12.1 Weight gain and junk food. The dependent variable is weight gain (grams) and the independent variable is diet type (1 = standard diet, 2 = junk food, 3 = health food). The study was done in laboratory mice (for obvious reasons); there are 5 mice per group (small sample). The study was set up to learn about the effect of diet on weight gain.
(A) Means and standard deviations
n_{1} = 5, _{1} = 11.14, s_{1} = 1.27
n_{2} = 5, _{2} = 13.44, s_{2} = 0.623
n_{3} = 5, _{3} = 9.14, s_{3} = 0.581
(B) Boxplot: Locations (averages) demonstrate clear differences. The
small samples ( n_{i} = 5) preclude robust statements
about shape and location.
(C) Replicate descriptive statistics and boxplot in SPSS
(D) ANOVA calculations
To determine the approximate P-value, draw the F_{2,12} curve and then look up the landmark for alpha = 0 .05 in the F table, which is F_{2,12,.95} = 3.89. You should place the landmark on the curve, noting that the area under the curve to the right of this landmark is .05. Then put the F_{stat} (which is 29.69) far to the right of the landmark. The area under the curve to the right of the F_{stat} should be shaded to represent the p value. It should be clear now that p < .05. The precise P-value (StaTable) @ 0.000.
The conclusion is to reject H_{0} and conclude the average differed significantly.
ANOVA table:
Source SS df MS
Between 46.30 2 23.15
Within 9.37 12 .78
(E) Replicate ANOVA in SPSS.
12.3 Maternal adaptation.
(A) Explore the data with side-by-side boxplots. The SPSS boxplots are shown below. (The labels on the X-axis failed to print in the transfer to html. Here are the group descriptions we are going to have to keep in mind when interpreting these data: Group 1 = LBW + intervention, Group 2 = LBW + no intervention, Group 3 = normal birth weight, no intervention.)
Report the most salient findings from this exploration. Side-by-side boxplots reveal outside values in Group 1 (LBW + intervention) and Group 3 (normal BW + no intervention). Group 2 (LBW + no intervention) shows higher average values than both Group 1 or Group 3.
What do you make of the outside values? These outside values represent women with high scores -- women having excessive trouble adapting to motherhood -- and should be investigated.
(B) Group summary statistics are given in the problem. Construct a one-way ANOVA table based on thee summary statistics. See below.
Report the F statistic and P-value used to test H_{0}: µ_{1} = µ_{2} = µ_{3.} F_{stat} = 5.53 with 2 and 90 df; P = 0.005. Therefore, the difference among groups is significant.
(C) In rejecting H_{0}, are you concluding that all three groups differ? No!
12.5 Sense of coherence
(A) Boxplots