The Sample Size windows and computations to test sample sizes and power for proportions are similar to those for testing means. You enter a true Proportion and choose an Alpha level. Then, for the one-sample proportion case, enter the Sample Size and Null Proportion to obtain the Power. Or, enter the Power and Null Proportion to obtain the Sample Size. Similarly, to obtain a value for Null Proportion, enter values for Sample Size and Power. For the two-sample proportion case, either the two sample sizes or the desired Power must be entered. (See Power and Sample Window for One-Sample Proportions and Difference Between Two Proportions for a Two-Sided Test.)
Clicking the One Sample Proportion option on the Sample Size and Power window yields a One Proportion window. In this window, you can specify the alpha level and the true proportion. The sample size, power, or the hypothesized proportion is calculated. If you supply two of these quantities, the third is computed, or if you enter any one of the quantities, you see a plot of the other two.
For example, if you have a hypothesized proportion of defects, you can use the One Sample Proportion window to estimate a large enough sample size to guarantee that the risk of accepting a false hypothesis (β) is small. That is, you want to detect, with reasonable certainty, a difference in the proportion of defects.
where p is the population proportion and p0 is the null proportion to test against. Note that if you are interested in testing whether the population proportion is greater than or less than the null proportion, you use a one-sided test. The one-sided alternative is either
is the proportion to test against (p0) or is left blank for computation. The default value is 0.2.
is the sample size, or is left blank for computation. If Sample Size is left blank, then values for Proportion and Null Proportion must be different.
1.
Select DOE > Sample Size and Power.
2.
Click One Sample Proportion.
3.
Leave Alpha as 0.05.
5.
Leave the Method as Exact Agresti-Coull.
6.
Accept the default option of Two-Sided. (A one-sided test is selected if you are interested in testing if the proportion is either greater than or less than the Null Proportion.)
7.
8.
Enter 100 as the Sample Size.
9.
Click Continue.
The Power is calculated and is shown as approximately 0.7 (see Power and Sample Window for One-Sample Proportions). Note the Actual Test Size is 0.0467, which is slightly less than the desired 0.05.
Power and Sample Window for One-Sample Proportions
The Two Sample Proportions option computes the power or sample sizes needed to detect the difference between two proportions, p1 and p2.
where p1 and p2 are the population proportions from two populations, and D0 is the hypothesized difference in proportions.
is the proportion difference (D0) to test against, or is left blank for computation. The default value is 0.2.
Sample Size 1 and Sample Size 2
1.
Select DOE > Sample Size and Power.
2.
Click Two Sample Proportions.
3.
4.
Enter 0.08 for Proportion 1.
5.
Enter 0.06 for Proportion 2.
7.
Enter 0.0 for Null Difference in Proportion.
8.
9.
Leave Sample Size 1 and Sample Size 2 blank.
10.
Click Continue.
The Sample Size window shows sample sizes of 2554. (see Difference Between Two Proportions for a Two-Sided Test.) Testing for a one-sided test is conducted similarly. Simply select the One-Sided option.
Difference Between Two Proportions for a Two-Sided Test
1.
Select DOE > Sample Size and Power.
2.
Click Two Sample Proportions.
3.
4.
Enter 0.6 for Proportion 1.
5.
Enter 0.5 for Proportion 2.
6.
Select One-Sided.
7.
Enter 0.01 as the Null Difference in Proportion.
8.
Enter 400 for Sample Size 1.
9.
Enter 400 for Sample Size 2.
10.
Leave Power blank.
11.
Click Continue.
Difference Between Two Proportions for a One-Sided Test shows the Two Proportions windows with the estimated Power calculation of 0.82.
Difference Between Two Proportions for a One-Sided Test