Please do not touch anything in this section, otherwise this notebook might not work properly. You have been warned! Also, if you have no clue what you are staring at, please consult our Preface chapter.
source("run_me_first.R")
The following example can be found on Wolfgang Viechtbauer's website and is based on a publication by Konstantopoulos (2011; which can be found on Ilias)}. The following study description is essentially copy-and-paste from Viechtbauer's website.
The meta-analysis examines the effects of modified school calendars on student achievement. In particular, instead of following the more traditional school calendar with a long summer break (in addition to a short winter and spring break), some schools have switched to a modified school calendar comprising more frequent but shorter intermittent breaks (e.g., 9 weeks of school followed by 3 weeks off), while keeping the total number of days at school approximately the same.
The dataset contains the results from 56 studies, each comparing the level of academic achievement in a group of students following a modified school calendar with that of a group of students following a more traditional school calendar. The difference between the two groups was quantified in terms of a standardized mean difference (with positive values indicating a higher mean level of achievement in the group following the modified school calendar).
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Use the command head()
to inspect the dataset.
Plot of histogram of the effect sizes (hist()
). How does the plot look like in terms of the normality assumption?
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Estimate an overall effect size estimate. Which modell would you use and why?
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Draw a simple forest plot.
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Draw a forest plot which is ordered by effect size.
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Create a funnel plot. Does it look suspicious in terms of publication bias?
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Conduct a statistical test to test for funnel plot asymmetry.
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Explore the trim-and-fill approach.
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Investigate the impact of study year (year
) on the effect sizes by estimating a simple meta-regression model. Create a scatterplot effect size by year.
Note: Since this dataset contains dependent effect sizes, this is not the recommended approach. See the section on multilevel meta-analysis for a more appropriate approach.
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Are there any influential ES estimates?
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The studies were conducted at various schools that were clustered within districts. The data therefore have a multilevel structure, with studies nested within districts. A multilevel meta-analysis of these data can be used to estimate and account for the amount of heterogeneity between districts and between schools within districts.
Estimate a multilevel random-effects model.
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Create a profile plot.
(*) This exercise is a little more challenging in terms of R knowledge: Can you calculate the ICC (intraclass correlation coefficient). You will need the sigma2
element within the rma.mv
object.
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Finally, we can estimate a multilevel meta-regression model by including year
.
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