Two Sample Proportions

The Two Sample Proportions option computes the power or sample sizes needed to detect the difference between two proportions, p1 and p2.

For the two sample proportion, the hypothesis supported is

and the two-sided alternative is

where p1 and p2 are the population proportions from two populations, and D0 is the hypothesized difference in proportions.

The one-sided alternative is either

Two Sample Proportion Window Specifications

Specifications for the Two Sample Proportions window include:

Alpha

is the significance level of your test. The default value is 0.05.

Proportion 1

is the proportion for population 1, which could be known or hypothesized. The default value is 0.5.

Proportion 2

is the proportion for population 2, which could be known or hypothesized. The default value is 0.1.

One-Sided or Two-Sided

Specify either a one-sided or a two-sided test. The default setting is the two-sided test.

Null Difference in Proportion

is the proportion difference (D0) to test against, or is left blank for computation. The default value is 0.2.

Sample Size 1

is the sample size for population 1, or is left blank for computation.

Sample Size 2

is the sample size for population 2, or is left blank for computation.

Power

is the desired power, or is left blank for computation.

If you enter any two of the following three quantities, the third quantity is computed:

•

Null Difference in Proportion

•

Sample Size 1 and Sample Size 2

•

Power

Example of Determining Sample Sizes with a Two-Sided Test

As an example, suppose you are responsible for two silicon wafer assembly lines. Based on the knowledge from many runs, one of the assembly lines has a defect rate of 8%; the other line has a defect rate of 6%. You want to know the sample size necessary to have 80% power to reject the null hypothesis of equal proportions of defects for each line.

To estimate the necessary sample sizes for this example:

Select DOE > Design Diagnostics > Sample Size and Power.

Click Two Sample Proportions.

Accept the default value of Alpha as 0.05.

Enter 0.08 for Proportion 1.

Enter 0.06 for Proportion 2.

Accept the default option of Two-Sided.

Enter 0.0 for Null Difference in Proportion.

Enter 0.8 for Power.

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

Example of Determining Power with Two Sample Proportions Using a One-Sided Test

Suppose you want to compare the effectiveness of a two chemical additives. The standard additive is known to be 50% effective in preventing cracking in the final product. The new additive is assumed to be 60% effective. You plan on conducting a study, randomly assigning parts to the two groups. You have 800 parts available to participate in the study (400 parts for each additive). Your objective is to determine the power of your test, given a null difference in proportions of 0.01 and an alpha level of 0.05. Because you are interested in testing that the difference in proportions is greater than 0.01, you use a one-sided test.

Select DOE > Design Diagnostics > Sample Size and Power.

Click Two Sample Proportions.

Accept the default value of Alpha as 0.05.

Enter 0.6 for Proportion 1.

Enter 0.5 for Proportion 2.

Select One-Sided.

Enter 0.01 as the Null Difference in Proportion.

Enter 400 for Sample Size 1.

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

You conclude that there is about an 82% chance of rejecting the null hypothesis at the 0.05 level of significance, given that the sample sizes for the two groups are each 400. Note the Actual Test Size is 0.0513, which is slightly larger than the stated 0.05.