Analysis of variance (ANOVA)

An investigator compares the difference in the amount of 20% sucrose solution removed by pollinators between unadulterated solution and solutions with 50, 100, 150, and 200 parts per million of caffeine. The results are expressed as differences in grams for the following caffeine concentrations:

50 ppm caffeine: -0.4 0.34. 0.19, 0.05, -0.14

100 ppm caffeine: 0.01, -0.39, -0.08, -0.09, -0.31

150 ppm caffeine: 0.65, 0.53, 0.39, -0.15, 0.46

200 ppm caffeine: 0.24, 0.44, 0.13, 1.03, 0.05

Does the mean amount of nectar taken depend on the concentration of caffeine in the nectar?

Carry out an analysis of variance (ANOVA) to find out.

a. State the null and alternative hypotheses appropriate for this question.

b. Calculate the following summary statistics for each group: n_i, Y-bar_i, and s_i.

c. Set up an ANOVA table to keep track of your results.

d. What is the mean square error MS_error?

e. How many degrees of freedom are associated with error? How many with groups?

f. Calculate the estimate of the grant mean.

g. Calculate the group sum of squares.

h. Calculate the group degrees of freedom and the group mean square.

i. What is F for this example?

j. Use a statistical table or Excel to find the P-value for this test.