Practice Exam - Statistical Methods II | STAT 516 | Exams Data Analysis & Statistical Methods

Statistics 516 - Spring 2003 - Practice Exam 2

Part I: Answer the two following questions. Eight points each.

1) In performing an ANOVA, what four assumptions must be satisfied?

2) Define what is meant by the p-value (or empirical significance level) of a test.

Part II: Answer 12 of the following 13 questions. Seven Points each.

1) Consider a one-way ANOVA with three factor levels red, blue, and green. Because the SSB for this ANOVA would have

two-degrees of freedom we would need to use two dummy variables if we wanted to perform the ANOVA using dummy

variables. Give an example of two dummy variables that would work here, being careful to specify when each would take

the value zero or one.

Problems 2 refers to the partial analysis below faces that is based on an article that appeared in the Fall 1996 issue of the

Journal of Nonverbal Behavior. A sample of 36 students was randomly divided into six groups and each group was assigned

to view one of six slides showing a person making a facial expression. The six expressions were Angry, Disgusted,

Fearful, Happy, Sad, or Neutral. After viewing the faces the students were asked to rate the degree of dominance

they inferred from the facial expressions (a scale ranging from -15 to 15).

DATA faces;

INPUT expression $ dominance @@;

CARDS;

Angry 2.10 Angry 0.64 Angry 0.47

Angry 0.37 Angry 1.62 Angry -0.08

Disgusted 0.40 Disgusted 0.73 Disgusted -0.07

Disgusted -0.25 Disgusted 0.89 Disgusted 1.93

Fearful 0.82 Fearful -2.93 Fearful -0.74

Fearful 0.79 Fearful -0.77 Fearful -1.60

Happy 1.71 Happy -0.04 Happy 1.04

Happy 1.44 Happy 1.37 Happy 0.59

Sad 0.74 Sad -1.26 Sad -2.27

Sad -0.39 Sad -2.65 Sad -0.44

Neutral 1.69 Neutral -0.60 Neutral -0.55

Neutral 0.27 Neutral -0.57 Neutral -2.16

;

PROC GLM ORDER=DATA;

CLASS expression;

MODEL dominance = expression;

ESTIMATE ‘Angry vs. Disgusted’ expression 1 -1 0 0 0 0;

RUN;

The GLM Procedure

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 5 23.08522222 4.61704444 3.96 0.0071

Error 30 34.98700000 1.16623333

Corrected Total 35 58.07222222

Standard

Parameter Estimate Error t Value Pr > |t|

Angry vs. Disgusted 0.24833333 0.62349374 0.40 0.6932

2) Construct a 95% confidence interval for the difference between the true average dominance rating of the angry and

disgusted groups.

Practice Exam - Statistical Methods II | STAT 516, Exams of Data Analysis & Statistical Methods

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Statistics 516 - Spring 2003 - Practice Exam 2

Part I: Answer the two following questions. Eight points each.

1) In performing an ANOVA, what four assumptions must be satisfied?

2) Define what is meant by the p-value (or empirical significance level) of a test.

Part II: Answer 12 of the following 13 questions. Seven Points each.

1) Consider a one-way ANOVA with three factor levels red, blue, and green. Because the SSB for this ANOVA would have

two-degrees of freedom we would need to use two dummy variables if we wanted to perform the ANOVA using dummy

variables. Give an example of two dummy variables that would work here, being careful to specify when each would take

the value zero or one.

Problems 2 refers to the partial analysis below faces that is based on an article that appeared in the Fall 1996 issue of the

Journal of Nonverbal Behavior. A sample of 36 students was randomly divided into six groups and each group was assigned

to view one of six slides showing a person making a facial expression. The six expressions were Angry, Disgusted,

Fearful, Happy, Sad, or Neutral. After viewing the faces the students were asked to rate the degree of dominance

they inferred from the facial expressions (a scale ranging from -15 to 15).

DATA faces;

INPUT expression $ dominance @@;

CARDS;

Angry 2.10 Angry 0.64 Angry 0.

Angry 0.37 Angry 1.62 Angry -0.

Disgusted 0.40 Disgusted 0.73 Disgusted -0.

Disgusted -0.25 Disgusted 0.89 Disgusted 1.

Fearful 0.82 Fearful -2.93 Fearful -0.

Fearful 0.79 Fearful -0.77 Fearful -1.

Happy 1.71 Happy -0.04 Happy 1.

Happy 1.44 Happy 1.37 Happy 0.

Sad 0.74 Sad -1.26 Sad -2.

Sad -0.39 Sad -2.65 Sad -0.

Neutral 1.69 Neutral -0.60 Neutral -0.

Neutral 0.27 Neutral -0.57 Neutral -2.

PROC GLM ORDER=DATA;

CLASS expression;

MODEL dominance = expression;

ESTIMATE ‘Angry vs. Disgusted’ expression 1 -1 0 0 0 0;

RUN;

2) Construct a 95% confidence interval for the difference between the true average dominance rating of the angry and

disgusted groups.

Problems 3 and 4 refer to the following partial analysis below. Seven different types of material (labeled A-F) were sent out

to a sample of 13 laboratories for stress testing (since different laboratories use different testing methods). The PROC GLM

code used was:

PROC GLM;

3) Find the value of the F statistic for testing that σ^2 lab=0 against σ^2 lab >0.

4) Find an estimate of σ^2 lab.

5) Justify that the above design is factorial, balanced, with replications.

6) On the above data set, using the notation from class, identify y 111 , y 112 , y 121 , y 342 ,

y , and y • • •.

7) Write the model equation for the two-way ANOVA with interactions, and identify the parameters you used.

y ijk =

8) The DF and SS for Factor C were deleted. What values should they have?

SS= df=

9) Use the Holm procedure to construct a display showing which levels of Factor A are significantly different from each

other at a family-wise αT=0.10.

10) For each of the cases below, determine which test is appropriate:

• the overall p-value from the ANOVA table

• one of the type III tests (say which factor or interaction)

• a contrast (say which factor, and what the coefficients would be)

• Holm’s test performed on all pairs of factor levels (say which factor)

• cannot be tested for this data-set

a) It is desired to test whether the Factor C has any effect on average on the output values.

b) It is desired to test whether Factor C has the same effect on the output values regardless of the level of

Factor A.

c) It is desired to test whether level 1 of Factor C differs from level 4 of Factor C.

d) It is desired to simultaneously test whether there is an effect due to Factor A, Factor C, or an interaction.

Problems 11-13 use the attached partial analysis of the data set vitaminb. It is similar to results reported in the July 1995

issue of Journal of Nutrition. It concerns the effect of a vitabin B supplement on the weights of the kidneys of Zucker rats.

Half of the rats were classified as obese, and half were classified as lean. The two groups of rats were then randomly

assigned to receive either the regular diet or the diet with the vitamin b supplement. At the end of twenty weeks, the weights

of the rats’ kidneys were measured in grams.

11) Check the assumptions for performing this two-way ANOVA. Say how you checked them and whether they were

satisfied.

12) Identify which group was used as the baseline group.

13) Consider the three p-values from the box of Type III Tests. Assuming that all of the assumptions are met, use an α=0.

for each of these three tests and report the conclusion you can draw from each one of them. Phrase your conclusions in terms

of what the scientists were looking for in the problems. (e.g. There is/is not a significant effect on the kidney weight due to

the choice of diet.)

DATA vitaminb;

INPUT diet $ size $ kidney @@;