Pair-wise Comparisons for ANOVA – Learn It 2

  • Complete pair-wise comparisons for ANOVA
  • Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means

Pair-wise Comparisons

Previously, we explored a one-way ANOVA hypothesis test that allowed us to compare means from two or more groups/populations. More specifically, we performed calculations to determine if there was evidence that the means associated with the populations were statistically different from one another. However, because we are comparing two or more means, which means are different? We can perform multiple comparisons to identify the differences.

pair-wise comparison

The pair-wise comparison for ANOVA is a process of analyzing groups/populations by comparing them against each other in pairs.

 

When conducting pair-wise comparisons for ANOVA, we will be conducting multiple two-sample tests in order to find the significant difference(s) among the means.

The null hypothesis ([latex]H_0[/latex]): It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

  • Null hypothesis: [latex]H_0: \mu_1=\mu_2[/latex] or [latex]H_0: \mu_1-\mu_2=0[/latex]

The alternative hypothesis ([latex]H_A[/latex]): It is a claim about the population that is contradictory to [latex]H_0[/latex] and what we conclude when we reject [latex]H_0[/latex].

  • Alternative hypothesis:
    • [latex]H_A: \mu_1\lt \mu_2[/latex] or [latex]H_A: \mu_1-\mu_2\lt 0[/latex]
    • [latex]H_A: \mu_1>\mu_2[/latex] or [latex]H_A: \mu_1-\mu_2>0[/latex]
    • [latex]H_A: \mu_1\ne \mu_2[/latex] or [latex]H_A: \mu_1-\mu_2\ne0[/latex]