretically uninteresting systematic noise [@orben_crud_2020]. For example, @ferguson_providing_2021 suggests a smallest effect size of interest of *r* = 0.1 (or *d* = 0.2) because such effect sizes can be observed for nonsensical variables, and are likely purely driven by (methodological) confounds. Another approach that has been proposed is to combine the effect size of the original study and the replication study in a meta-analysis, and test whether the meta-analytic effect is statistically different from zero. This approach is interesting if there is no bias, but when there is bias the weakness of this approach outweighs its usefulness. As publication bias and selection bias [inflated effect sizes](#sec-effectinflated) the meta-analytic effect size will also be inflated. This in turn inflates the probability that the meta-analytic effect size is statistically significant, when there is no effect. diff --git a/changelog.qmd b/changelog.qmd index 2a80e139..28d3b385 100644 --- a/changelog.qmd +++ b/changelog.qmd @@ -4,7 +4,7 @@ Sys.setlocale("LC_TIME", "C") ``` -The current version of this textbook is 1.5.0 +The current version of this textbook is 1.5.1 This version has been compiled on `r format(Sys.Date(), '%B %d, %Y')`. diff --git a/docs/01-pvalue_files/figure-html/fig-fig131-1.png b/docs/01-pvalue_files/figure-html/fig-fig131-1.png new file mode 100644 index 0000000000000000000000000000000000000000..ac23cb0d589b07f826a01087e296058a877d8593 GIT binary patch literal 12977 zcmdseXH=6**C+`=ngRlXN|T<5fPw-E?NKcBL{JeBPzgn{_U}0hXlYl1(l-MsNUG3sMw;S*dnOHi0v(k?d^^2Wt8Dr%JAs2D5&7eqN2*8ipq-c zWkpeCMNp-;tT(Exx2UWasxZnJy=4prH406Q!c&W&5=AX4qV__im)gsqGJ2^D#!g7c zP7!{mH)^N1Xs5S#hf%b{fPNW7m*YGTqnx+(E$^_fh(+xFgT+iPJFu`EVKF#+`qJIB zg<>XrM?Z?yWkoXU`iE>2nd6yLH~Htw$2HyqtnDk2}9?u(b5*xAvRz00Qj@(;b( zX<8jNLtY4V?@!pz{oj0#!;gGELfgwSVFIe_spciR8%N!nM0MjK_>-PB~&MsxNrPend;kF z9jzL@xh`2p#m@>0b#I5LB*kQiyZ+>q1;bMohuenH%Y?chmBOZ5tQfJZch>VdAN_-> zPl1s}I zbm|~VaQU@CMeA!ql=_0i>w%iZay9AY&c9+JCq0$2N+*4zty!!56!N%Bo^Q_49IQKE zm)q7?X{qvhCRYxG$5=^MlKGT)V^^52oIQFimeQjLMvbc5}FIn=Hi^!d8-> z{AnINR{Gc-Z(r6|h#gyY4g&f-9meUi5!OnsJ5%_na=Uup0Pzu(J9&{sjGyDtlD0nt zDG8d7+4H+;18G4*C^XzEXLf|SBWK|1SGf&md|Pv-JxOWtG|p0682`m`D=}(H>n&M!uSsQr{P9XHjqvjY0f=Ub=RkEw>kplBdznw781zk%z;U!?#@Er6Q;4e9{xdBNlD^QB8-9M2Zfk&4y6wTA-F8kbi7Z*~&ivtXMJU2Ka^>5c!#g$B zs!)Z6X;OBKU?(XTV;vS4q6mugm6tvmD@%4A6`t4rcu#JeB3ee~DHdMmho>BcDfR>} zWh~xV51m&4i;b*d=^4l!jm^ASAM5G0{LxwuyQ(kWnyWoBnIe(XxzoIdMs`+s^Xn9y zLO0jk^IufBPhDB$riqOKOG@JDN6}h) z+gOhKcD1XrwVkFJPL`C%aC&qorx|1!$^MGiAxv#J6p`3;Zc<)ZGi1 zKS6m7ov=jgjIjiDQ-WC=8~XBV4c$J@Gbya(?sIQ?HE*A?JM-?G<}*Kp&##*Gc$#dn zMQT}+J$21}4mPZEM}fV2lV^EQ5rOb|Ka&xTO@Y?4(jSY(@3bw$G1YHcUJuHH&Ac+zZ? 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After this intensive effort to reproduce a sample of published psychological findings, how many of the effects have we established are true? Zero. And how many of the effects have we established are false? Zero. Is this a limitation of the project design? No. It is the reality of doing science, even if it is not appreciated in daily practice. Humans desire certainty, and science infrequently provides it. As much as we might wish it to be otherwise, a single study almost never provides definitive resolution for or against an effect and its explanation. The original studies examined here offered tentative evidence; the replications we conducted offered additional, confirmatory evidence. In some cases, the replications increase confidence in the reliability of the original results; in other cases, the replications suggest that more investigation is needed to establish the validity of the original findings. Scientific progress is a cumulative process of uncertainty reduction that can only succeed if science itself remains the greatest skeptic of its explanatory claims.

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A replication study is an experiment where the methods and procedures in a previous study are repeated by collecting new data. Typically, the term direct replication study is used when the methods and measures are as similar to the earlier study as possible. In a conceptual replication study a researcher intentionally introduces differences with the original study, either because they aim to systematically explore the impact of this change, or because they are not able to use the same methods and procedures. It is important to distinguish replication, where new data is collected, from reproducibility, where the same data is used to reproduce the reported results. In reproducibility checks the goal is to examine the presence of errors in the analysis files. Confusingly, the large-scale collaborative research project where 100 studies in psychology were replicated, and which is often considered an important contributor to the replication crisis, was called the Reproducibility Project: Psychology (Open Science Collaboration, 2015). It should have been called the Replication Project: Psychology. Our apologies.

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A replication study is an experiment where the methods and procedures in a previous study are repeated by collecting new data. Typically, the term direct replication study is used when the methods and measures are as similar to the earlier study as possible. In a conceptual replication study a researcher intentionally introduces differences with the original study with the aim to test the generalization of the effect, either because they aim to systematically explore the impact of this change, or because they are not able to use the same methods and procedures. It is important to distinguish replication, where new data is collected, from reproducibility, where the same data is used to reproduce the reported results. In reproducibility checks the goal is to examine the presence of errors in the analysis files. Confusingly, the large-scale collaborative research project where 100 studies in psychology were replicated, and which is often considered an important contributor to the replication crisis, was called the Reproducibility Project: Psychology (Open Science Collaboration, 2015). It should have been called the Replication Project: Psychology. Our apologies.

The goal of direct replication studies is first of all to identify Type 1 or Type 2 errors in the literature. In any original study with an alpha of 5% and a statistical power of 80% there is a probability of making an erroneous claim. Direct replication studies (especially those with low error rates) have the goal to identify these errors in the scientific literature, which is an important part of having a reliable knowledge base. It is especially important given that the scientific literature is biased, which increases the probability that a published claim is a Type 1 error. Schmidt (2009) also notes that claims can be erroneous because they were based on fraudulent data. Although direct replication studies can not identify fraud, they can point out erroneous claims due to fraud.

The second important goal of direct replications is to identify factors in the study that were deemed irrelevant, but were crucial in generating the observed data (Tunç & Tunç, 2023). For example, researchers might discover that an original and replication study yielded different results because the experimenter in one study treated the participants in a much more friendly manner than the experimenter in the other study. Such details are typically not reported in the method section, as they are deemed irrelevant, but direct replication studies might identify such factors. This highlights how replication studies are never identical in the social sciences. They are designed to be similar in all ways that a researcher thinks will matter. But not all factors deemed irrelevant will by irrelevant (and vice versa).

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The goal of conceptual replication studies is to examine the generalizability of effects (Sidman, 1960). Researchers intentionally vary factors in the experiment to examine if this leads to variability in the results. Sometimes this variability is theoretically predicted, and sometimes researchers simply want to see what will happen. I would define a direct replication as a study where a researcher has the goal to not introduce variability compared to the original study, while in a conceptual replication variability is introduced intentionally. This distinction means that it is possible that what one researcher aims to be a direct replication is seen by a peer as a conceptual replication. For example, if a researcher sees no reason why an effect tested in Germany would not be identical in The Netherlands, they will consider it a direct replication. A peer might believe there are theoretically relevant differences between the two countries that make this a conceptual replication, as they would interpret the study as intentionally introducing variability by not keeping an important factor constant. The only way to clarify which factors are deemed theoretically relevant is to write a constraints on generalizability statement in the discussion where researchers specify which contexts they theoretically expect the effect to replicate in, and where variability in the results would not be considered problematic for their original claim (Simons et al., 2017).

