Which of the following statistical tests examines the equality of two means?

A. F-test
B. ‘t’-test
C. Chi-square (χ²) test
D. Mann-Whitney ‘U’ test
E. Kolmogorov-Smirnov test

Choose the correct answer from the options given below:

Correct option is B

The question focuses on statistical tests that specifically assess whether two means are equal—this can involve parametric or non-parametric approaches depending on the data distribution.

• The ‘t’-test is a parametric test that compares the means of two groups (e.g., independent or paired samples) to determine if they are statistically different from each other. It assumes normal distribution and is widely used when the sample size is small and variance is unknown.

• The Mann-Whitney U test is a non-parametric test used to compare medians or ranks when the data doesn't meet the assumptions of a t-test (i.e., normality). It is often applied when testing the equality of two independent groups' central tendencies (i.e., mean or median) under ordinal or non-normal interval data.

Hence, both B (‘t’-test) and D (Mann-Whitney U test) are appropriate for examining equality of two means or their equivalent in non-parametric context.

Information Booster:

• ‘t’-test is used for comparing two means when population variance is unknown and sample size is small.

• It assumes data is normally distributed and uses Student’s t-distribution.

• Mann-Whitney U test is useful for ordinal data or when data does not follow normal distribution.

• It compares two independent samples by ranking data and analyzing differences in rank sums.

• Both tests are applicable in hypothesis testing involving two groups only.

• t-tests are more powerful when assumptions are met, but Mann-Whitney is more robust under violations of assumptions.

• These tests are foundational tools in inferential statistics for determining statistical significance between two datasets.

Additional Knowledge:

• A. F-test:
  The F-test is generally used to compare variances, not means. It is also used in ANOVA, which compares more than two means. While it indirectly relates to means in ANOVA, it is not used to compare exactly two means.

• C. Chi-square (χ²) test:
  The Chi-square test is used for categorical data, particularly to test association or independence between variables in a contingency table or to test goodness-of-fit. It does not test the equality of means.

• E. Kolmogorov-Smirnov test:
  The K-S test is used to compare distributions, particularly to test whether a sample comes from a specified distribution or to compare two distributions. It does not directly assess the equality of means.