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O'Brien's Two-Sample Tests

  • Tests for whether two independent groups have different means.
  • Include parametric and nonparametric options for different data conditions.
  • Commonly applied to evaluate treatments or relationships; rely on assumptions (independence, homogeneity of variances, normality).

O’Brien’s two-sample tests are statistical procedures used to compare the means of two independent groups to determine whether there is a significant difference between them.

These tests are applied when researchers want to assess whether a dependent variable differs across two independent groups. Different variants address different data conditions: parametric tests (e.g., the independent t-test) assume approximate normality and similar variances, while nonparametric alternatives (e.g., the Mann-Whitney U test) are used when normality or other assumptions are not met. Successful application depends on meeting assumptions such as independence of observations, homogeneity of variances, and normality of the data; failure to meet these assumptions can bias results.

A researcher tests a new medication for reducing anxiety in patients with generalized anxiety disorder (GAD). Participants are randomly assigned, with half of the participants in the treatment group receiving the new medication and the other half in the control group receiving a placebo. Anxiety levels are measured using a standardized anxiety scale before and after the treatment period. If the mean anxiety levels of the treatment group are significantly lower than the mean anxiety levels of the control group, the researcher can conclude that the new medication is effective at reducing anxiety in patients with GAD.

A researcher examines the relationship between social support and depression in older adults. A sample of older adults is recruited and their levels of social support and depression are measured using standardized scales. If the mean levels of depression are significantly lower in the group with higher levels of social support, the researcher can conclude that social support is related to lower levels of depression in older adults.

  • Comparing the effectiveness of different treatments or interventions.
  • Examining the relationship between a dependent variable and an independent variable when there are two independent groups.
  • Key assumptions: independence of observations, homogeneity of variances, and normality of the data.
  • If these assumptions are not met, test results may be biased or unreliable.
  • Independent t-test
  • Mann-Whitney U test