In the present study, we employed a broader basis of empirical studies and compared the results of original research that has either been published traditionally and might therefore be affected by the causes of bias just mentioned or been made available in the course of a pre-registration procedure therefore probably not affected by these biases.
Haase et al. Rubio-Aparicio et al. Richard et al. For standardized mean differences i. Some of these studies might have been selective in that they were covering only studies from textbooks that might be biased toward larger effects or referring only to one specific kind of effect size.
But as a whole, they indicate that sub-disciplines might not be comparable. With our study, we made this question more explicit and collected representative data for the whole range of psychological sub-disciplines. In sum, our aim was 1 to quantify the impact of potential biases e. Aim 1 pertains to the comparison approach: If published effects are not representative of the effects in the population as suggested by recent replication projects it is problematic to infer the meaningfulness of an effect by looking at those published effects.
There were three key methodological elements in our study. First, to get a representative overview of published effects in psychology, we analyzed a random selection of published empirical studies. Randomness ensured that each study had the same probability of being drawn, which is the most reliable path to generalizable conclusions.
Second, to estimate how strongly published effects might be biased, we distinguished between studies with and without pre-registration. Third, to compare different sub-disciplines, we categorized the manifold branches of psychology into nine clusters and randomly drew and analyzed effects within each cluster.
We now explain the procedure in more detail. To cover the whole range of psychological sub-disciplines we used the Social Sciences Citation Index SSCI that lists 10 categories for psychology: applied, biological, clinical, developmental, educational, experimental, mathematical, multidisciplinary, psychoanalysis, social.
Our initial goal was to sample effect sizes from each of these 10 categories, for 1, effect sizes in total. In the mathematical category, however, published articles almost exclusively referred to advances in research methods, not to empirical studies.
It was not possible to sample effect sizes, so this category was eventually excluded. Therefore, our selection of empirical effect sizes was based on the nine remaining categories, with a goal of effect sizes. For each category, the SSCI also lists relevant journals ranging from 14 journals for psychoanalysis to for multidisciplinary. Our random-drawing approach based on the AS pseudorandom number generator implemented in Microsoft Excel comprised the following steps. We excluded theoretical articles, reviews, meta-analyses, methodological articles, animal studies, and articles without enough information to calculate an effect size including studies providing non-parametric statistics for differences in central tendency and studies reporting multilevel or structural equation modeling without providing specific effect sizes.
If an article had to be skipped, the random procedure was continued within this journal until 10 suitable articles were identified. If for a journal fewer than four of the first 10 draws were suitable, the journal was skipped and another journal within the category was randomly drawn. We ended up with empirical effects representative of psychological research since its beginning see Table 1. In this sample, there were no articles adhering to a pre-registration procedure. Sampling was conducted from mid till end of Table 1.
Type, population, and design of the studies from which effects were obtained. One of the most efficient methods to reduce or prevent publication bias and questionable research practices is pre-registration e. This procedure is suggested to avoid questionable research practices such as HARKing, p -hacking, or selectively analyzing.
If the manuscript is accepted, it is published regardless of the size and significance of the effect s it reports so-called in-principle acceptance. Registered reports are the most effective way to also avoid publication bias; their effects can thus be considered to give a representative picture of the real distribution of population effects.
Since pre-registered studies have gained in popularity only in recent years, we did not expect there to be that many published articles adhering to a pre-registration protocol. We therefore set out to collect all of them instead of only drawing a sample. Collection of studies was conducted from mid till end of We used the title and abstract of an article to identify the key research question. The first reported effect that unambiguously referred to that key research question was then recorded for that article.
This was done to avoid including effects that simply referred to manipulation checks or any kind of pre-analysis, such as checking for gender differences.
For the remaining effects, the effect size had to be calculated from the significance test statistics. Because our aim was to get an impression of the distribution of effects from psychological science in general, we transformed all effect sizes to a common metric if possible. As the correlation coefficient r was the most frequently reported effect size and is often used as a common metric e. Other effect sizes were less frequent and are not analyzed here: R 2 , R 2 adjusted , w , and odds ratio.
