What are some of the limitations and assumptions of the t test?

Answer 1

The t-test assumes that the data is normally distributed and that the variances of the groups being compared are equal. Violation of these assumptions can lead to inaccurate results. Additionally, the t-test is sensitive to outliers and requires a relatively large sample size to ensure the validity of the results. It is also important to consider the type of t-test being used (independent, paired, or one-sample) and the appropriateness of the test for the specific research question at hand.

Answer 2

Oh honey, where do I even begin? The t test assumes your data is normally distributed, your sample is random, and your variances are equal. But let's be real, life ain't always that simple. Plus, with small sample sizes, the t test can be about as reliable as a Diet Soda - looks good on the surface, but lacks substance. Just remember, the t test is like that one friend who means well but can be a bit flaky at times.

Answer 3

Assumptions of the t test and F test for independent means

The t test for independent means and the F test for independent means are based upon several assumptions about the nature of reality. If these assumptions are not true then the results of your analysis could be seriously flawed without you realizing it.

1) The scores in the various groups are independent. This means that one person's score does not affect any other person's score, they are independent of each other. An obvious violation of this assumption would occur if you had more than one score per person in your data set, as those scores come from the same person they are obviously connected in an important way (i.e. are not independent). The statistical analysis will be seriously flawed if the scores are not independent.

2) The populations are normally distributed. By 'populations' were are referring to the populations represented by each group in the experiment. The t and F tests were built upon the assumption that each population in the experiment is normally distributed. This assumption ends up only being important if you have a small number of scores in teach group. If N=30 in each group then you don't need to worry about whether or not this assumption is true. If you have reason to think that the populations are somewhat close to being normally distributed then you can have less than 30 scores in each group.

3) All the populations have the same variance. The t and F tests were also built upon the assumption that every population in the experiment have identical variances. This assumption ends up only being important if you have widely different N in each group. If you have roughly the same number of scores in each group then you don't need to worry about whether or not this assumption is true.

Limitations

The t and F tests for independent means only examine means, they have virtually nothing to say about individual scores. It is important to keep track of the fact that our conclusions are about means, not about individuals. So, if we run a study with gender as an independent variable, and get a statistically significant result, then we can say that the mean of males differs from the mean of females in terms of the dependent variable, but we cannot say that any particular male will have a higher or lower score than any particular female.