Stats Help Here is the data time group 472 1 22 1 204 1 197

Stats Help!! (Here is the data)

time/ group
47.2 1
22 1
20.4 1
19.7 1
17.4 1
14.7 1
13.4 1
13 1
12.3 1
12.2 1
10.3 1
9.7 1
9.7 1
9.5 1
9.1 1
8.9 1
8.9 1
8.4 1
8.1 1
7.9 1
7.8 1
6.9 1
6.3 1
6.1 1
5.6 1

4.7 1

4.7 1

4.3 1
4.2 1
3.9 1
3.4 1
3.1 1
3.1 1
2.7 1
2.4 1
2.3 1
2.3 1
2.1 1
2.1 1
2 1
1.9 1
1.7 1
1.7 1
19.7 2
16.2 2
15.9 2
15.4 2
9.7 2
8.9 2
8.6 2
8.6 2
7.4 2
6.3 2
6.1 2
6 2
6 2
5.9 2
4.9 2
4.6 2
3.8 2
3.6 2
3.5 2
3.3 2
3.3 2
2.9 2
2.8 2
2.7 2
2.4 2
2.3 2
2 2
1.8 2
1.7 2
1.7 2
1.6 2
1.4 2
1.2 2
1.1 2
1 2

Question!

In theory, the ANOVA F-test can be used when there are only two samples if thenormality and homoscedasticity assumptions are met. However, it’s better to use Welch’st-test because it has weaker assumptions (e.g. variances may be dierent) while the F-test issensitive to violations of its assumptions when there are only two samples.
Recall for the untransformed stereogram data on Canvas (stereograms.txt in the Datafolder of FIles):

> stereograms = read.table(file.choose(), header=TRUE)

> treatment = stereograms$time[stereograms$group==2]

> control = stereograms$time[stereograms$group==1]

> t.test(treatment, control)

Welch Two Sample t-test
data: treatment and controlt = -2.0384, df = 70.039, p-value = 0.04529alternative hypothesis: true difference in means is not equal to 0
> t.test(treatment, control, var.equal=T)Two Sample t-testdata: treatment and control
t = -1.9395, df = 76, p-value = 0.05615alternative hypothesis: true difference in means is not equal to 0

1

So Welch’s test gives a P-value of 0.04529, while Student’s test gives a P-value of 0.05615.
Find a P-value for the F-test of the null hypothesis that the treatment and control populationshave the same mean. How does this compare to the Welch and Student P-values?

Solution

Sol)

Null hypothesis: All the means are equal

Alternative hypothesis: All the means are not equal

Test Statistics:

Using SPSS

Conclusion: F cal=3.762 and P value=0.056

and alpha=0.05

P value > alpha, we accept the null hypothesis.