Question

How do you calculate ANOVA with uneven sets of numbers?

Answer 1

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For calculating ANOVA with uneven st of numbers or with the unequal sample is a bit difficult. Because it can lead to:

• Unequal variances between samples, which affect the assumption of equal variances in tests like ANOVA. Having both unequal sample sizes and variances dramatically affect statistical power and Type I error rates (Rusticus & Lovato, 2014).
• A general loss of power. Equal-sized groups maximize statistical power.
• Issues with confounding variables.

It is ok if your groups have different sample sizes as long as each has a minimum number of cases in them (min 30 cases each).

If your Leven's test is significant then inequality of variances is assumed and you should use the P-value and assess its significance under unequal variances.

You can calculate and consider the effect size when comparing the two means which takes into account the sample size effect... your other option is to try to downsample your big group to an equal size and then reassess the group differences.

Unequal Sample Sizes

Hypothesis Testing > Unequal Sample Sizes

Problems with Unequal Sample Sizes

Unequally sized groups are common in research and may be the result of simple randomization, planned differences in group size or study dropouts. Unequal sample sizes can lead to:

• Unequal variances between samples, which affects the assumption of equal variances in tests like ANOVA. Having both unequal sample sizes and variances dramatically affects statistical power and Type I error rates (Rusticus & Lovato, 2014).
• A general loss of power. Equal-sized groups maximize statistical power.
• Issues with confounding variables.

Where, exactly this starts to matter isn’t clear. Keppel (1993) states that a rule of thumb for a magic cut-off point doesn’t seem to exist. That said, you don’t need equally sided groups to calculate accurate statistics, and most software will adjust for differences.

Tests

Some tests are set up specifically to deal with the problem of unequal sample sizes and unequal variances:

• Dunnett’s T3 or Dunnett’s C can be used for pairwise comparisons. Use T3 for small samples, and C for larger samples.
• Games-Howell Pairwise Comparison Test: an extension of the Tukey-Kramer test to handle unequal variances. Although it has more power (narrower confidence intervals) than Dunnett’s tests, alpha inflation can be a problem.
• Tamhane’s T2: combines Sidak’s multiplicative inequality test with Welch’s approximate solution.
• Welch’s Test for Unequal Variances is a modified Student’s t-test. The modified degrees of freedom tends to increase the test power for samples with unequal variance.