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The goal of conceptual replication studies is to examine the generalizability of effects (Sidman, 1960). Researchers intentionally vary factors in the experiment to examine if this leads to variability in the results. Sometimes this variability is theoretically predicted, and sometimes researchers simply want to see what will happen. I would define a direct replication as a study where a researcher has the goal to not introduce variability in the effect size compared to the original study, while in a conceptual replication variability is introduced intentionally with the goal to test the generalizability of the effect. This distinction means that it is possible that what one researcher aims to be a direct replication is seen by a peer as a conceptual replication. For example, if a researcher sees no reason why an effect tested in Germany would not be identical in The Netherlands, they will consider it a direct replication. A peer might believe there are theoretically relevant differences between the two countries that make this a conceptual replication, as they would interpret the study as intentionally introducing variability by not keeping an important factor constant. The only way to clarify which factors are deemed theoretically relevant is to write a constraints on generalizability statement in the discussion where researchers specify which contexts they theoretically expect the effect to replicate in, and where variability in the results would not be considered problematic for their original claim (Simons et al., 2017).

It should be clear that the goals of replication studies are rather modest. At the same time, they are essential for a well-functioning empirical science. They provide a tool to identify false positive or false negative results, and can reveal variability across contexts that might falsify theoretical predictions, or lead to the generation of new theories. Being able to systematically replicate and extend a basic effect is one of the most important ways in which scientists develop and test theories. Although there are other approaches to generating reliable knowledge, such as triangulation where the same theory is tested in different but complementary ways, in practice the vast majority of scientifically established claims are based on replicable effects.

Not all researchers agree that their science has inter-subjectively repeatable observations. In what is called the ‘crisis in social psychology’ Gergen (1973) argued social psychology was not a cumulative science:

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Although a statistical difference between effect sizes is one coherent approach to decide whether a study has been replicated, researchers are sometimes interested in a different question: Was there a significant result in the replication study? In this approach to analyzing replication studies there is no direct comparison with the effect observed in the original study. The question is therefore not so much ‘is the original effect replicated?’ but ‘if we repeat the original study is a statistically significant effect observed?’. In other words, we are not testing whether an effect has been replicated, but whether a predicted effect has been observed. Another way of saying this is that we are not asking whether the observed effect replicated, but whether the original ordinal claim of the presence of an non-zero effect is replicated. In the example in Figure 17.2 the replication study has an effect size of 0, so there is no statistically significant effect, and the original effect did not replicate (in the sense that repeated the procedure did not yield a significant result).

Let’s take a step back, and consider which statistical test best reflects the question ‘did this study replicate’. On the one hand it seems reasonable to consider an effect ‘not replicated’ if there is a statistically significant difference between the effect sizes. However, this can mean that a non-significant effect in the replication studies leads to a ‘replication’ just because the effect size estimate is not statistically smaller than the original effect size. On the other hand, it seems reasonable to consider an effect replicated if it is statistically significant in the replication study. These two approaches can lead to a conflict, however. Some statistically significant effects are statistically smaller than the original study. Should these be considered ‘replicated’ or not? We might want to combine both statistical tests, and consider a study a replication if the effect is both statistically different from 0 (i.e., p < .05 in a traditional significance test), and the difference in effect sizes is not statistically different from 0 (i.e., p > .05 for a test of heterogeneity in a meta-analysis of both effect sizes). We can perform both tests, and only consider a finding replicated if both conditions are met. Logically, a finding should then be considered as a non-replication if the opposite is true (i.e., p > .05 for significance test of the replication study, and p < .05 for the test of heterogeneity).

However, due to the low power of the test for a difference between the effect sizes in the original and replication study, it is not easy to meet the bar of an informative result. In practice, many replication studies that do not yield a statistically significant result will also not show a statistically significant difference as part of the test of heterogeneity. In a preprint (that we never bothered to resubmit after we received positive reviews) Richard Morey and I (Richard D. Morey & Lakens, 2016) summarized this problem in our title “Why most of psychology is statistically unfalsifiable”. If we want to have an informative test for replication following the criteria outlined above, most tests will be uninformative, and lead to inconclusive results.

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As we can never increase the sample size of original studies, and we also can not do science if we can not conclude claims in the literature can not be replicated, we will need to be pragmatic and develop alternative statistical procedures to claim an effect can not be replicated. As the large uncertainty in the original effect sizes are the main cause of the problem, a logical solution is to move to statistical approaches where this uncertainty is not part of the test. An intuitive approach would be to test if the effect size in the replication study is statistically smaller than the effect in the original study. In the example above we would test whether the 95% confidence interval around the effect size in the replication study excludes the effect in the original study (i.e., 0.6, or 0.592 when converted to Hedges’g). In essence this is a two-sided test against the original effect size. This is the equivalent of changing a independent t-test where two groups are compared to a one-sample t-test where the 95% confidence interval in one group is compared against the observed mean in the other group, ignoring uncertainty in this other group. We do not accept this approach when we compare two means, and we should not accept this approach when we compare two standardized mean differences from an original and replication study. The problem is that this test will too easily reject the null-hypothesis that the two effects are equal, because it ignores the variability in one of the two effect sizes.

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This problem becomes even bigger if we admit that we often consider some effects too small to matter. Anderson & Maxwell (2016) mention an additional approach to analyzing replication studies where we do not just test the difference in effect sizes between an original and replication study, but combine this with an equivalence test to examine if the difference - if any - is too small to matter. With very large sample sizes tiny differences between studies can become statistically significant, which would result in the conclusion that a study did not replicate, even if the difference is considered too small to matter.

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Anderson also point out the importance of incorporating a smallest effect size of interest when interpreting whether a replication study yields a null effect. For example, McCarthy et al. (2018) replicated a hostility priming study originally reported to have an effect size of d = 3.01. In a multi-lab replication they observed an effect very close to zero: d = 0.06, 95% CI = [0.01, 0.12]. This effect was statistically different from the original, but statistically significant. McCarthy and colleagues argue this effect, even if significant, is too small to matter, and conclude “Our results suggest that the procedures we used in this replication study are unlikely to produce an assimilative priming effect that researchers could practically and routinely detect. Indeed, to detect priming effects as small as the 0.08-scale-unit difference we observed (which works out to approximately d = 0.06, 95% CI = [0.01, 0.12]), a study would need 4,362 participants in each priming condition to have 80% power with an alpha set to .05.”

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Should we consider the replication study with d = 0.06 a successful replication, just because the effect is significant in a very large sample? As explained in the chapter on equivalence testing, effects very close to zero are often considered equivalent to the absence of an effect because the effect is practically insignificant, theoretically smaller than expected, or impossible to reliably investigate given the resources that researchers have available. As McCarthy et al. (2018) argue, the very small effect they observed is no longer practically feasible to study, and psychologists would therefore consider such effects equivalent to a null result. It is recommended to specify a smallest effect of interest in replication studies, where possible together with the original author (see the example by Richard D. Morey et al. (2021) below) and evaluate replication studies with an equivalence test against the smallest effect size of interest.

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As noted above, although ideally we directly test the difference between effect sizes, the uncertainty in the original effect size estimate when sample sizes are small can make lead to a test with very low power. As we can never increase the sample size of original studies, and we also can not do science if we can not conclude claims in the literature can not be replicated, we will need to be pragmatic and develop alternative statistical procedures to claim an effect can not be replicated. As the large uncertainty in the original effect sizes are the main cause of the problem, a logical solution is to move to statistical approaches where this uncertainty is not part of the test. An intuitive approach would be to test if the effect size in the replication study is statistically smaller than the effect in the original study. In the example above we would test whether the 95% confidence interval around the effect size in the replication study excludes the effect in the original study (i.e., 0.6, or 0.592 when converted to Hedges’g). In essence this is a two-sided test against the original effect size. This is the equivalent of changing a independent t-test where two groups are compared to a one-sample t-test where the 95% confidence interval in one group is compared against the observed mean in the other group, ignoring uncertainty in this other group. We do not accept this approach when we compare two means, and we should not accept this approach when we compare two standardized mean differences from an original and replication study. The problem is that this test will too easily reject the null-hypothesis that the two effects are equal, because it ignores the variability in one of the two effect sizes.

