Question

You reject Ho for a t-test for two independent samples. Indicate which of the following are potentially viable criticisms for your conclusion and why. If valid, how could you address the issue?
a) sample size is too small
b) did not use a one-tailed test
c) variances differ in the two equally sized sampled groups
d) variances differ where one group has many more cases
e) the dependent variable is ordinal with only four possible values
f) the 95% confidence interval does not include zero
g) the 99% confidence interval does not include zero

Answer 1

You reject Ho for a t-test for two independent samples. Indicate which of the following are potentially viable criticisms for your conclusion and why. If valid, how could you address the issue?

t-test for independent samples is conducted for the equality of the population means. It can one tailed or two tailed. Although 1 tailed is stricter. So that means if you reject null at one tailed, it will also be rejected at 2 tailed test.

t-test can only be used when we do not have the population variances and n > 30 or the data follows normal distribution. T-test can be used in form of hypothesis testing or the confidence intervals

a) sample size is too small

This can be a criticism because if the data does not follow normal and n < 30, t-test is not valid. This can be addresed by increasing the sample size.

b) did not use a one-tailed test

The result can be different for different tails. It depends on the claim to be tested. So it can be invalied if we want to test in one direction and we are conducting a two tailed test. This can be solved by testing in one direction.

c) variances differ in the two equally sized sampled groups

This is not a criticism because there is a procedure to test two means with different variances.

d) variances differ where one group has many more cases

This is not a criticism because there is a procedure to test two means with different variances with different sample sizes.

e) the dependent variable is ordinal with only four possible values

This is a criticism because t-test can't be conducted with ranked or ordinal data. This can be addresed using Mann Whitney U test.

f) the 95% confidence interval does not include zero

This is not a criticism since if the interval does not include '0' then we would reject the null hypothesis. We are rejecting the null hypothesis here.

g) the 99% confidence interval does not include zero

This is not a criticism since if the interval does not include '0' then we would reject the null hypothesis. We are rejecting the null hypothesis here.