You can use the t-test for the following:
1. To test whether a sample mean is different from a hypothesized value. For example, for a sample of students you would expect an average SAT score of 1500 but for this specific sample you got, let’s say 1300. Giving the sample size, the question becomes whether this sample score of 1300 is significantly different from the expected value of 1500.
The general format is: ttest [variable] = [hypothesized value]
Example: ttest satscore = 1500
Decision: if P>|t| or P>t are lower than 0.05 then they are different.
2. To compare two sample means. Let’s say for example a pre-electoral campaign poll in a city gave 35% of electoral preference to a particular candidate. After the candidate’s visit to this city a similar post-electoral campaign poll gave the same candidate a preference of 45%. To measure the impact of the visit you want to see whether 35% differs statistically significant from 45%.
The general format is: ttest [variable1] = [variable2]
Example: ttest preferencepre = preferencepost
Decision: if P>|t| or P>t are lower than 0.05 then they are different. The candidate’s visit may have had some impact on his electoral preferences.
3. To compare two sample means by groups. For example you may want to see whether males and females differ in their opinions regarding a particular topic (for example, presidential agreement).
The general format is: ttest [variable], by([group variable])
Example: ttest agree, by(gender) /*This assumes equal variances, standard deviation for males is similar to sd for females*/
Example: ttest agree, by(gender) unequal /*Use this when sd for males is quite different from that for females*/
Decision: if P>|t| or P>t are lower than 0.05 then agreement with the president differs between males and females.
Examples under construction…