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Two-Factor ANOVA

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What Do We Mean By Two Factor? This is when we are studying the effect of more than one factor (variable) simultaneously. 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. 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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Main Effects and Interactions The mean difference among the levels of one factor are referred to as the main effect of that factor. 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. 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. When the effect of one factor depends on the different levels of a second factor, then there is an interaction between the factors.

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Formulae SSw = (X ijk – X. jk ) 2 SSw = (X ijk – X. jk ) 2 SSbet = n jk (X. jk – X...) 2 SSbet = n jk (X. jk – X...) 2 SStot = (X ijk – X...) 2 SStot = (X ijk – X...) 2 SSbet = SSj + SSk + SS jxk SSbet = SSj + SSk + SS jxk SSj = n j. (X. j. – X...) 2 SSj = n j. (X. j. – X...) 2 SSk = n. k (X.. k – X...) 2 SSk = n. k (X.. k – X...) 2 dfw = df dfw = df dfbet = jk – 1 dfbet = jk – 1 dftot = N – 1 dftot = N – 1 dfj = j-1 dfj = j-1 dfk = k-1 dfk = k-1

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Nested Designs Study vs Control Site. Nested Experiments In some two-factor experiments the level of one factor, say B, is not “cross” or “cross classified”

Nested Designs Study vs Control Site. Nested Experiments In some two-factor experiments the level of one factor, say B, is not “cross” or “cross classified”

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