Homework: Sampling and Data Collection
You will recall from your readings that there are two times that we compute the sample size and statistical power: before the research is conducted (a priori) and again after the research is conducted. Before conducting the research, we compute an a priori sample size to plan the data collection process. We compute the planned sample size based on our desired statistical significance and statistical power, and our best estimates for the effects size. Once we have conducted the research, we can use the actual effect size, sample size, and desired statistical significance to compute the statistical power.
For this homework you will compute the statistical power for the journal article used in the previous two units.
Step I: Install G*Power
If you have not done so, download and install G*Power (linked in Resources), following the instructions in this unit's studies.
Step II: Determine the Size of the Effects in Your Article
Identify an effect that is reported in the article that you chose in Unit 1 (or the current one that you have selected to replace that one). This should be the strength of a reported association or correlation between variables or the strength of a difference between groups or conditions. The article probably reports the level of statistical significance for the finding, but this is not what we are looking for here.
The table below shows the typically reported effects and their sizes for different statistical tests. Find the statistical test that applies to your result, look to see if the statistic is reported, and note its strength.
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Cohen's Effect Size Benchmarks
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Type of Test
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Statistic
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Small Effect Size
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Medium Effect Size
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Large Effect Size
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T-test for independent groups/conditions
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Cohen's d
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0.20
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0.50
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0.80
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ANOVA
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f
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0.10
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0.25
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0.40
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ANOVA
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η-squared
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0.01
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0.06
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0.14
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Correlation
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r
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0.10
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0.15
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0.25
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Variance
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r-squared
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0.01
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0.09
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0.25
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Multiple Regression
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f-squared
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0.02
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0.15
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0.35
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Multiple Regression
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R-squared
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0.02
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0.13
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0.26
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Adapted from Ellis, P. D. (2010). The Essential Guide to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research Results. Cambridge University Press.
For example, suppose that your article reported the results of a multiple regression that found a relationship strength in R-squared of 0.18. Using the above table, you can see that this is a medium effect. When you get to Step 3, if you find that the effect unit used in G*Power is different from the one your article uses, you may be able to convert it using the table. In our example, G*Power uses f-squared as its unit for effect size in multiple regression. In this case, you can convert the R-squared value to a medium effect. A medium effect in f-squared for a multiple regression is 0.15. You can use this value as your estimated effect size reported in the article for your next step.
Step III: Determine and Understand Effect Size and How it Relates to Statistical Power
A. Identify the required significance level (alpha error probability) from the journal article.
B. Identify the sample size actually obtained in the journal article.
C. Identify the statistical test used in the journal article.
D. Enter the effect size(s) from your journal article into the Effect box, converting as described in Step 2 as necessary.
E. Using these four inputs, determine the desired statistical power for the results in the journal article.
Format your homework according to the give formatting requirements:
A. The answer must be double spaced, typed, using Times New Roman font (size 12), with one-inch margins on all sides.
B. The response also includes a cover page containing the title of the homework, the course title, the student's name, and the date. The cover page is not included in the required page length.
C. Also include a reference page. The references and Citations should follow APA format. The reference page is not included in the required page length.