An alternative approach is to test against a more conservative effect size, and consider an original finding not replicated if this conservative effect size can be rejected. In practice researchers are primarily interested in the question whether the effect size in the replication study is statistically smaller that the effect size in the original study. This questions is answered by an inferiority test, which is statistically significant if the 90% confidence interval around the effect size in the replication study does not contain the conservative effect size estimate. One implementation of an inferiority test is the small telescopes approach (Simonsohn, 2015). In the small telescopes approach a test is performed against the effect the original study had 33% power to detect. In the example in Figure 17.2 the original study had 33% power to detect and effect of d = 0.4.

pwr::pwr.t.test(
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The 95% confidence interval of the replication study shows effects larger than 0.277 can be rejected, so a 90% confidence interval would be able to reject even smaller effect sizes. Therefore, the small telescopes approach would allow researchers to conclude that the original effect could not be replicated. The small telescopes is popular especially when replicating small original studies, as the smaller the sample size, the larger the effect size the study had 33% power to detect, and this the easier it is to reject in a replication study. This is the opposite of what happens if we want to test the two effect sizes against each other, where smaller original studies reduce the power of the test.

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A fair point of criticism of the small telescopes approach is that the convention to test against an effect the original study had 33% power to detect is completely arbitrary. Ideally researchers would specify the smallest effect size of interest and perform an inferiority test against the smallest effect that would actually matter. Specifying a smallest effect size of interest is difficult, however. In some cases researchers involved in the original study might specify the smallest effect they care about. For example, in a multi-lab replication study of the action-sentence compatibility effect the researchers who published the original study stated that they considered an effect of 50 milliseconds or less theoretically negligible (Richard D. Morey et al., 2021). The large sample size allowed the authors to conclusively reject the presence of effects as large or larger than were considered theoretically negligible.

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A fair point of criticism of the small telescopes approach is that the convention to test against an effect the original study had 33% power to detect is completely arbitrary. Ideally researchers would specify the smallest effect size of interest and perform an inferiority test against the smallest effect that would actually matter. Specifying a smallest effect size of interest is difficult, however. In some cases researchers involved in the original study might specify the smallest effect they care about. For example, in a multi-lab replication study of the action-sentence compatibility effect the researchers who published the original study stated that they considered an effect of 50 milliseconds or less theoretically negligible (Richard D. Morey et al., 2021). The large sample size allowed the authors to conclusively reject the presence of effects as large or larger than were considered theoretically negligible. Another approach is to set the smallest effect size of interest based on theoretical predictions. Alternatively, researchers might set the smallest effect size of interest to be larger than the crud factor, which is the effect size in a literature due to theoretically uninteresting systematic noise (Orben & Lakens, 2020). For example, Ferguson & Heene (2021) suggests a smallest effect size of interest of r = 0.1 (or d = 0.2) because such effect sizes can be observed for nonsensical variables, and are likely purely driven by (methodological) confounds.

Another approach that has been proposed is to combine the effect size of the original study and the replication study in a meta-analysis, and test whether the meta-analytic effect is statistically different from zero. This approach is interesting if there is no bias, but when there is bias the weakness of this approach outweighs its usefulness. As publication bias and selection bias inflated effect sizes the meta-analytic effect size will also be inflated. This in turn inflates the probability that the meta-analytic effect size is statistically significant, when there is no effect.

17.4 Replication studies or lower alpha levels?

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Epstein, S. (1980). The stability of behavior: II. Implications for psychological research. American Psychologist, 35(9), 790–806. https://doi.org/10.1037/0003-066X.35.9.790
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+Ferguson, C. J., & Heene, M. (2021). Providing a lower-bound estimate for psychology’s “crud factor”: The case of aggression. Professional Psychology: Research and Practice, 52(6), 620–626. https://doi.org/http://dx.doi.org/10.1037/pro0000386 +
Fishman, D. B., & Neigher, W. D. (1982). American psychology in the eighties: Who will buy? American Psychologist, 37(5), 533–546. https://doi.org/10.1037/0003-066X.37.5.533
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Maier, M., & Lakens, D. (2022). Justify your alpha: A primer on two practical approaches. Advances in Methods and Practices in Psychological Science. https://doi.org/10.31234/osf.io/ts4r6
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The current version of this textbook is 1.5.0

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This version has been compiled on June 25, 2024.

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This version was generated from Git commit #efb02e32. All version controlled changes can be found on GitHub.

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The current version of this textbook is 1.5.1

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This version has been compiled on June 28, 2024.

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This version was generated from Git commit #c852c7b4. All version controlled changes can be found on GitHub.

This page documents the changes to the textbook that were more substantial than fixing a typo.

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June 20, 2024:

