Abstract
This chapter provides methods for computing the a priori power of the test of the mean effect size. Both fixed and random effects models tests are discussed. In addition, examples are provided for computing the number of studies needed to detect a substantively important effect size, and the detectable effect size with a given number of studies.
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Appendix
Appendix
4.1.1 Computing Power for Examples in Section 4.3
The examples require the computation of the area under the standard normal distribution that is either less than or greater than a given critical value, cα. Below I give the functions and commands necessary to obtain the power for the example in Sect. 4.3.4.
4.1.1.1 Excel
In Excel, the function NORMSDIST(x) is the cumulative normal distribution. For Example 4.3.4,
The value given in Excel is the cumulative area less than or equal to x.
4.1.1.2 SPSS
Using the Compute menu in SPSS, the function CDF.NORMAL(quant, mean, sd) provides the values for the cumulative normal distribution. To compute the power for Example 4.3.4,
returns the value 0.71, or in other words, the cumulative area that is less than or equal to 0.71.
4.1.1.3 SAS
In SAS, the function CDF(‘NORMAL’, x, mean, sd) provides the value of the cumulative normal distribution function that is less than x for a normal distribution with the specified mean and standard deviation. To compute the power for Example 4.3.1,
The above function results in a value of 0.709.
4.1.1.4 R
In R, the function PNORM(x) gives the area for the cumulative standard normal distribution to the right of a positive value of x and to the left of a negative value of x. For Example 4.3.4, the following command produces the area that is greater than x (since x is positive), or, P(X > x). The command pnorm(0.55) in R would produce the same result as we see below.
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Pigott, T.D. (2012). Power Analysis for the Mean Effect Size. In: Advances in Meta-Analysis. Statistics for Social and Behavioral Sciences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-2278-5_4
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