Activity 5 Two way ANOVA With two factors there is an additional question beyond whether each factor separately is significant Is there an interaction between the two factors That is does the effect of one factor depend on the level of the other factor To illustrate this let s consider the effects of ethanolic NaOH concentration and coal type on total acidity Each of these factors has three levels Open the data from the website 1 First let s look at an interaction plot Go to Stat ANOVA Interactions Plot Enter Acidity as the response and NaOH and Coal Type as the factors in that order Copy and paste the interaction plot below For Morwell coal what concentration of NaOH gives the highest mean acidity for Yallourn for Maddingley Since the lines for each concentration of NaOH are roughly parallel it appears that the effect of NaOH concentration does not depend on the type of coal This suggests that there is NO INTERACTION between the factors Thus when we perform a two way ANOVA the interaction term will probably not be significant Check but do not answer Do you get a different intuition if you produce an interaction plot with the factors in the other order 2 So let s look at the results Go to Stat ANOVA Two way Enter Acidity as the response NaOH as the row factor and Coal Type as the column factor Copy and paste the ANOVA table and ONLY the table below What are the test statistic and p value for the interaction term What can you conclude If the interaction term is not significant then we can focus on the main effects the effects of the individual factors 3 Since the interaction term isn t significant let s not waste those 4 degrees of freedom on the interaction when they could be used to give a more accurate estimate of the mean square error Refit the model without the interaction term by clicking the Fit additive model box in Stat ANOVA Two way Paste the new ANOVA table below Does NaOH concentration have a significant effect on acidity What about the type of coal Let s consider a different example the effects of brand of pen and writing surface on writing lifetime 4 Obtain an interaction plot paste it below Which brand of pen lasted longest on the first surface the second surface the third surface Here the effect of brand depends on the surface This suggests that THERE IS AN INTERACTION between the two factors Notice that the lines cross intersect multiple times Thus we will most likely find a significant interaction term 5 Perform a two way ANOVA Be sure NOT to fit the additive model so that you can obtain an interaction term What are the test statistic and p value for the interaction term What can you conclude That s it However a word to the wise Be sure you know how to use the Stat ANOVA General Linear Model function to obtain a two way ANOVA table with an interaction term just in case you need it for the homework in order to obtain Tukey tests
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