diff --git a/docs/search.json b/docs/search.json index fbdd424a..17af1695 100644 --- a/docs/search.json +++ b/docs/search.json @@ -1654,7 +1654,7 @@ "href": "17-replication.html#analyzing-replication-studies.", "title": "17  Replication Studies", "section": "\n17.3 Analyzing Replication Studies.", - "text": "17.3 Analyzing Replication Studies.\nThere are multiple ways to statistically analyze a replication study (Anderson & Maxwell, 2016). The most straightforward statistical approach is also the least common: Testing whether the effect sizes in the original and replication studies are statistically different from each other. Two effect sizes from an independent t-test can be tested against each other using:\n\\[\nZ_{Diff} = \\frac{{{\\delta}}_{1}{- {\\delta}}_{2}}{\\sqrt{{V}_{\\delta_{1}} + {V}_{\\delta_{2}}}}\n\\]\nwhere the difference between the two Cohen’s d effect sizes is divided by the standard error of the difference score, based on the square root of the combined variances of the effect sizes (Borenstein, 2009, formula 19.6 and 19.7). This formula provides a hint why researchers rarely test for differences between effect sizes. The standard error of the difference score is based on the variance in the original and replication study. If the original study has a small sample size, the variance will be large, and a test of the difference between effect sizes can have very low power.\nLet’s take a look at an original non-preregistered study which observed an effect size of d = 0.6 in an independent t-test with 30 participants in each group. A preregistered replication study is performed which observed an effect size of 0 with 150 participants in each group. Testing the two effect sizes against each other can be achieved in three ways that are in principle identical (although the exact implementation, such as computing Cohen’s d or Hedges’ g, might yield slightly different p-values). The first is to compute the corresponding p-value for the Z-test in the formula above. The other two ways are implemented in the metafor package and consist of a heterogeneity analysis and a moderator analysis. These two approaches are mathematically identical. In the heterogeneity analysis we test if the variability in effect sizes (even though there are only two) is greater than expected based only on random variation.\n\nd1 <- escalc(n1i = 30, \n n2i = 30, \n di = 0.6, \n measure = \"SMD\")\nd2 <- escalc(n1i = 100, \n n2i = 100, \n di = 0.0, \n measure = \"SMD\")\nmetadata <- data.frame(yi = c(d1$yi, d2$yi), \n vi = c(d1$vi, d2$vi), \n study = c(\"original\", \"replication\"))\n\n# Test based on heterogeneity analysis\nres_h <- rma(yi, \n vi, \n data = metadata, \n method = \"FE\")\nres_h\n\n# The moderator test would be: rma(yi, vi, mods = ~study, method = \"FE\", data = metadata, digits = 3)\n\n\nFixed-Effects Model (k = 2)\n\nI^2 (total heterogeneity / total variability): 74.45%\nH^2 (total variability / sampling variability): 3.91\n\nTest for Heterogeneity:\nQ(df = 1) = 3.9146, p-val = 0.0479\n\nModel Results:\n\nestimate se zval pval ci.lb ci.ub \n 0.1322 0.1246 1.0607 0.2888 -0.1121 0.3765 \n\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\n\nThe result yields p-value of 0.048, which is statistically significant, and therefore allows us to statistically conclude that the two effect sizes differ from each other. We can also perform this test as a moderator analysis.\n\nres_mod <- rma(yi, \n vi, \n mods = ~study,\n method = \"FE\",\n data = metadata,\n digits = 3)\n\nThis result yields the same p-value of 0.048. This same test was recently repackaged by Spence and Stanley (2024) as a prediction interval, but this approach is just a test of the difference between effect sizes.\nIt is worth pointing out that in the example above the difference between the effect sizes was large, the replication study had a much larger sample size than the original study, but the differences was only just statistically significant. As we see in Figure 17.2 the original study had large uncertainty, which as explained above is part of the variance of the estimate of the difference between effect sizes. If the replication study had yielded an effect size that was even slightly in the positive direction (which should happen 50% of the time if the true effect size is 0) the difference would no longer have been statistically significant. In general, power is low when original studies have small sample sizes. Despite this limitation, directly testing the difference between effect sizes is the most intuitive and coherent approach to claiming that a study failed to replicate.\n\n\n\n\n\n\n\nFigure 17.2: Forest plot for an original study (N = 60, d = 0.6) and a replication study (N = 200, d = 0).\n\n\n\n\nAlthough a statistical difference between effect sizes is one coherent approach to decide whether a study has been replicated, researchers are sometimes interested in a different question: Was there a significant result in the replication study? In this approach to analyzing replication studies there is no direct comparison with the effect observed in the original study. The question is therefore not so much ‘is the original effect replicated?’ but ‘if we repeat the original study is a statistically significant effect observed?’. In other words, we are not testing whether an effect has been replicated, but whether a predicted effect has been observed. Another way of saying this is that we are not asking whether the observed effect replicated, but whether the original ordinal claim of the presence of an non-zero effect is replicated. In the example in Figure 17.2 the replication study has an effect size of 0, so there is no statistically significant effect, and the original effect did not replicate (in the sense that repeated the procedure did not yield a significant result).\nLet’s take a step back, and consider which statistical test best reflects the question ‘did this study replicate’. On the one hand it seems reasonable to consider an effect ‘not replicated’ if there is a statistically significant difference between the effect sizes. However, this can mean that a non-significant effect in the replication studies leads to a ‘replication’ just because the effect size estimate is not statistically smaller than the original effect size. On the other hand, it seems reasonable to consider an effect replicated if it is statistically significant in the replication study. These two approaches can lead to a conflict, however. Some statistically significant effects are statistically smaller than the original study. Should these be considered ‘replicated’ or not? We might want to combine both statistical tests, and consider a study a replication if the effect is both statistically different from 0 (i.e., p < .05 in a traditional significance test), and the difference in effect sizes is not statistically different from 0 (i.e., p > .05 for a test of heterogeneity in a meta-analysis of both effect sizes). We can perform both tests, and only consider a finding replicated if both conditions are met. Logically, a finding should then be considered as a non-replication if the opposite is true (i.e., p > .05 for significance test of the replication study, and p < .05 for the test of heterogeneity).\nHowever, due to the low power of the test for a difference between the effect sizes in the original and replication study, it is not easy to meet the bar of an informative result. In practice, many replication studies that do not yield a statistically significant result will also not show a statistically significant difference as part of the test of heterogeneity. In a preprint (that we never bothered to resubmit after we received positive reviews) Richard Morey and I (Richard D. Morey & Lakens, 2016) summarized this problem in our title “Why most of psychology is statistically unfalsifiable”. If we want to have an informative test for replication following the criteria outlined above, most tests will be uninformative, and lead to inconclusive results.\nAs we can never increase the sample size of original studies, and we also can not do science if we can not conclude claims in the literature can not be replicated, we will need to be pragmatic and develop alternative statistical procedures to claim an effect can not be replicated. As the large uncertainty in the original effect sizes are the main cause of the problem, a logical solution is to move to statistical approaches where this uncertainty is not part of the test. An intuitive approach would be to test if the effect size in the replication study is statistically smaller than the effect in the original study. In the example above we would test whether the 95% confidence interval around the effect size in the replication study excludes the effect in the original study (i.e., 0.6, or 0.592 when converted to Hedges’g). In essence this is a two-sided test against the original effect size. This is the equivalent of changing a independent t-test where two groups are compared to a one-sample t-test where the 95% confidence interval in one group is compared against the observed mean in the other group, ignoring uncertainty in this other group. We do not accept this approach when we compare two means, and we should not accept this approach when we compare two standardized mean differences from an original and replication study. The problem is that this test will too easily reject the null-hypothesis that the two effects are equal, because it ignores the variability in one of the two effect sizes.\nAn alternative approach is to test against a more conservative effect size, and consider an original finding not replicated if this conservative effect size can be rejected. In practice researchers are primarily interested in the question whether the effect size in the replication study is statistically smaller that the effect size in the original study. This questions is answered by an inferiority test, which is statistically significant if the 90% confidence interval around the effect size in the replication study does not contain the conservative effect size estimate. One implementation of an inferiority test is the small telescopes approach (Simonsohn, 2015). In the small telescopes approach a test is performed against the effect the original study had 33% power to detect. In the example in Figure 17.2 the original study had 33% power to detect and effect of d = 0.4.