A local school board was interested in comparing test scores on a standardized r

Question

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 students at each of four different elementary schools in the district and recorded the test scores.The data is shown below:

Perform ANOVA using Excel or Minitab.

At the 0.05 level of significance, evaluate the effect of each factor and its interaction.

Gender School 1 School 2 School 3 School 4 Male 631 642 651 350 566 710 611 565 620 649 755 543 542 596 693 509 560 660 620 494 Female 669 722 709 505 644 769 545 498 600 723 657 474 610 649 722 470 559 766 711 463

Explanation / Answer

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.

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