12 Key, Odd

Review Questions

  1. grand
  2. group
  3. i and i, respectively
  4. True.
  5. H0: 1 = 2 = . . . = k  (equivalently, H0: s2Between s2Within)
  6. dfB = 4-1 = 3; dfw = 32-4 = 28
  7. The dependent variable is glucose level. The independent variable is the sex of the taxi driver.
  8. the grand mean 
  9. nominal . . . scale (although ordinal data can also be analyzed). 
  10. independent t test (assuming equal variance)
  11. i 
  12. within
  13. dfw 
  14. greater than
  15. dfB 

Exercises

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 

n1 = 5, 1 = 11.14, s1 = 1.27
n2 = 5, 2 = 13.44, s2 = 0.623 
n3 = 5, 3 = 9.14, s3 = 0.581

(B) Boxplot:  Locations (averages) demonstrate clear differences. The small samples ( ni = 5) preclude robust statements about shape and location.

(C) Replicate descriptive statistics and boxplot in SPSS
(D) ANOVA calculations

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 H0: 1 = 2 = 3.  Fstat = 5.53 with 2 and 90 df; P = 0.005.  Therefore, the difference among groups is significant.

(C) In rejecting H0, are you concluding that all three groups differ?  No!

12.5 Sense of coherence 

(A) Boxplots