\n\npwr::pwr.t.test(\n n = 30,\n sig.level = 0.05,\n power = 0.33,\n type = \"two.sample\",\n alternative = \"two.sided\"\n)\n\n\n Two-sample t test power calculation \n\n n = 30\n d = 0.3988825\n sig.level = 0.05\n power = 0.33\n alternative = two.sided\n\nNOTE: n is number in *each* group\n\n\nThe 95% confidence interval of the replication study shows effects larger than 0.277 can be rejected, so a 90% confidence interval would be able to reject even smaller effect sizes. Therefore, the small telescopes approach would allow researchers to conclude that the original effect could not be replicated. The small telescopes is popular especially when replicating small original studies, as the smaller the sample size, the larger the effect size the study had 33% power to detect, and this the easier it is to reject in a replication study. This is the opposite of what happens if we want to test the two effect sizes against each other, where smaller original studies reduce the power of the test.\nA fair point of criticism of the small telescopes approach is that the convention to test against an effect the original study had 33% power to detect is completely arbitrary. Ideally researchers would specify the smallest effect size of interest and perform an inferiority test against the smallest effect that would actually matter. Specifying a smallest effect size of interest is difficult, however. In some cases researchers involved in the original study might specify the smallest effect they care about. For example, in a multi-lab replication study of the action-sentence compatibility effect the researchers who published the original study stated that they considered an effect of 50 milliseconds or less theoretically negligible (Richard D. Morey et al., 2021). The large sample size allowed the authors to conclusively reject the presence of effects as large or larger than were considered theoretically negligible.\nAnother approach that has been proposed is to combine the effect size of the original study and the replication study in a meta-analysis, and test whether the meta-analytic effect is statistically different from zero. This approach is interesting if there is no bias, but when there is bias the weakness of this approach outweighs its usefulness. As publication bias and selection bias inflated effect sizes the meta-analytic effect size will also be inflated. This in turn inflates the probability that the meta-analytic effect size is statistically significant, when there is no effect.", + "text": "17.3 Analyzing Replication Studies.\nThere are multiple ways to statistically analyze a replication study (Anderson & Maxwell, 2016). The most straightforward statistical approach is also the least common: Testing whether the effect sizes in the original and replication studies are statistically different from each other. Two effect sizes from an independent t-test can be tested against each other using:\n\\[\nZ_{Diff} = \\frac{{{\\delta}}_{1}{- {\\delta}}_{2}}{\\sqrt{{V}_{\\delta_{1}} + {V}_{\\delta_{2}}}}\n\\]\nwhere the difference between the two Cohen’s d effect sizes is divided by the standard error of the difference score, based on the square root of the combined variances of the effect sizes (Borenstein, 2009, formula 19.6 and 19.7). This formula provides a hint why researchers rarely test for differences between effect sizes. The standard error of the difference score is based on the variance in the original and replication study. If the original study has a small sample size, the variance will be large, and a test of the difference between effect sizes can have very low power.\nLet’s take a look at an original non-preregistered study which observed an effect size of d = 0.6 in an independent t-test with 30 participants in each group. A preregistered replication study is performed which observed an effect size of 0 with 150 participants in each group. Testing the two effect sizes against each other can be achieved in three ways that are in principle identical (although the exact implementation, such as computing Cohen’s d or Hedges’ g, might yield slightly different p-values). The first is to compute the corresponding p-value for the Z-test in the formula above. The other two ways are implemented in the metafor package and consist of a heterogeneity analysis and a moderator analysis. These two approaches are mathematically identical. In the heterogeneity analysis we test if the variability in effect sizes (even though there are only two) is greater than expected based only on random variation.\n\nd1 <- escalc(n1i = 30, \n n2i = 30, \n di = 0.6, \n measure = \"SMD\")\nd2 <- escalc(n1i = 100, \n n2i = 100, \n di = 0.0, \n measure = \"SMD\")\nmetadata <- data.frame(yi = c(d1$yi, d2$yi), \n vi = c(d1$vi, d2$vi), \n study = c(\"original\", \"replication\"))\n\n# Test based on heterogeneity analysis\nres_h <- rma(yi, \n vi, \n data = metadata, \n method = \"FE\")\nres_h\n\n# The moderator test would be: rma(yi, vi, mods = ~study, method = \"FE\", data = metadata, digits = 3)\n\n\nFixed-Effects Model (k = 2)\n\nI^2 (total heterogeneity / total variability): 74.45%\nH^2 (total variability / sampling variability): 3.91\n\nTest for Heterogeneity:\nQ(df = 1) = 3.9146, p-val = 0.0479\n\nModel Results:\n\nestimate se zval pval ci.lb ci.ub \n 0.1322 0.1246 1.0607 0.2888 -0.1121 0.3765 \n\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\n\nThe result yields p-value of 0.048, which is statistically significant, and therefore allows us to statistically conclude that the two effect sizes differ from each other. We can also perform this test as a moderator analysis.\n\nres_mod <- rma(yi, \n vi, \n mods = ~study,\n method = \"FE\",\n data = metadata,\n digits = 3)\n\nThis result yields the same p-value of 0.048. This same test was recently repackaged by Spence and Stanley (2024) as a prediction interval, but this approach is just a test of the difference between effect sizes.\nIt is worth pointing out that in the example above the difference between the effect sizes was large, the replication study had a much larger sample size than the original study, but the differences was only just statistically significant. As we see in Figure 17.2 the original study had large uncertainty, which as explained above is part of the variance of the estimate of the difference between effect sizes. If the replication study had yielded an effect size that was even slightly in the positive direction (which should happen 50% of the time if the true effect size is 0) the difference would no longer have been statistically significant. In general, power is low when original studies have small sample sizes. Despite this limitation, directly testing the difference between effect sizes is the most intuitive and coherent approach to claiming that a study failed to replicate.\n\n\n\n\n\n\n\nFigure 17.2: Forest plot for an original study (N = 60, d = 0.6) and a replication study (N = 200, d = 0).\n\n\n\n\nAlthough a statistical difference between effect sizes is one coherent approach to decide whether a study has been replicated, researchers are sometimes interested in a different question: Was there a significant result in the replication study? In this approach to analyzing replication studies there is no direct comparison with the effect observed in the original study. The question is therefore not so much ‘is the original effect replicated?’ but ‘if we repeat the original study is a statistically significant effect observed?’. In other words, we are not testing whether an effect has been replicated, but whether a predicted effect has been observed. Another way of saying this is that we are not asking whether the observed effect replicated, but whether the original ordinal claim of the presence of an non-zero effect is replicated. In the example in Figure 17.2 the replication study has an effect size of 0, so there is no statistically significant effect, and the original effect did not replicate (in the sense that repeated the procedure did not yield a significant result).\nLet’s take a step back, and consider which statistical test best reflects the question ‘did this study replicate’. On the one hand it seems reasonable to consider an effect ‘not replicated’ if there is a statistically significant difference between the effect sizes. However, this can mean that a non-significant effect in the replication studies leads to a ‘replication’ just because the effect size estimate is not statistically smaller than the original effect size. On the other hand, it seems reasonable to consider an effect replicated if it is statistically significant in the replication study. These two approaches can lead to a conflict, however. Some statistically significant effects are statistically smaller than the original study. Should these be considered ‘replicated’ or not? We might want to combine both statistical tests, and consider a study a replication if the effect is both statistically different from 0 (i.e., p < .05 in a traditional significance test), and the difference in effect sizes is not statistically different from 0 (i.e., p > .05 for a test of heterogeneity in a meta-analysis of both effect sizes). We can perform both tests, and only consider a finding replicated if both conditions are met. Logically, a finding should then be considered as a non-replication if the opposite is true (i.e., p > .05 for significance test of the replication study, and p < .05 for the test of heterogeneity).