Add the number of successes in group one to the number of successes in group two. Add the sample size of group one to the sample size of group two. Divide the total number of successes by the total sample size to get the common proportion.
Divide one by the sample size of each group. Add these two fractions together and multiply the result by the common proportion. Subtract the common proportion from one and multiply by the result of the previous calculation. Take the square root of this number to get the standard error.
Subtract the group two proportion from the group one proportion. Divide by the standard error to get the test statistic.
Look up the test statistic on a normal distribution table. Read down the far left column to find the row with ones and tenths places for your statistic. Move to the right along that row until you reach the column labeled with the hundredths place of your statistic. If your test statistic is 1.97, for example, find the intersection of the row labeled 1.9 and the column labeled 0.07 to get a value of 0.9756.
Subtract the value you found in the table from one. Use this value for a one-tailed test, or multiply by two to find the p-value for a two-tailed test. Compare the p-value to alpha; if the p-value is less than alpha, reject the null hypothesis and conclude there is a significant difference between the two proportions. If the p-value is greater than alpha, you cannot conclude there is a significant difference.