This test selection is used to determine if there is a difference between the means from two groups. The groups can be from the same or different samples. If you know the mean, standard deviation and size of both groups, this test may be used to determine if there is a reliable difference between the means.
The groups may be created from one or two samples and may be different sizes. The only requirement is that there is no overlap. That is, people in one group may not also be part of the other group. For example, you would not use this test to compare a sample to the population because the same people would be part of both groups.
The groups may be formed by splitting the data based on a variable. For example, after collecting data, you could split it into two groups of males and females. The groups may also be formed because the data was collected from two different sources. For example, a study done a shopping center A could be compared to data collected at shopping center B.
There are actually two different formulas to calculate the t-statistic for independent groups. The t-statistics calculated by both formulas will be similar but not identical. Which formula you choose depends on whether the variances of the two groups are equal or unequal. In actual practice, most researchers assume that the variances are unequal because it is the most conservative approach and is least likely to produce a Type I error. Thus, the formula used in Market Research App assumes unequal variances.
Example
Two new product formulas were developed and tested. A twenty-point scale was used to measure the level of product approval. Six subjects tested the first formula. They gave it a mean rating of 12.3 with a standard deviation of 1.4. Nine subjects tested the second formula, and they gave it a mean rating of 14.0 with a standard deviation of 1.7. The question we might ask is whether the observed difference between the two formulas is reliable.
Mean of the first group: 12.3
Unbiased standard deviation of the first group: 1.4
Sample size of the first group: 6
Mean of the second group: 14.0
Unbiased standard deviation of the second group: 1.7
Sample size of the second group: 9
t value = 2.027
Degrees of freedom = 13
Two-tailed probability = .064
You might make a statement in a report like this: An independent groups t-test was performed to compare the mean ratings between the two formulas. The t-statistic was not significant at the .05 critical alpha level, t(13)=2.027, p=.064. Therefore, we fail to reject the null hypothesis and conclude that there was no significant difference between the ratings for the two formulas.
