Quasi-F

Differences

Technically, the classic F statistic in ANOVA requires strict orthogonality in the test, which means the estimates are independent for considering the marginal means. In a strict sense, orthogonality exists when each cell (or unique combination of independent variables) has exactly the same sample size. Unequal sample size creates a situation in which the analysis usually weights each element of the calculation by the respective sample size and this inequity of weighting violates the assumption of orthogonality. However, examination of the impact of this inequity demonstrates little impact on the accuracy of the F test unless it is related to assumptions dealing with within-cell variance. While the design with unequal sample sizes is technically considered unbalanced and the estimate is considered as a quasi-F, this particular entry does not consider such conditions as functioning as a quasi-F because the assignment of which error term should be used remains unaffected.

Sources of Variability

Sources of variability in ANOVA can be either (a) fixed or random and/or (b) crossed or nested. Quasi-F designs generally will involve at least one random and one nested factor. Most often, there exists a random factor nested within a fixed factor. The following sections explain those terms and the challenge of generating the appropriate statistical examination that requires a quasi-F. A quasi-F is distinguished from the normal F statistic because it indicates that the error term, or denominator in the ratio, represents only an approximation of the within-group variability. The impact of the use of the mixed design becomes a form of hierarchical linear modeling and generates some unique challenges for statistical analysis.

The sources of variability, referred to as a factor, can be considered either random or fixed. A fixed factor has known or accepted sets of values that are relative to each other (e.g., a message with versions that are written as high fear appeals, medium fear appeals, and low fear appeals). A participant in the investigation receives one of the three messages, and the comparison or ANOVA considers whether any difference in dependent measure is observed between the versions of the message. The source of variability is considered fixed as well as crossed.

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