\nHowever, due to the low power of the test for a difference between the effect sizes in the original and replication study, it is not easy to meet the bar of an informative result. In practice, many replication studies that do not yield a statistically significant result will also not show a statistically significant difference as part of the test of heterogeneity. In a preprint (that we never bothered to resubmit after we received positive reviews) Richard Morey and I (Richard D. Morey & Lakens, 2016) summarized this problem in our title “Why most of psychology is statistically unfalsifiable”. If we want to have an informative test for replication following the criteria outlined above, most tests will be uninformative, and lead to inconclusive results.\nThis problem becomes even bigger if we admit that we often consider some effects too small to matter. Anderson & Maxwell (2016) mention an additional approach to analyzing replication studies where we do not just test the difference in effect sizes between an original and replication study, but combine this with an equivalence test to examine if the difference - if any - is too small to matter. With very large sample sizes tiny differences between studies can become statistically significant, which would result in the conclusion that a study did not replicate, even if the difference is considered too small to matter.\nAnderson also point out the importance of incorporating a smallest effect size of interest when interpreting whether a replication study yields a null effect. For example, McCarthy et al. (2018) replicated a hostility priming study originally reported to have an effect size of d = 3.01. In a multi-lab replication they observed an effect very close to zero: d = 0.06, 95% CI = [0.01, 0.12]. This effect was statistically different from the original, but statistically significant. McCarthy and colleagues argue this effect, even if significant, is too small to matter, and conclude “Our results suggest that the procedures we used in this replication study are unlikely to produce an assimilative priming effect that researchers could practically and routinely detect. Indeed, to detect priming effects as small as the 0.08-scale-unit difference we observed (which works out to approximately d = 0.06, 95% CI = [0.01, 0.12]), a study would need 4,362 participants in each priming condition to have 80% power with an alpha set to .05.”\nShould we consider the replication study with d = 0.06 a successful replication, just because the effect is significant in a very large sample? As explained in the chapter on equivalence testing, effects very close to zero are often considered equivalent to the absence of an effect because the effect is practically insignificant, theoretically smaller than expected, or impossible to reliably investigate given the resources that researchers have available. As McCarthy et al. (2018) argue, the very small effect they observed is no longer practically feasible to study, and psychologists would therefore consider such effects equivalent to a null result. It is recommended to specify a smallest effect of interest in replication studies, where possible together with the original author (see the example by Richard D. Morey et al. (2021) below) and evaluate replication studies with an equivalence test against the smallest effect size of interest.\nAs noted above, although ideally we directly test the difference between effect sizes, the uncertainty in the original effect size estimate when sample sizes are small can make lead to a test with very low power. As we can never increase the sample size of original studies, and we also can not do science if we can not conclude claims in the literature can not be replicated, we will need to be pragmatic and develop alternative statistical procedures to claim an effect can not be replicated. As the large uncertainty in the original effect sizes are the main cause of the problem, a logical solution is to move to statistical approaches where this uncertainty is not part of the test. An intuitive approach would be to test if the effect size in the replication study is statistically smaller than the effect in the original study. In the example above we would test whether the 95% confidence interval around the effect size in the replication study excludes the effect in the original study (i.e., 0.6, or 0.592 when converted to Hedges’g). In essence this is a two-sided test against the original effect size. This is the equivalent of changing a independent t-test where two groups are compared to a one-sample t-test where the 95% confidence interval in one group is compared against the observed mean in the other group, ignoring uncertainty in this other group. We do not accept this approach when we compare two means, and we should not accept this approach when we compare two standardized mean differences from an original and replication study. The problem is that this test will too easily reject the null-hypothesis that the two effects are equal, because it ignores the variability in one of the two effect sizes.\nAn alternative approach is to test against a more conservative effect size, and consider an original finding not replicated if this conservative effect size can be rejected. In practice researchers are primarily interested in the question whether the effect size in the replication study is statistically smaller that the effect size in the original study. This questions is answered by an inferiority test, which is statistically significant if the 90% confidence interval around the effect size in the replication study does not contain the conservative effect size estimate. One implementation of an inferiority test is the small telescopes approach (Simonsohn, 2015). In the small telescopes approach a test is performed against the effect the original study had 33% power to detect. In the example in Figure 17.2 the original study had 33% power to detect and effect of d = 0.4.\n\npwr::pwr.t.test(\n n = 30,\n sig.level = 0.05,\n power = 0.33,\n type = \"two.sample\",\n alternative = \"two.sided\"\n)\n\n\n Two-sample t test power calculation \n\n n = 30\n d = 0.3988825\n sig.level = 0.05\n power = 0.33\n alternative = two.sided\n\nNOTE: n is number in *each* group\n\n\nThe 95% confidence interval of the replication study shows effects larger than 0.277 can be rejected, so a 90% confidence interval would be able to reject even smaller effect sizes. Therefore, the small telescopes approach would allow researchers to conclude that the original effect could not be replicated. The small telescopes is popular especially when replicating small original studies, as the smaller the sample size, the larger the effect size the study had 33% power to detect, and this the easier it is to reject in a replication study. This is the opposite of what happens if we want to test the two effect sizes against each other, where smaller original studies reduce the power of the test.\nA fair point of criticism of the small telescopes approach is that the convention to test against an effect the original study had 33% power to detect is completely arbitrary. Ideally researchers would specify the smallest effect size of interest and perform an inferiority test against the smallest effect that would actually matter. Specifying a smallest effect size of interest is difficult, however. In some cases researchers involved in the original study might specify the smallest effect they care about. For example, in a multi-lab replication study of the action-sentence compatibility effect the researchers who published the original study stated that they considered an effect of 50 milliseconds or less theoretically negligible (Richard D. Morey et al., 2021). The large sample size allowed the authors to conclusively reject the presence of effects as large or larger than were considered theoretically negligible. Another approach is to set the smallest effect size of interest based on theoretical predictions. Alternatively, researchers might set the smallest effect size of interest to be larger than the crud factor, which is the effect size in a literature due to theoretically uninteresting systematic noise (Orben & Lakens, 2020). For example, Ferguson & Heene (2021) suggests a smallest effect size of interest of r = 0.1 (or d = 0.2) because such effect sizes can be observed for nonsensical variables, and are likely purely driven by (methodological) confounds.\nAnother approach that has been proposed is to combine the effect size of the original study and the replication study in a meta-analysis, and test whether the meta-analytic effect is statistically different from zero. This approach is interesting if there is no bias, but when there is bias the weakness of this approach outweighs its usefulness. As publication bias and selection bias inflated effect sizes the meta-analytic effect size will also be inflated. This in turn inflates the probability that the meta-analytic effect size is statistically significant, when there is no effect.", "crumbs": [ "17  Replication Studies" ] @@ -1684,7 +1684,7 @@ "href": "17-replication.html#why-are-replication-studies-so-rare", "title": "17  Replication Studies", "section": "\n17.6 Why are replication studies so rare?", - "text": "17.6 Why are replication studies so rare?\n“It is difficult to deny that there is more thrill, and usually more glory, involved in blazing a new trail than in checking the pioneer’s work” (Mack, 1951). Throughout history, researchers have pointed out that the reward structures value novel research over replication studies (Fishman & Neigher, 1982; Koole & Lakens, 2012). Performing replication studies is a social dilemma: It is good for everyone if scientists perform replication studies, but it is better for an individual scientist to perform a novel study than a replication study. Exact numbers of how many replication studies are performed are difficult to get, as there is no complete database that keeps track of all replication studies (but see Curate Science, Replication WIKI or the Replication Database.