Where a = number of levels in factor A and b = number of levels in factor B.įactor A has more than two levels and Factor B two levelsįactors A and B have more than two levelsANOVA stands for “Analysis of Variance”, is a comparative test used to test the difference in the mean of data for more than two groups. Where ha = absolute value (t(α2, dfe)), a = number of levels in factor A, b = number of levels in factor B, n = number of observations for each interaction between factors, q = degrees of freedom for interaction effects, (a - 1)(b - 1) and dfe = degrees of freedom for error, abn - ab.įactor A has two levels and Factor B has more than two levels The terms are defined differently based on the number of levels and observations in each factor. Listed below are the general formulas for the upper and lower decision limits for the interaction of factors A and B. Points that lie outside the upper decision limit (UDL) or lower decision limit (LDL) indicate that the interaction is statistically significant. The decision limits indicate whether the interaction is significant. Where MSE = mean square error (from an ANOVA with terms A, B, and AB), n T = total number of observations in the sample, n 1= number of observations at each level of the factor, and h α = absolute value (t(α2, df) where a2 = (1- (1- a )** (1 / a)) / 2 and df = abn - ab. Where MSE = mean square error (from an ANOVA with terms A, B, and AB), a = number of factor levels in factor A, and n 1= number of observations at each level of the factor.įor values of alpha outside the range of 0.001 and 0.1, the decision limits are: Where ha = absolute value(t(a / 2 abn - ab), MSE = mean square error (from an ANOVA with terms A, B, and AB) and n 1 = number of observations at each level of the factor A. The upper and lower decision limits for factor A are: To calculate the decision limits for factor B, replace terms specific to factor A with equivalent terms for factor B. The formulas below show the upper and lower decision limits for factor A. The calculation of the upper and lower decision limits varies based on the number of levels in the factor and the number of observations at each level. Points that lie outside the upper decision limit (UDL) or lower decision limit (LDL) are statistically different from the grand mean. The decision limits indicate whether factor level means are different from the grand mean.
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