Question

Normal No Spacing Head 3. Fourth-Grade Test Scores A local school board was interested in comparing test scores on a standardized reading test for fourth-grade students in their district. They selected a random sample of five male and five female fourth grade students at each of four different elementary schools in the district and recorded the test scores. The results are shown in the table below. School 1 Gender Male School 4 350 565 566 620 School 2 642 710 649 596 660 722 769 723 649 766 School 3 651 611 755 693 620 709 545 Female 9 644 600 763 657 610 559 a. What type of experimental design is this? What are the experimental units? What are the factors and levels of interest to the school board? b. Perform the appropriate analysis of variance for this experiment. Include your hypotheses and ANOVA table in your answer. c. Do the data indicate that effect of gender on the average test score is different depending on the student's school? Test the appropriate hypothesis using a .05. Provide your conclusion and justification for it. d. Plot the average scores using an interaction plot. How would you describe the effect of gender and school on the average test scores? e. Do the data indicate that either of the main effects is significant? If the main effect is significant, use Tukey's method of paired comparisons to examine the differences in detail. Use a = .01.

Answer 1

Definition: • The response variable(dependent variable is the variable of interest to be measured in the experiment. • Factors are the variables whose effect on the response variable is studied in the experiment. • Factor levels are the values of a factor in the experiment. • Treatments are the possible factor level combinations in the experiment. (One factor level for each factor is combined with factor level from other factors) • A designed experiment is an experiment in which the researcher chooses the treatments to be analyzed and the method for assigning individuals to treatments.

Response variable: reading score (numerical) Factor variables: gender and the elementary school the student is attending (factors are categorical). Level of gender are male/female

From following results we observe that

1-Interaction between gender and school has not a significant impact on test scores as F(3,32)=1.19,p=0.329>0.05

2-Main effect of gender has not a significant impact on test scores as F(1,32)=2.09,p=0.158>0.05

3-Main effect of school has a significant impact on test scores as F(3,32)=27.75,p=0.000<0.05

As school has significant impact on test scores, we applied Tukey test and found that Schools 2 and 3 do not differ significantly in mean test scores and while all other pairs of schools differ significantly.

General Linear Model: Test Score versus Gender, School

Method

Factor coding (-1, 0, +1)

Factor Information

Factor Type   Levels Values

Gender Fixed       2 Female, Male

School Fixed       4 1, 2, 3, 4

Analysis of Variance

Source           DF Adj SS Adj MS F-Value P-Value

Gender          1    6200    6200     2.09    0.158

School          3 246726   82242    27.75    0.000

Gender*School   3   10575    3525     1.19    0.329

Error            32   94826    2963

Total            39 358326

Tukey Pairwise Comparisons: Response = Test Score, Term = School

Grouping Information Using the Tukey Method and 95% Confidence

School   N   Mean Grouping

2       10 688.6 A

3       10 667.4 A

1       10 600.1      B

4       10 487.1         C

Means that do not share a letter are significantly different.