Question

The following scores are from an independent-measures study comparing two treatment conditions. (Be sure to include your critical values)

a. Use an independent -measures t-test with a = 0.05 to determine whether there is a significant mean difference between the two treatments.

b. Use an ANOVA with a = 0.05 to determine whether there is a significant mean difference between the two treatments. You should find that F = t2.

Treatment I Treatment II

10	7	n=16
8	4	g=120
7	9	Σx2 = 1036
9	3
13	7
7	6
6	10
12	2

Answer 1

Hypotheses are:

a)

Following is the output of independent sample t test:

Hypothesis Test: Independent Groups (t-test, pooled variance)
	T1	T2
	9.00	6.00	mean
	2.51	2.83	std. dev.
	8	8	n
		14	df
		3.000	difference (T1 - T2)
		7.143	pooled variance
		2.673	pooled std. dev.
		1.336	standard error of difference
		0	hypothesized difference
		2.24	t
		.0414	p-value (two-tailed)
	F-test for equality of variance
		8.00	variance: T2
		6.29	variance: T1
		1.27	F
		.7585	p-value

The p-vaue of t test is; 0.0414

Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that there is a significant mean difference between the two treatments.

Critical values:

Degree of freedom: df=n-1=14

Test is two tailed so critical values of t test using excel function "=TINV(0.05,14)" are: +/- 2.145

Rejection region:

If t < -2.145 or t > 2.145, reject H0

b)

Following is the output of ANOVA:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
T1	8	72	9	6.285714
T2	8	48	6	8
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	36	1	36	5.04	0.041443	4.60011
Within Groups	100	14	7.142857
Total	136	15

The p-value of F test is: 0.0414

Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that there is a significant mean difference between the two treatments.

Here we have F = 5.04 and t = 2.24

t^2 = 2.24*2.24 = 5.0176

That is F = t^2 verified.

Critical values:

Using excel function "=FINV(0.05,1,14)" is: 4.600

Rejection region:

If F > 4.600, reject H0