Factors Affecting Power: Sample Size (1 of 2)

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Increasing N, the sample size, decreases the denominator of the equation for z:



and therefore increases power.

The graphs below show the sampling distribution of M (for the example) when σ = 50 and µ_diff = 20. The cutoff points for being significant at the 0.05 level were determined using the formulas:



and



Note how the cutoff point and the variance of the distribution change as N increases. The mean of the distribution does not change.