Question

A psychologist would like to examine the effects of different teaching strategies on the final performance of 6^th grade students. One group is taught using material presented in class along with outdoor discovery, one group is taught using material taught in class alone, and the third group is taught using only the outdoor discovery method. At the end of the year, the psychologist interviews each student to get a measure of the student’s overall knowledge of the material.

Use an analysis of variance with α = .05 to determine whether these data indicate any significant mean differences among the treatments (teaching strategies). Remember to 1) State the null hypothesis, 2) Show all of your calculations, 3) Make a decision about your null hypothesis, 4) Make a conclusion including an APA format summary of your findings (include a measure of effect size if necessary), and 5) Indicate what you would do next given your findings.

In Class & Outdoor	In Class Only	Outdoor Only
4	1	0
6	4	2	G = 43
3	5	0	ƩX2 = 193
7	2	2
5	2	0
T = 25	T = 14	T = 4
SS = 10	SS = 10.8	SS = 4.8

Answer 1

a)

Ho: µ1=µ2=µ3
H1: not all means are equal

2)

treatment	In Class & Outdoor	In Class Only	Outdoor Only
count, ni =	5	5	5
mean , x̅ i =	5.000	2.80	0.80
std. dev., si =	1.581	1.643	1.095
sample variances, si^2 =	2.500	2.700	1.200
total sum	25	14	4		43	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				2.87
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	4.551	0.004	4.271
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	22.756	0.022	21.356		44.13333
SS(within ) = SSW = Σ(n-1)s² =	10.000	10.800	4.800		25.600

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   15
df within = N-k =   12
  
mean square between groups , MSB = SSB/k-1 =    22.0667
  
mean square within groups , MSW = SSW/N-k =    2.1333
  
F-stat = MSB/MSW =    10.3438
P value =   0.0024

3)

p-value<α , reject null hypothesis

4)

conclusion: conclude that data indicate any significant mean differences among the treatments….......

5) next step is to determine which means are significantly different by doing pairwise comparison using post hoc test