Question

Researchers are interested in examining the impact of three different Math instruction modules on standardized Math achievement in 6^th grade. Researchers sampled 13 6^th grade students, and tested them each four times: after 1 month of standard instruction (control), after 1 month of module A, after 1 month of module B, and after 1 month of Module C. Researchers chose an alpha level of 0.05.

SS _total = 50; SS _{between subjects} = 10; SS ₁ = 10; SS ₂ = 8; SS ₃ = 6; SS ₄ = 6

H₀: All μ’s are equal (μ1=μ2=μ3=μ4).

H₁: There is at least one significant mean difference.

1. Critical Value?

2. Test statistic?

3. Statistical decision (Fail to reject the null hypothesis or Reject the null hypothesis)

4. What is the most appropriate description of the findings based on the hypothesis test performed? (multiple choice) A) Modules do not impact standardized Math achievement, B) Modules impact standardized Math achievement, C) Modules are not superior to standard instruction, D) Modules are superior to standard instruction

Answer 1

The ANOVA table

Source of variation	df	SS	MS	F
Between	4-1=3	10	3.333333	4
Within	52-4=48	40	0.833333
Total	13*4-1=51	50

1. From the above ANOVA table , we can see that degrees of freedom for F statistic is

numerator df = 3

denominator df = 48

df = (3,48)

For with df = (3,48) critical value of F is

9= 0,05

Fc = 2.798 ( from F critical value  table)

2. Test statistic

F= MS ( between) / MS (within)

= 3.33/0.83

= 4

3. Since calculated F > 2.798

Reject the null hypothesis

4. Answer is

B) Modulus impact standardised math achievement .