Homework SourseThe following data summarize the results from an independent
The following data summarize the results from an independent-measure study by comparing three treatments conditions.
N=12
G=48
Calculate the sample variance for each of the thee samples(Fill in the blanks)
Variance for sample I=______
Variance for sample II=_______
Variance for sample III=________
Complete the ANOVA table using two decimal places for sum of squares,mean squares, and F.(Fill in the blanks)
Multiple Choice:
A)Fail to reject the null hypotheis. There are significant differences among the three treatments
B)Fail to rejest the null hypothesis.There are no significant differences among the three treatments
C)Reject the null hypothesis.There are no significant differences among the three treatments.
D) Reject the null hypothesis. There are significant differences among the three treatments.
| I | II | III |
|---|---|---|
| 4 | 3 | 8 |
| 3 | 1 | 4 |
| 5 | 3 | 6 |
| 4 | 1 | 6 |
| M=4 | M=2 | M=6 |
| T=16 | T=8 | T=24 |
| SS=2 | SS=4 | SS=8 |
Solution
Variance for sample I=__0.667____
Variance for sample II=__1.333_____
Variance for sample III=__2.667__
H0: All the Treatment means are equal
H1: All the treatment means are not equal
alpha is 5%
ANOVA TABLE
COncluison: P value=0.004 and alpha=0.05
P < alpha, we reject the null hypothesis.
| Anova: Single Factor | ||||||
| SUMMARY | ||||||
| Groups | Count | Sum | Average | Variance | ||
| I | 4 | 16 | 4 | 0.666667 | ||
| II | 4 | 8 | 2 | 1.333333 | ||
| III | 4 | 24 | 6 | 2.666667 | ||
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 32 | 2 | 16 | 10.28571 | 0.004733 | 4.256495 |
| Within Groups | 14 | 9 | 1.555556 | |||
| Total | 46 | 11 |
