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

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.

The correlation coefficient between study hours and exam scores needs to exceed a specific critical value.

The sample sizes for both groups being compared must be exactly equal.

There has to be a randomized experiment rather than an observational study.

There must be control for potential lurking variables that could affect both the study hours and exam scores.

Sample mean difference

Weighted average variance

Combined sample standard deviation

Pooled sample variance

There could be an inflation or deflation of Type I error rates leading to incorrect conclusions.

Random assignment within each sample might not be ensured, affecting external validity.

The test may violate the Central Limit Theorem unnecessarily complicating calculations.

Sample size requirements for asymptotic normality can become misrepresented.

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.