Comparisons among means for one factor in a two-way analysis. We have illustrated Tukey pairwise comparisons among all treatment means in both one-way and two-way settings. The method can also compare the mean responses to just one of the two factors in a two-way setting:
do a one-way ANOVA on the two-way data listing only one factor as an explanatory variable. This combines data for all levels of the other factor, so it is useful only when interactions are small. Return to the data on phosphorus in tomato plants, Table 29.4. Do a one-way ANOVA that uses all 36 observations with fertilizer type as the only factor. Ask for Tukey pairwise comparisons among the three levels of fertilizer, with overall confidence level 95%.
(a) How many observations per group does your analysis use?
(b) What do you conclude from the F statistic and its P-value?
(c) Use Tukey: which pairwise differences of means for the 3 fertilizer levels are significant at the overall 5% level?
(d) Do you think these pairwise comparisons are useful for these data? (Hint: What population does each of the three samples represent?)