Factors affecting power: Variance (1 of 2)

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The larger the variance (σ²), the lower the power. In the formula for z:



increasing σ² increases the denominator and therefore lowers z and power. For the example, σ is the standard deviation of the difference scores. The power of the test using the .05 significance level, for N = 25, µdiff= 20, and various values of σ is shown in the table on the right side of this page. The table below shows that the power decreases as σ increases.

σ
Power
50
75
100
125
150
0.52
0.26
0.17
0.12
0.10


There are ways that an experimenter can reduce variance to increase power. One is to define a relatively homogeneous population. For instance, if one were studying reading speed, one could begin by studying the population of people in their first year at a selective college rather than the population of all English-speaking adults. The variance would be much reduced.
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