I conducted pre- and post- tests (each graded with a quantitative score) among three different grade levels in a middle school where each grade level had a different number of students (23, 20, and 21 respectively).

  • What type of ANOVA test should I use??

    My first thought was to use an "ANOVA: Two-Factor with Replication", but it cannot be completed without equal sample sizes. I also thought about running two separate One-Way ANOVAs and subsequent Post Hoc tests, but that would give me too small of an alpha because of so many tests. Thank you in advance for your help!

  • 1
    $\begingroup$ Not sure what software you are using, but an ANOVA with a between-subjects factor and a within-subjects factor will work and does not require balanced cell sizes (equal sample sizes). $\endgroup$
    – dbwilson
    May 31, 2017 at 22:20

1 Answer 1


If I understand what you did, you have three factors and no replication:

  • Grade level: Fixed effects factor with 3 levels.
  • Student: Random effects factor with an unbalanced number of levels, nested within grade level factor.
  • Pre/post: Fixed effects factor with 2 levels, crossed with student and grade level.

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