Analysis of variance (ANOVA)
An investigator compares the difference in the amount of 20%sucrose solution removed by pollinators between unadulteratedsolution and solutions with 50, 100, 150, and 200 parts per millionof caffeine. The results are expressed as differences in grams forthe 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 concentrationof caffeine in the nectar?
Carry out an analysis of variance (ANOVA) to find out.
a. State the null and alternative hypotheses appropriate forthis question.
b. Calculate the following summary statistics for each group:ni, Y-bari, andsi.
c. Set up an ANOVA table to keep track of your results.
d. What is the mean square error MSerror?
e. How many degrees of freedom are associated with error? Howmany 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 meansquare.
i. What is F for this example?
j. Use a statistical table or Excel to find the P-valuefor this test.
