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Statistical power and sample size (n)

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Statistical Power

Read the following scenario and explain what power issues may arise. What factors influence statistical power?

A researcher is interested in investigating how teaching style (structured vs. unstructured) affects learning of vocabulary in children who are developmentally delayed, typically developing and gifted. The researcher organizes an after-school program and all participants are given a pretest. The program consists of 30 minute sessions, two times a week for four weeks. A total of 15 participants are randomly assigned to the 'high structure' class" or the 'low structure' class. All classes focus on word knowledge and vocabulary. At the end of the program, the researcher assesses 'word knowledge' for developmentally delayed, typical and gifted students in the high structure group, as well as developmentally delayed, typical and gifted students in the low structure group. The researcher is wondering whether the level of structure (high vs. low) might affect the participant groups differently.

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The issue here is that the sample size is far too small. Power is directly related to sample size; if we want to increase power, the easiest way to do it is to increase sample size. In this case, we essentially have 6 groups: high structure/developmentally delayed, high structure/typical, high structure/gifted, low structure/developmentally delayed, low ...

Solution Summary

Explains how low sample size influences power.

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Statistics: Use Cohen's d to evaluate treatment; power of a test

18. A sample of n=16 individuals is selected from a normal population with a mean of µ=48 and a standard deviation of ±=12. After receiving a treatment, the sample mean is found to be M = 52.

a. Compare Cohen's d to evaluate the size of the treatment effect.

b. If the sample size were n = 36, what value would be obtained for Cohen's d? How does sample size influence the measure of effect size?

c. If the population standard deviation were ±= 24, what value would be obtained for Cohen's d? How does standard deviation influence the measure of effect size?

d. If the sample mean were M +56, what value would the obtained for cohen's d? How does the size of the mean difference influence the measure of effect size?

22. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant.

a. Increasing the alpha level from .01 to .05.
b. changing from a one tailed test to a two tailed test.

24. A researcher is evaluating the influence of a treatment using a sample selected form a normal distribution population with a mean u =8and a standard deviation of ±= 20. The researchers expects 12-point treatment effect and plans to use a two-tailed hypothesis test with ±= .05 .

a. Compute the power of the test if the researcher uses a sample of n = 16 individuals.
b. Compare the power of the test if the researcher uses a sample of n= 25 individuals.

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