This test can be performed to determine whether respondents are more likely to prefer one alternative or another.
Example:
The research question is: Is there a significant difference between the percent of people who say they would vote for candidate A and the percent of people who say they will vote for candidate B? The null hypothesis is: There is no significant difference between the percent of people who say they will vote for candidate A or candidate B. The results of the survey were:
Plan to vote for candidate A = 35.5%
Plan to vote for candidate B = 22.4%
Sample size = 107
The sum of the two percents does not have to be equal to 100 (there may be candidates C and D, and people that have no opinion). Use a one-sample t-test because both percentages came from a single sample.
Use a two-tailed probability because the null hypothesis does not state the direction of the difference. If the hypothesis is that one particular choice has a greater percentage, use a one-tailed test (divide the two-tailed probability by two).
Enter the first percent: 35.5
Enter the second percent: 22.4
Enter the sample size: 107
t-value = 1.808
Degrees of freedom = 106
Two-tailed probability = .073
You might make a statement in a report like this: A one-sample t-test between proportions was performed to determine whether there was a significant difference between the percent choosing candidate A and candidate B. The t-statistic was not significant at the .05 critical alpha level, t(106)=1.808, p=.073. Therefore, we fail to reject the null hypothesis and conclude that the difference was not significant.
