Two-sample location tests are statistical procedures used to compare the central tendency (e.g., mean or median) of two independent samples. They help determine whether the two groups come from populations with the same location parameter, which often refers to the mean or median.
1. Two-Sample t-test (Parametric)
The two-sample t-test, also known as the independent t-test, is used to compare the means of two independent groups. It assumes that the data in both samples are normally distributed and that the variances are equal (homoscedasticity). The test assesses whether the difference between the sample means is statistically significant.
- Null Hypothesis (H₀): The means of the two populations are equal ().
- Alternative Hypothesis (H₁): The means of the two populations are not equal ().
The test statistic is calculated by dividing the difference in sample means by the standard error of the difference, which accounts for sample size and variance. If the calculated t-value exceeds the critical value from the t-distribution, the null hypothesis is rejected.
2. Mann-Whitney U-test (Non-parametric)
The Mann-Whitney U-test, also called the Wilcoxon rank-sum test, is a non-parametric alternative to the t-test. It is used when the data do not meet the assumptions of normality or homoscedasticity. Instead of comparing means, it ranks all the values in the two samples and evaluates whether one group tends to have higher or lower ranks than the other.
- Null Hypothesis (H₀): The distributions of the two populations are equal.
- Alternative Hypothesis (H₁): The distributions of the two populations are different.
This test is ideal for ordinal data, continuous data with non-normal distributions, or when sample sizes are small.
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