Question

8.26     In an experiment, participants were randomly divided into three groups and shown a list of 10 words to memorize.  Participants were instructed to either draw an image for each word, visualize an image for each word, or write the word.  The summary statistics for number of words recalled (out of 10) are shown in the table below.  Construct an ANOVA table to assess the difference in mean word recall between the three groups and answer the following questions

1. Which method had the highest mean recall in the sample?  Which had the lowest?
2. What is the F-statistic?
3. Either:
   1. What is the p-value?, or
   2. What is the F_,05 value for 2 and 24 degrees of freedom?
4. At a 5% level, what is the conclusion of the test?
5. According to this experiment, does it matter what you do if you want to memorize a list of words, and, if it matters, what should you do?

Group	n	Mean	St. Dev.
Draw	9	5.1	1.1
Visualize	9	3.7	1.7
Write	9	3.2	1.3
Overall	27	4.0	1.566

Answer 1

a)

Draw has the highest mean recall.

Write had the lowest.

b)

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different

Number of treatment, k = 3

Total sample Size, N =27

df(between) = k-1 =2

df(within) = N-k = 24

df(total) = N-1 = 26

SS(between) = (x̅1)²*n1 + (x̅2)²*n2 + (x̅3)²*n3 - (Grand Mean)²*N =17.46

SS(within) = (n1-1)*s1² + (n2-1)*s2² + (n3-1)*s3² = 46.32

SS(total) = SS(between) + SS(within) =63.78

MS(between) = SS(between)/df(between) =8.73

MS(within) = SS(within)/df(within) =1.93

F = MS(between)/MS(within) = 4.5233

c)

p-value = F.DIST.RT(4.5233, 2, 24) = 0.0215

Critical value Fc = F.INV.RT(23.5, 2, 24) = 3.403

d) Conclusion:

p-value < 0.05, Reject the null hypothesis.

e) Yes, according to this experiment, it matter what you do if you want to memorize a list of words.

We should perform a post Hoc test.