Question

In a 5 x 4 factorial design with 10 participants in each group, df(error) = and df(interaction) = ?

Answer 1

In a 5 x 4 factorial design with 10 participants in each group, df(error) = and df(interaction) = ?

here number of rows are 5 and number of column 4 and replication is 10 therefore ,

df( factor 1 ) = 5 -1 = 4   

df (factor 2) = 4-1 = 3

df ( interaction ) = df (factor 1) * df( factor 2 ) = 4 * 3 = 12

df total = n-1 here n = 5 * 4 * 10 = 200 ( ie factor 1 * factor 2 * replication )  

df fotal = 200 -1 = 199

df for error = df total - df ( factor 1 ) - df ( factor 2) - df ( interaction )

= 199 - 4 - 3 - 12

= 180

In a 5 x 4 factorial design with 10 participants in each group, df(error) = 180

and df(interaction) = 12