\nAlthough the reward structures have remained the same, there are some positive developments. At the start of the replication crisis failed replications of Bem’s pre-cognition study were desk-rejected by the editor of JPSP, Eliot Smith, who stated “This journal does not publish replication studies, whether successful or unsuccessful” and “We don’t want to be the Journal of Bem Replication” (Aldhous, 2011). This led to public outcry, and numerous journals have started to explicitly state they accept replication studies. An increasing number of studies are accepting Registered Report publications, which can also be replication studies, and Peer Community Inn: Registered Reports initiative is publishing replication studies. The APA has created specific reporting guidelines for replication studies. Some science funders have developed grants for replication research. At the same time, replication studies are still rewarded less than novel work, which means researchers who want to build a career are still pushed towards novel research instead of replication studies. So despite positive developments, in many disciplines there is still some way to go before replication studies become a normal aspect of scientific research.\n\n\n\n\nAldhous, P. (2011). Journal rejects studies contradicting precognition. New Scientist. https://www.newscientist.com/article/dn20447-journal-rejects-studies-contradicting-precognition/\n\n\nAnderson, S. F., & Maxwell, S. E. (2016). There’s more than one way to conduct a replication study: Beyond statistical significance. Psychological Methods, 21(1), 1–12. https://doi.org/10.1037/met0000051\n\n\nBonett, D. G. (2012). Replication-Extension Studies. Current Directions in Psychological Science, 21(6), 409–412. https://doi.org/10.1177/0963721412459512\n\n\nBorenstein, M. (Ed.). (2009). Introduction to meta-analysis. John Wiley & Sons.\n\n\nde Groot, A. D. (1969). Methodology (Vol. 6). Mouton & Co.\n\n\nEbersole, C. R., Mathur, M. B., Baranski, E., Bart-Plange, D.-J., Buttrick, N. R., Chartier, C. R., Corker, K. S., Corley, M., Hartshorne, J. K., IJzerman, H., Lazarević, L. B., Rabagliati, H., Ropovik, I., Aczel, B., Aeschbach, L. F., Andrighetto, L., Arnal, J. D., Arrow, H., Babincak, P., … Nosek, B. A. (2020). Many Labs 5: Testing Pre-Data-Collection Peer Review as an Intervention to Increase Replicability. Advances in Methods and Practices in Psychological Science, 3(3), 309–331. https://doi.org/10.1177/2515245920958687\n\n\nEpstein, S. (1980). The stability of behavior: II. Implications for psychological research. American Psychologist, 35(9), 790–806. https://doi.org/10.1037/0003-066X.35.9.790\n\n\nFishman, D. B., & Neigher, W. D. (1982). American psychology in the eighties: Who will buy? American Psychologist, 37(5), 533–546. https://doi.org/10.1037/0003-066X.37.5.533\n\n\nFreedman, J. L., & Fraser, S. C. (1966). Compliance without pressure: The foot-in-the-door technique. Journal of Personality and Social Psychology, 4(2), 195–202. https://doi.org/10.1037/h0023552\n\n\nGergen, K. J. (1973). Social psychology as history. Journal of Personality and Social Psychology, 26, 309–320. https://doi.org/10.1037/h0034436\n\n\nGreenwald, A. G. (Ed.). (1976). An editorial. Journal of Personality and Social Psychology, 33(1), 1–7. https://doi.org/10.1037/h0078635\n\n\nIsager, P. M., van Aert, R. C. M., Bahník, Š., Brandt, M. J., DeSoto, K. A., Giner-Sorolla, R., Krueger, J. I., Perugini, M., Ropovik, I., van ’t Veer, A. E., Vranka, M., & Lakens, D. (2023). Deciding what to replicate: A decision model for replication study selection under resource and knowledge constraints. Psychological Methods, 28(2), 438–451. https://doi.org/10.1037/met0000438\n\n\nJunk, T., & Lyons, L. (2020). Reproducibility and Replication of Experimental Particle Physics Results. Harvard Data Science Review, 2(4). https://doi.org/10.1162/99608f92.250f995b\n\n\nKoole, S. L., & Lakens, D. (2012). Rewarding replications A sure and simple way to improve psychological science. Perspectives on Psychological Science, 7(6), 608–614. https://doi.org/10.1177/1745691612462586\n\n\nLoevinger, J. (1968). The \"information explosion.\". American Psychologist, 23(6), 455–455. https://doi.org/10.1037/h0020800\n\n\nLubin, A. (1957). Replicability as a publication criterion. American Psychologist, 12, 519–520. https://doi.org/10.1037/h0039746\n\n\nLuttrell, A., Petty, R. E., & Xu, M. (2017). Replicating and fixing failed replications: The case of need for cognition and argument quality. Journal of Experimental Social Psychology, 69, 178–183. https://doi.org/10.1016/j.jesp.2016.09.006\n\n\nLykken, D. T. (1968). Statistical significance in psychological research. Psychological Bulletin, 70, 151–159. https://doi.org/10.1037/h0026141\n\n\nMack, R. W. (1951). The Need for Replication Research in Sociology. American Sociological Review, 16(1), 93–94. https://doi.org/10.2307/2087978\n\n\nMaier, M., & Lakens, D. (2022). Justify your alpha: A primer on two practical approaches. Advances in Methods and Practices in Psychological Science. https://doi.org/10.31234/osf.io/ts4r6\n\n\nMellers, B., Hertwig, R., & Kahneman, D. (2001). Do frequency representations eliminate conjunction effects? An exercise in adversarial collaboration. Psychological Science, 12(4), 269–275. https://doi.org/10.1111/1467-9280.00350\n\n\nMiller, J. (2009). What is the probability of replicating a statistically significant effect? Psychonomic Bulletin & Review, 16(4), 617–640. https://doi.org/10.3758/PBR.16.4.617\n\n\nMorey, Richard D., Kaschak, M. P., Díez-Álamo, A. M., Glenberg, A. M., Zwaan, R. A., Lakens, D., Ibáñez, A., García, A., Gianelli, C., Jones, J. L., Madden, J., Alifano, F., Bergen, B., Bloxsom, N. G., Bub, D. N., Cai, Z. G., Chartier, C. R., Chatterjee, A., Conwell, E., … Ziv-Crispel, N. (2021). A pre-registered, multi-lab non-replication of the action-sentence compatibility effect (ACE). Psychonomic Bulletin & Review. https://doi.org/10.3758/s13423-021-01927-8\n\n\nMorey, Richard D., & Lakens, D. (2016). Why most of psychology is statistically unfalsifiable. https://raw.githubusercontent.com/richarddmorey/psychology_resolution/master/paper/response.pdf\n\n\nNeher, A. (1967). Probability Pyramiding, Research Error and the Need for Independent Replication. The Psychological Record, 17(2), 257–262. https://doi.org/10.1007/BF03393713\n\n\nNosek, B. A., & Errington, T. M. (2020). What is replication? PLOS Biology, 18(3), e3000691. https://doi.org/10.1371/journal.pbio.3000691\n\n\nOpen Science Collaboration. (2015). Estimating the reproducibility of psychological science. Science, 349(6251), aac4716–aac4716. https://doi.org/10.1126/science.aac4716\n\n\nPereboom, A. C. (1971). Some Fundamental Problems in Experimental Psychology: An Overview. Psychological Reports, 28(2). https://doi.org/10.2466/pr0.1971.28.2.439\n\n\nPopper, K. R. (2002). The logic of scientific discovery. Routledge.\n\n\nSamelson, F. (1980). J B Watson’s Little Albert, Cyril Burt’s twins, and the need for a critical science. American Psychologist, 35(7), 619–625. https://doi.org/10.1037/0003-066X.35.7.619\n\n\nSchmidt, S. (2009). Shall we really do it again? The powerful concept of replication is neglected in the social sciences. Review of General Psychology, 13(2), 90–100. https://doi.org/10.1037/a0015108\n\n\nSidman, M. (1960). Tactics of Scientific Research: Evaluating Experimental Data in Psychology (New edition). Cambridge Center for Behavioral.\n\n\nSimons, D. J., Shoda, Y., & Lindsay, D. S. (2017). Constraints on Generality (COG): A Proposed Addition to All Empirical Papers. Perspectives on Psychological Science, 12(6), 1123–1128. https://doi.org/10.1177/1745691617708630\n\n\nSimonsohn, U. (2015). Small telescopes: Detectability and the evaluation of replication results. Psychological Science, 26(5), 559–569. https://doi.org/10.1177/0956797614567341\n\n\nSmith, N. C. (1970). Replication studies: A neglected aspect of psychological research. American Psychologist, 25(10), 970–975. https://doi.org/10.1037/h0029774\n\n\nSpence, J. R., & Stanley, D. J. (2024). Tempered Expectations: A Tutorial for Calculating and Interpreting Prediction Intervals in the Context of Replications. Advances in Methods and Practices in Psychological Science, 7(1), 25152459231217932. https://doi.org/10.1177/25152459231217932\n\n\nStroebe, W., & Strack, F. (2014). The Alleged Crisis and the Illusion of Exact Replication. Perspectives on Psychological Science, 9(1), 59–71. https://doi.org/10.1177/1745691613514450\n\n\nTunç, D. U., & Tunç, M. N. (2023). A Falsificationist Treatment of Auxiliary Hypotheses in Social and Behavioral Sciences: Systematic Replications Framework. Meta-Psychology, 7. https://doi.org/10.15626/MP.2021.2756", + "text": "17.6 Why are replication studies so rare?\n“It is difficult to deny that there is more thrill, and usually more glory, involved in blazing a new trail than in checking the pioneer’s work” (Mack, 1951). Throughout history, researchers have pointed out that the reward structures value novel research over replication studies (Fishman & Neigher, 1982; Koole & Lakens, 2012). Performing replication studies is a social dilemma: It is good for everyone if scientists perform replication studies, but it is better for an individual scientist to perform a novel study than a replication study. Exact numbers of how many replication studies are performed are difficult to get, as there is no complete database that keeps track of all replication studies (but see Curate Science, Replication WIKI or the Replication Database.\nAlthough the reward structures have remained the same, there are some positive developments. At the start of the replication crisis failed replications of Bem’s pre-cognition study were desk-rejected by the editor of JPSP, Eliot Smith, who stated “This journal does not publish replication studies, whether successful or unsuccessful” and “We don’t want to be the Journal of Bem Replication” (Aldhous, 2011). This led to public outcry, and numerous journals have started to explicitly state they accept replication studies. An increasing number of studies are accepting Registered Report publications, which can also be replication studies, and Peer Community Inn: Registered Reports initiative is publishing replication studies. The APA has created specific reporting guidelines for replication studies. Some science funders have developed grants for replication research. At the same time, replication studies are still rewarded less than novel work, which means researchers who want to build a career are still pushed towards novel research instead of replication studies. So despite positive developments, in many disciplines there is still some way to go before replication studies become a normal aspect of scientific research.