Abstract

Perform a wide variety of statistical significance tests including standard deviation, mean, sum and sample size estimation. It’s ideal for marketing research use.

Market Research Statistical Calculator

The Quirks.com free statistics calculator lets you perform a wide variety of statistical significance tests including standard deviation, mean, sum and sample size estimation. It’s ideal for marketing research use.

IMPORTANT: Do not use commas in any of the fields (e.g. use 5000 not 5,000).

Two samples t-test between percents

Enter the first percent:

Enter the sample size for the first percent:

Enter the second percent:

Enter the sample size for the second percent:

Exit

This test can be used to compare percentages drawn from two independent samples. It can also be used to compare two subgroups from a single sample.

Example

After conducting a survey of customers, you want to compare the attributes of men and women. Even though all respondents were part of the same survey, the men and women are treated as two samples. The percent of men with a particular attribute is calculated using the total number of men as the denominator for the fraction, and the percent of women with the attribute is calculate using the total number of women as the denominator. Since the denominators for the two fractions represent different people, a two-samples t-test between percents is appropriate.

The research question is: Is there a significant difference between the proportion of men having the attribute and the proportion of women having the attribute? The null hypothesis is: There is no significant difference between the proportion of men having the attribute and the proportion of women having the attribute. The results of the survey were:

86 men were surveyed and 22 of them (25.6%) had the attribute.
49 women were surveyed and 19 of them (38.8%) had the attribute.

Enter the first percent: 25.6
Enter the sample size for the first percent: 86
Enter the second percent: 38.8
Enter the sample size for the second percent: 49

t-value = 1.603
Degrees of freedom = 133
Two-tailed probability = .111

You might make a statement in a report like this: A two-samples t-test between proportions was performed to determine whether there was a significant difference between men and women with respect to the percent who had the attribute. The t-statistic was not significant at the .05 critical alpha level, t(133)=1.603, p=.111. Therefore, we fail to reject the null hypothesis and conclude that the difference between men and women was not significant.

Another example

Suppose interviews were conducted at two different shopping centers. A two samples t-test between percents could be used to determine if the responses from the two shopping centers were different.

The research question is: Is there a significant difference between shopping centers A and B with respect to the percent that say they would buy product X? The null hypothesis is: There is no significant difference between shopping centers A and B with respect to the percent of people that say they would buy product X. A two-tailed probability will be used because the hypothesis does not state the direction of the difference. The results of the survey were:

89 people were interviewed as shopping center A and 57 of them (64.0%) said they would buy product X.
92 people were interviewed as shopping center B and 51 of them (55.4%) said they would buy product X.

Enter the first percent: 64.0
Enter the sample size for the first percent: 89
Enter the second percent: 55.4
Enter the sample size for the second percent: 92

t-value = 1.179
Degrees of freedom = 179
Two-tailed probability = .240

You might write a paragraph in a report like this: A two-samples t-test between proportions was performed to determine whether there was a significant difference between the two shopping centers with respect to the percent who said they would buy product X. The t-statistic was not significant at the .05 critical alpha level, t(179)=1.179, p=.240. Therefore, we fail to reject the null hypothesis and conclude that the difference in responses between the two shopping centers was not significant.