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# Researchers in child development are interested in developing ways to increase the spatial-temporal reasoning of preschool children.

Researchers in child development are interested in developing ways to increase the spatial-temporal reasoning of preschool children. The researchers want to design a study to evaluate which of several methods proposed to accelerate the growth in spatial-temporal reasoning yields the greatest increase in a child's development in this area. There are three methods proposed: three months of playing piano lessons, three months of playing specially developed computer video games, and specially designed games in small groups supervised by a trained instructor. The researchers measure the effectiveness of the three programs by assessing the children and assigning them a reasoning score both before and after their participation in the program. The difference in these two scores is the response variable. A control group is also included to measure the change in reasoning for children not given any special instruction. Twenty-five students were randomly assigned to each of the four methods of instruction: no instruction (control), piano lessons, computer video games, or instructor.

Use the SAS output shown here to answer the questions.

The ANOVA Procedure

Class Levels Values

Method 4 Computer video instructor no instruction piano lessons

Number of observations used 100

The ANOVA Procedure

Dependent Varibale: Effectiveness score

Source DF Sum of Squares Mean Square F Value PR>F

Model 3 725.235500 242.411833 24.44 <.0001

Error 96 952.302400 9.919817

Corrected

Total 96 1679.537900

R-Square Coeff Var Root MSE Effectiveness score Mean

0.432997 79.51462 3.149574 3.961000

The ANOVA Procedure

Tukey's Studenitized Range test for effectivness score

Alpha 0.05

Error Degrees of Freedom 96

Error Mean Square 9.919817

Critical Value of Studentized Range 3.69761

Minimum Signifiant difference 2.3292

Means with the same letter are not significantly different

Tukey Grouping Mean N Method

A 7.4000 25 Instructor

B 4.7640 25 Computer Video

B

B 3.7920 25 Piano Lessons

C -0.1120 25 no instruction

The ANOVA Procedure

Alpha .05

Error Degrees of Freedom 96

Error Mean Square 9.919817

Critical Value of t 2.69403

Minumum Significant Difference 2.3999

Means with the same letter are not significantly different

Bon Grouping Mean N Method

A 7.4000 25 instructor

B 4.7640 25 computer video

B

B 3.7920 25 Piano Lessons

C -0.1120 25 No instruction

(a). What are the values for the sum of squares between and the sum of squares within and their degrees of freedoms?

(b) State the null and alternative hypotheses being tested by the F-statistic in the ANOVA

(c). Is there a significant difference in the mean effectiveness of the methods of instruction units produced between four different methods using α = .05.

(d) If the differences between methods are significantly different, use the Tukey's method to see which methods are different. Compare the results with that of the Bonferroni.

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