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Two-Factor ANOVA

Two-Factor ANOVA. What Do We Mean By Two Factor?. This is when we are studying the effect of more than one factor (variable) simultaneously. Each factor has a number of levels. Lets say factor A has two levels and factor B has three levels, we would call this a 2x3 ANOVA.

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Two-Factor ANOVA

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  1. Two-Factor ANOVA

  2. What Do We Mean By Two Factor? • This is when we are studying the effect of more than one factor (variable) simultaneously. • Each factor has a number of levels. Lets say factor A has two levels and factor B has three levels, we would call this a 2x3 ANOVA.

  3. Main Effects and Interactions • The mean difference among the levels of one factor are referred to as the main effect of that factor. • An interaction between two factors occurs whenever the mean differences between individual treatment conditions, or cells, are different from what would be predicted from the overall main effects of the factors. • When the effect of one factor depends on the different levels of a second factor, then there is an interaction between the factors.

  4. Formulae • SSw =  (Xijk – X.jk)2 • SSbet = njk (X.jk – X...)2 • SStot =  (Xijk – X...)2 • SSbet = SSj + SSk + SSjxk • SSj = nj.(X.j . – X...)2 • SSk = n.k (X..k – X...)2 • dfw =  df • dfbet = jk – 1 • dftot = N – 1 • dfj = j-1 • dfk = k-1

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