Because of the difference in how the error variance is calculated in between-subjects versus within-subject study designs it is actually not advisable to lump effects from one with effects from the other. However, this is often done when applying benchmarks for small, medium, and large effects. We therefore provide analyses for both the whole set of effects and the effects from between-subjects designs and within-subject designs separately.
Some used the means and standard deviations of the distributions; others used the median and certain quantiles. We deemed it most sensible to divide the distributions of effect sizes into three even parts and take the medians of these parts i. Effects came from articles published between and , of course with many more being from recent years.
See Table 1 for other descriptors and Table 2 for detailed statistics of the sample sizes separately for between-subjects designs and within-subject designs as well as sub-disciplines. With regard to between-subjects designs, the median and mean samples sizes differ considerably between studies published with and without pre-registration.
Studies with pre-registration were conducted with much larger samples than studies without pre-registration, which might be due to the higher standards and sensitivity regarding statistical power, not only in recent years but also particularly with journals advocating pre-registration.
By contrast, regarding within-subject designs, the sample sizes were smaller in studies with pre-registration than in studies without pre-registration. This makes the whole picture quite complicated because we would have expected the same influence of sensitivity regarding statistical power for both kinds of study design.
One tentative explanation for this paradox might be that researchers, when conducting a replication study, indeed ran a power analysis that, however, yielded a smaller sample size than the original study had because within-subject studies generally have higher power.
Table 2. Median, mean, and SD of sample size, and percentage of significant effects for all studies where an effect size r was extracted or calculated. Table 2 also shows the percentage of significant effects, both for all studies and separately for studies with between-subjects and studies with within-subject designs for studies published without pre-registration, in addition, for all sub-disciplines.
The likelihood of obtaining a significant result was considerably smaller in studies published with pre-registration.
Figure 1 upper part shows the empirical distribution of effects from psychological publications without pre-registration in general, and Table 3 provides the descriptive statistics. The distribution is fairly symmetrical and only slightly right-skewed, having its mean at 0. That is, effects in psychology that have been published in studies without pre-registration in the past concentrate around a value of 0.
However, looking at the lower third of the distribution of r reveals that the lower median i. Similarly, the upper median i.
Figure 1. The distributions contain all effects that were extracted as or could be transformed into a correlation coefficient r. Table 3. Descriptive statistics of empirical effects all transformed to r from studies published with and without pre-registration.
Figure 1 lower part shows the empirical distribution of effects from psychological publications with pre-registration in general, and Table 3 provides the descriptive statistics.
The distribution is considerably different from the distribution of the effects from studies without pre-registration in two respects. First, it is markedly right-skewed and suggests that the effects concentrate around a very small modal value. Second, the distribution is made up of markedly smaller values: It has its mean at 0. Looking at the lower third of the distribution of r reveals that the lower median is 0.
Similarly, the upper median is 0. Interestingly, the medians of the within-subject design studies 0. In sum, the distributions of effects from published studies in psychology differ considerably between studies with and without pre-registration.
While studies without pre-registration have revealed effects that were larger than what Cohen had previously suggested as a benchmark, studies with pre-registration, in contrast, revealed smaller effects see Figure 2. In addition, it seems impossible to compare effects from studies with between-subjects designs and within-subject designs, particularly when it comes to large effects. Figure 2. For Cohen , p. Note that this analysis could only be done for the studies published without pre-registration because studies with pre-registration were too few to be sensibly divided into sub-categories.
Figure 3. The bars contain all effects that were extracted as or could be transformed into a correlation coefficient r. The vertical line is the grand median. The largest effects come from disciplines such as experimental and biological psychology where the use of more reliable instruments and devices is common.
Disciplines such as social and developmental psychology provide markedly smaller effects. Note that, for instance, there is not even an overlap of the confidence intervals of social and biological psychology.
This simply means that in terms of effect sizes, we are talking about completely different universes when we talk about psychological research as a whole. The differences between the sub-disciplines shown in Figure 3 largely match the differences between the results of the studies discussed in the Introduction. By contrast, Richard et al. Effect sizes were smaller the larger the samples see Figures 4 , 5. One obvious explanation for these strong correlations is the publication bias, since effects from large samples have enough statistical power to become significant regardless of their magnitude.