\n\n\n\n\nAldhous, P. (2011). Journal rejects studies contradicting precognition. New Scientist. https://www.newscientist.com/article/dn20447-journal-rejects-studies-contradicting-precognition/\n\n\nAnderson, S. F., & Maxwell, S. E. (2016). There’s more than one way to conduct a replication study: Beyond statistical significance. Psychological Methods, 21(1), 1–12. https://doi.org/10.1037/met0000051\n\n\nBonett, D. G. (2012). Replication-Extension Studies. Current Directions in Psychological Science, 21(6), 409–412. https://doi.org/10.1177/0963721412459512\n\n\nBorenstein, M. (Ed.). (2009). Introduction to meta-analysis. John Wiley & Sons.\n\n\nde Groot, A. D. (1969). Methodology (Vol. 6). Mouton & Co.\n\n\nEbersole, C. R., Mathur, M. B., Baranski, E., Bart-Plange, D.-J., Buttrick, N. R., Chartier, C. R., Corker, K. S., Corley, M., Hartshorne, J. K., IJzerman, H., Lazarević, L. B., Rabagliati, H., Ropovik, I., Aczel, B., Aeschbach, L. F., Andrighetto, L., Arnal, J. D., Arrow, H., Babincak, P., … Nosek, B. A. (2020). Many Labs 5: Testing Pre-Data-Collection Peer Review as an Intervention to Increase Replicability. Advances in Methods and Practices in Psychological Science, 3(3), 309–331. https://doi.org/10.1177/2515245920958687\n\n\nEpstein, S. (1980). The stability of behavior: II. Implications for psychological research. American Psychologist, 35(9), 790–806. https://doi.org/10.1037/0003-066X.35.9.790\n\n\nFerguson, C. J., & Heene, M. (2021). Providing a lower-bound estimate for psychology’s “crud factor”: The case of aggression. Professional Psychology: Research and Practice, 52(6), 620–626. https://doi.org/http://dx.doi.org/10.1037/pro0000386\n\n\nFishman, D. B., & Neigher, W. D. (1982). American psychology in the eighties: Who will buy? 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Reproducibility and Replication of Experimental Particle Physics Results. Harvard Data Science Review, 2(4). https://doi.org/10.1162/99608f92.250f995b\n\n\nKoole, S. L., & Lakens, D. (2012). Rewarding replications A sure and simple way to improve psychological science. Perspectives on Psychological Science, 7(6), 608–614. https://doi.org/10.1177/1745691612462586\n\n\nLoevinger, J. (1968). The \"information explosion.\". American Psychologist, 23(6), 455–455. https://doi.org/10.1037/h0020800\n\n\nLubin, A. (1957). Replicability as a publication criterion. American Psychologist, 12, 519–520. https://doi.org/10.1037/h0039746\n\n\nLuttrell, A., Petty, R. E., & Xu, M. (2017). Replicating and fixing failed replications: The case of need for cognition and argument quality. Journal of Experimental Social Psychology, 69, 178–183. https://doi.org/10.1016/j.jesp.2016.09.006\n\n\nLykken, D. T. (1968). Statistical significance in psychological research. Psychological Bulletin, 70, 151–159. https://doi.org/10.1037/h0026141\n\n\nMack, R. W. (1951). The Need for Replication Research in Sociology. American Sociological Review, 16(1), 93–94. https://doi.org/10.2307/2087978\n\n\nMaier, M., & Lakens, D. (2022). Justify your alpha: A primer on two practical approaches. Advances in Methods and Practices in Psychological Science. https://doi.org/10.31234/osf.io/ts4r6\n\n\nMcCarthy, R. J., Skowronski, J. J., Verschuere, B., Meijer, E. H., Jim, A., Hoogesteyn, K., Orthey, R., Acar, O. A., Aczel, B., Bakos, B. E., Barbosa, F., Baskin, E., Bègue, L., Ben-Shakhar, G., Birt, A. R., Blatz, L., Charman, S. D., Claesen, A., Clay, S. L., … Yıldız, E. (2018). Registered Replication Report on Srull and Wyer (1979). Advances in Methods and Practices in Psychological Science, 1(3), 321–336. https://doi.org/10.1177/2515245918777487\n\n\nMellers, B., Hertwig, R., & Kahneman, D. (2001). Do frequency representations eliminate conjunction effects? 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American Psychologist, 25(10), 970–975. https://doi.org/10.1037/h0029774\n\n\nSpence, J. R., & Stanley, D. J. (2024). Tempered Expectations: A Tutorial for Calculating and Interpreting Prediction Intervals in the Context of Replications. Advances in Methods and Practices in Psychological Science, 7(1), 25152459231217932. https://doi.org/10.1177/25152459231217932\n\n\nStroebe, W., & Strack, F. (2014). The Alleged Crisis and the Illusion of Exact Replication. Perspectives on Psychological Science, 9(1), 59–71. https://doi.org/10.1177/1745691613514450\n\n\nTunç, D. U., & Tunç, M. N. (2023). A Falsificationist Treatment of Auxiliary Hypotheses in Social and Behavioral Sciences: Systematic Replications Framework. Meta-Psychology, 7. https://doi.org/10.15626/MP.2021.2756", "crumbs": [ "17  Replication Studies" ] @@ -1704,7 +1704,7 @@ "href": "changelog.html", "title": "Change Log", "section": "", - "text": "The current version of this textbook is 1.5.0\nThis version has been compiled on June 25, 2024.\nThis version was generated from Git commit #efb02e32. All version controlled changes can be found on GitHub.\nThis page documents the changes to the textbook that were more substantial than fixing a typo.\nUpdates\nJune 20, 2024:\nAdded CH17\nMarch 22, 2024:\nUpdated CI figure in CH7, incorporated feedback LeFoll, updated references\nFebruary 21, 2024:\nAdded section on subgroup analyses, updates section on heterogeneity in CH 11\nFebruary 15, 2024:\nExpanded section on “Why Effect Sizes Selected for Significance are Inflated” in CH 6\nJanuary 10, 2024:\nAdded the section ‘Deviating from a Preregistration’ in CH 13\nOctober 15, 2023:\nIncorporated extensive edits by Nick Brown in CH 4-6.\nSeptember 6, 2023:\nIncorporated extensive edits by Nick Brown in CH 1-3.\nAugust 27, 2023:\nAdd CH 16 on confirmation bias and organized skepticism. Add Bakan 1967 quote to CH 13.\nAugust 12, 2023:\nAdded section on why standardized effect sizes hinder the interpretation of effect sizes in CH 6. Added Spanos 1999 to CH 1. Split up the correct interpretation of p values for significant and non-significant results CH 1. Added new Statcheck study CH 12. Added Platt quote CH 5.\nJuly 21, 2023:\nAdded “Why Effect Sizes Selected for Significance are Inflated” section to CH 6, moved main part of “The Minimal Statistically Detectable Effect” from CH 8 to CH 6, replaced Greek characters by latex, added sentence bias is expected for papers that depend on main hypothesis test in CH 12.\nJuly 13, 2023:\nUpdated Open Questions in CH 1, 2, 3, 4, 6, 7, 8 and 9. Added a figure illustrating how confidence intervals become more narrow as N increases in CH 7.\nJuly 7, 2023:\nAdded this change log page.\nJune 12, 2023:\nAdded an updated figure from Carter & McCullough, 2014, in the chapter in bias detection, now generated from the raw data.\nMay 5, 2023:\nAdded the option to download a PDF and epub version of the book.\nMarch 19, 2023:\nUpdated CH 5 with new sections on falsification, severity, and risky predictions, and a new final section on verisimilitude.\nMarch 3, 2023:\nUpdated book to Quarto. Added webexercises to all chapters.\nFebruary 27, 2023:\nAdded a section “Dealing with Inconsistencies in Science” to CH 5.\nOctober 4, 2022:\nAdded CH 15 on research integrity.", + "text": "The current version of this textbook is 1.5.1\nThis version has been compiled on June 28, 2024.\nThis version was generated from Git commit #c852c7b4. All version controlled changes can be found on GitHub.\nThis page documents the changes to the textbook that were more substantial than fixing a typo.\nUpdates\nJune 20, 2024:\nAdded CH17\nMarch 22, 2024:\nUpdated CI figure in CH7, incorporated feedback LeFoll, updated references\nFebruary 21, 2024:\nAdded section on subgroup analyses, updates section on heterogeneity in CH 11\nFebruary 15, 2024:\nExpanded section on “Why Effect Sizes Selected for Significance are Inflated” in CH 6\nJanuary 10, 2024:\nAdded the section ‘Deviating from a Preregistration’ in CH 13\nOctober 15, 2023:\nIncorporated extensive edits by Nick Brown in CH 4-6.\nSeptember 6, 2023:\nIncorporated extensive edits by Nick Brown in CH 1-3.\nAugust 27, 2023:\nAdd CH 16 on confirmation bias and organized skepticism. Add Bakan 1967 quote to CH 13.\nAugust 12, 2023:\nAdded section on why standardized effect sizes hinder the interpretation of effect sizes in CH 6. Added Spanos 1999 to CH 1. Split up the correct interpretation of p values for significant and non-significant results CH 1. Added new Statcheck study CH 12. Added Platt quote CH 5.\nJuly 21, 2023:\nAdded “Why Effect Sizes Selected for Significance are Inflated” section to CH 6, moved main part of “The Minimal Statistically Detectable Effect” from CH 8 to CH 6, replaced Greek characters by latex, added sentence bias is expected for papers that depend on main hypothesis test in CH 12.\nJuly 13, 2023:\nUpdated Open Questions in CH 1, 2, 3, 4, 6, 7, 8 and 9. Added a figure illustrating how confidence intervals become more narrow as N increases in CH 7.\nJuly 7, 2023:\nAdded this change log page.\nJune 12, 2023:\nAdded an updated figure from Carter & McCullough, 2014, in the chapter in bias detection, now generated from the raw data.\nMay 5, 2023:\nAdded the option to download a PDF and epub version of the book.\nMarch 19, 2023:\nUpdated CH 5 with new sections on falsification, severity, and risky predictions, and a new final section on verisimilitude.\nMarch 3, 2023:\nUpdated book to Quarto. Added webexercises to all chapters.\nFebruary 27, 2023:\nAdded a section “Dealing with Inconsistencies in Science” to CH 5.\nOctober 4, 2022:\nAdded CH 15 on research integrity.", "crumbs": [ "Change Log" ]