What is Welch’s t-test?

Welch’s t-test is a statistical tool used to compare the averages of two groups. It’s helpful when the groups have different amounts of variability (like how spread out their scores are). Traditional methods assume the variability is the same, but Welch’s t-test adjusts for these differences, making comparisons fairer and more accurate.

[Tex]t = \frac{{\bar{x}_1 – \bar{x}_2}}{{\sqrt{\frac{{s_1^2}}{{n_1}} + \frac{{s_2^2}}{{n_2}}}}} [/Tex]

Where,

• t is the t-statistic that follows a t-distribution with degrees of freedom calculated using the Welch-Satterthwaite equation.
• x₁ and x₂ bar are the sample means of two independent groups.
• s²₁ and s²₂ are the sample variances of the two groups.
• n₁ and n₂ are the sample sizes of the two groups.

Syntax:

t.test(x, y, alternative = “two.sided”, var.equal = FALSE)

Here ,

• x and y are the vectors containing the sample data for the two groups being compared.
• alternative specifies the alternative hypothesis and can be set to “two.sided” for a two-tailed test, “greater” for a one-tailed test where the alternative hypothesis is that the mean of x is greater than the mean of y, or “less” for a one-tailed test where the alternative hypothesis is that the mean of x is less than the mean of y.
• var.equal is a logical argument that indicates whether to assume equal variances between the groups (TRUE) or not (FALSE). In Welch’s t-test, this should be set to FALSE to account for unequal variances.

In statistical analysis, comparing the means of two groups is a common task. However, traditional methods like the Student’s t-test assume equal variances between groups, which may not hold true in real-world data. Welch’s t-test, named after its developer B. L. Welch, provides a robust solution for comparing means when dealing with unequal variances or sample sizes between groups in the R Programming Language.