However, a look at Figure 5 reveals that with studies published with pre-registration, hence potentially preventing publication bias, the correlation is indeed smaller but still far from zero.
This general correlation between sample size and effect size due to statistical power might also have led to a learning effect: in research areas with larger effects, scientists may have learned that small samples are enough while in research areas with smaller effects, they know that larger samples are needed.
Moreover, studies on social processes or individual differences can be done online with large samples; developmental studies can be done in schools, also providing large samples. By contrast, experimental studies or studies requiring physiological measurement devices are usually done with fewer participants but reveal larger effects.
However, when calculating the correlation between sample size and effect size separately for the nine sub-disciplines, it is still very large in most cases ranging from 0.
The relationship between larger effects and the use of more reliable measurement devices might of course also be there within the sub-disciplines but this explanation needs more empirical evidence. Figure 4. Relationship Loess curve 1 between sample size and effect size r for studies published without pre-registration. Figure 5. Relationship Loess curve between sample size and effect size r for studies published with pre-registration.
Is the year of publication associated with the effect size? For instance, the call for replication studies in recent years together with the decline effect e. As Figure 6 shows, however, there is no correlation between year of publication and size of the effects reported only done for studies published without pre-registration since studies with pre-registration started no earlier than Thus, effect sizes appear to be relatively stable over the decades so that, in principle, nothing speaks against providing fixed guidelines for their interpretation.
Figure 6. Effect size is not the same as statistical significance: significance tells how likely it is that a result is due to chance, and effect size tells you how important the result is. In a statement on statistical significance and P-values , the American Statistical Association explains, "Statistical significance is not equivalent to scientific, human, or economic significance. Smaller p-values do not necessarily imply the presence of larger or more important effects, and larger p-values do not imply a lack of importance or even lack of effect.
Any effect, no matter how tiny, can produce a small p-value if the sample size or measurement precision is high enough, and large effects may produce unimpressive p-values if the sample size is small or measurements are imprecise.
Similarly, identical estimated effects will have different p-values if the precision of the estimates differs. You can look at the effect size when comparing any two assessment results to see how substantially different they are. For example, you could look at the effect size of the difference between your pre- and post-test to learn about how substantially your students knowledge of the subject tested changed as a result of your course.
Because the standard deviation includes how many students you have, using the effect size allows you to compare teaching effectiveness between classes of different sizes more fairly. Effect size is a popular measure among education researchers and statisticians for this reason. By using effect size to discuss your course, you will better be able to speak across disciplines and with your administrators. The major mathematical difference between normalized gain and effect size is that normalized gain does not account for the size of the class or the variation in students within the class, but effect size does.
By accounting for the variance in individuals' scores, effect size is a lot more sensitive single number measure than the normalized gain. The difference is more pronounced in very small or diverse classes. It takes the difference between two means and expresses it in standard deviation units. It tells you how many standard deviations lie between the two means. The choice of standard deviation in the equation depends on your research design. You can use:. You can directly compare the strengths of all correlations with each other.
Other measures of effect size must be used for ordinal or nominal variables. See an example. A value closer to -1 or 1 indicates a higher effect size.
Knowing the expected effect size means you can figure out the minimum sample size you need for enough statistical power to detect an effect of that size. In statistics, power refers to the likelihood of a hypothesis test detecting a true effect if there is one. A statistically powerful test is more likely to reject a false negative a Type II error.
Your study might not have the ability to answer your research question. By performing a power analysis, you can use a set effect size and significance level to determine the sample size needed for a certain power level. Effect sizes are the raw data in meta-analysis studies because they are standardized and easy to compare.
A meta-analysis can combine the effect sizes of many related studies to get an idea of the average effect size of a specific finding. But meta-analysis studies can also go one step further and also suggest why effect sizes may vary across studies on a single topic.
This can generate new lines of research. There are dozens of measures of effect sizes. Statistical significance is denoted by p -values whereas practical significance is represented by effect sizes.
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