Question

How do you cross reference check a two sample t-test hypothesis?

Identify assumptions, cautions, limitations, and generalizations for a two sample t-test hypothesis.

Answer 1

let discuss about the assumptions of the t-test for independent means focus on sampling, research design, measurement, population distributions and population variance.

The t-test for independent means is considered typically "robust" for violations of normal distribution. This means that the assumption can be violated without serious error being introduced into the test in most circumstance. However, if we are conducting a one-tailed test and the data are highly skewed, this will cause a lot of error to be introduced into our test and a nonparametric test should be used.

The t-test for independent means is not robust for violations of equal variance. Remember that the shape of the sampling distribution is determined by the population variance (sigma.square) and the sample size. If the population variances are not equal, then when we calculate the difference between sample means, we do not have a sampling distribution with an expectable shape and cannot calculate an accurate critical value of the t distribution. This is a serious problem for our test. Our alternatives when the asssumption of equal variances has been violated are to use a nonparametric test( Kruskal-Wallis one-way analysis test) or levenes parametric test to check equality of variances which is Homogeneity of variance.

Similary to check Normality asumptions we can use Normal probability plot or qqplot to determine the normal probability distribution as samples coming from Normal population.