T-Test Calculator

Statistical t-tests are useful in determining and comparing significant differences between group means and evaluating if those differences are a result of chance. While the one-sample t-test analyzes the mean of one group against the set average (theoretical mean), the two-sample t-test compares means of two different samples for paired or unpaired data. Both methods assume a continuous data that is randomly selected and normally distributed with equal variances. Under the null hypothesis, which states that the means are equal, a t-statistic is calculated that follows a t-distribution with the associated degrees of freedom and a p value is obtained representing the probability that the null hypothesis is true. For t-statistic less than the t-critical at a p value greater than 0.05 (95% confidence interval), the null hypothesis is accepted. A negative t-statistic can be treated as their positive counterpart. A statistical summary of the data comprising of the mean, confidence interval, median, variance, standard deviation, minimum, maximum, and count is provided to quickly communicate the observations in the sample data. Histograms with embedded density plots, box plots, and normality plots are shown to visualize individual and group differences. A normal distribution for a Q-Q plot is observed when all the data points lie on the red line. Normality assumption is further verified with Shapiro Wilk test calculating a W-statistic. Consequently, for unpaired groups, a variance test based on the ratio of the homogeneity of variance between each group is carried out to determine the type of t-test to be performed. For a ratio of variance greater than or equal to 0.05, an equal variance is assumed and a two-sample unpaired t-test is given. On the other hand, when the ratio of variance between samples is less than 0.05, an unequal variance is assumed and a Welch’s t-test (also for unpaired data sets) is executed.