What is a Two-Sample t-test?

The two-sample t-test is a statistical method used to determine if there’s a significant difference between the means of two independent groups. It assesses whether the means of these groups are statistically different from each other or if any observed difference is due to random variation. For example, if we’re comparing test scores of two classes, we use this test to know if one class did better than the other by a meaningful amount, or if it’s just luck.

Before using a two-sample t-test, it’s important to make sure of the following:

• The data in each group are separate and have similar distributions.
• The populations from which the samples are taken follow a typical bell-shaped curve.
• The variations within the populations are similar (equal variances).

Syntax:

t.test(x, y, alternative = “two.sided”, mu = 0, paired = FALSE, var.equal = FALSE, conf.level = 0.95)

• x and y: These are the numeric vectors or data frames containing the two samples you want to compare.
• alternative: This specifies the alternative hypothesis. It can take values “two.sided”, “less”, or “greater”, indicating whether you’re testing for a two-tailed, left-tailed, or right-tailed test, respectively.
• mu: This is the hypothesized difference in means under the null hypothesis. The default is zero.
• paired: If set to TRUE, it indicates that the two samples are paired (e.g., before and after measurements). The default is FALSE for unpaired samples.
• var.equal: If set to TRUE, it assumes equal variances in the two groups. The default is FALSE.
• conf.level: This specifies the confidence level for the confidence interval. The default is 0.95.

In statistics, the two-sample t-test is like a measuring stick we use to see if two groups are different from each other. It helps us figure out if the difference we see is real or just random chance. In this article, we will calculate a Two-Sample t-test in the R Programming Language.