Means

To compare with the test statistic to make a decision

To determine the sample means

To calculate the p-value

To calculate the degrees of freedom

Binomial distribution

Chi-squared distribution

T-distribution

Normal distribution

Bar graphs

Pie charts

Histograms

Boxplots

Paired t-test

Chi-square test for independence

Equal-variance t-test (Student's t-test)

Welch’s t-test

Bonferroni correction by adjusting alpha level divided by the number of tests.

Post-hoc Tukey’s HSD test without adjusting overall alpha level.

Paired t-tests between each group mean without alpha adjustment.

Repeated measures analysis without considering individual comparisons.

Accepting a false null hypothesis

Failing to reject a true alternative hypothesis

Rejecting a true null hypothesis

Accepting a false alternative hypothesis

A difference in sample means that appears to be statistically significant.

Failure to control confounding variables in two groups being compared.

A smaller than usual effect size in the populations being studied.

Utilization of technology to run the test instead of manual calculations.

The data collected must come from a census of both populations.

The samples from both populations are independent random samples.

The sample size for both populations must be over 30.

Both populations have the same standard deviation.

More stringent significance criteria, such as lower alpha levels, thereby increasing the threshold of evidentiary support required before rejecting the null premise in favor of the alternative position.

Larger numbers of participating individuals, hence minimizing the potential for making a type II mistake as it occurs less often in larger groups.

Reduced effect size of medications, lowering the chances of detecting a true difference if it exists.

Increased variability within subject responses, which will eventually cancel out across the entire group, leaving a more pronounced overall trend visible despite increased spread of individual reactions.

It invalidates any form of t-tests requiring equal treatment on both variances.

It allows applying pooled variance estimates enhancing test precision significantly.

It solely affects calculation of margin of error but not overall feasibility or outcome of t-test.

It necessitates using modified degrees of freedom that may lead to a more conservative t-test result.