Question

The following data were collected from a repeated-measures study:

Determine if there are any significant differences among the four treatments. Use a .05 level of significance.

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.

	Participant	Treatments
		A	B	C	D
∑X2 = 332 G = 60	1 2 3 4	6 4 4 10	3 4 2 7	3 2 0 7	0 2 2 4
		T = 24 SS = 24	T = 16 SS = 14	T = 12 SS = 26	T = 8 SS = 8

Answer 1

1)

Ho: µ1=µ2=µ3=µ4
H1: not all means are equal

2)

treatment	A	B	C	D
count, ni =	4	4	4	4
mean , x̅ i =	6.000	4.00	3.00	2.00
std. dev., si =	2.828	2.160	2.944	1.633
sample variances, si^2 =	8.000	4.667	8.667	2.667
total sum	24	16	12	8	60	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				3.75
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	5.063	0.063	0.563	3.063
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	20.250	0.250	2.250	12.250	35
SS(within ) = SSW = Σ(n-1)s² =	24.000	14.000	26.000	8.000	72.000

no. of treatment , k =   4
df between = k-1 =    3
N = Σn =   16
df within = N-k =   12
  
mean square between groups , MSB = SSB/k-1 =    11.6667
  
mean square within groups , MSW = SSW/N-k =    6.0000
  
F-stat = MSB/MSW =    1.9444
P value =   0.1763

3)

p-value>α , do not reject null hypothesis

4)

there is no significant difference among means of different treatment F(3,12) = 1.94,p>0.10

5) there is no steps will be taken forward because null hypothesis is not rejected