Question

 

N =16 G = 120 ΣX² = 1036

The following scores are from an independent-measure study comparing two treatment conditions.

Treatment
I	II
10	7
8	4
7	9
9	3
13	7
7	6
6	10
12	2

1. Use an independent-measures t test with α = .05 to determine whether there is a significant mean difference between the two treatments. 
2. Use an ANOVA with α = .05 to determine whether there is a significant mean difference between the two treatments. 

Answer 1

First we need t find the mean and SD of both treatments. Following table shows the calculations:

	Treatment 1, X1	(X1-mean)^2	Treatment 2, X2	(X2-mean)^2
	10	1	7	1
	8	1	4	4
	7	4	9	9
	9	0	3	9
	13	16	7	1
	7	4	6	0
	6	9	10	16
	12	9	2	16
Total	72	44	48	56

Sample size

Mean:

Standard deviation:

(a)

Conclusion: We can conclude that at 5% level of significance,there is a significant mean difference between the two treatments.

(b)

First be need to find grand mean so

Let   shows the mean of the ith group. So

and

Therefore

----

Since there are 2 different groups so we have k=2. Therefore degree of freedoms are:

-------------

Now

F test statistics is

The p-value is 0.0414.

Since p-value is less than 0.05 so we reject the null hypothesis.

Conclusion: We can conclude that at 5% level of significance,there is a significant mean difference between the two treatments.