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Statistical Power - Size

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Chapter 6 talks about effect size and statistical power. What are these? How are they relevant to statistics and how do you use them? Since it is talking about effect size do you always want big or do sometimes you want a small or medium? How do you determine this? You can discuss and explain these topics by explaining what are the two factors that determine effect size? For each of these factors, how and why do they effect power?

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Effect size:
Effect size is a numerical measure of expressing the strength of relationship between two variables.
The formula for effect size based on means is

Where µ1 is the mean of population 1
µ2 is the mean of population 2
σ is the standard deviation either of the second population or the polled standard deviation of two groups.
Statistical power:
Power = probability of rejecting H0 when H0 is false (i.e., you [correctly] conclude that there is a treatment effect when there really is a treatment effect).
Power = 1 − β.
When statistical power increases the chance of type two error decreases
Statistical power depends on
• The structure of the experiment
• The method for analyzing the ...

Solution Summary

The effect size and statistical power are defined. How relevant to statistics and how to use them are determined.

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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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