In: Statistics and Probability
ANOVA TEST??
According to a maternity study, does mothers marital satisfaction increase, decrease or stay the same over time?? Use alpha .05.
M1MARSAT |
M2MARSAT |
M3MARSAT |
M4MARSAT |
1.952 |
1.849 |
2.457 |
2.902 |
2.947 |
2.706 |
2.804 |
2.744 |
1.591 |
1.545 |
1.098 |
0.156 |
2.842 |
2.947 |
2.282 |
2.352 |
2.292 |
1.44 |
0.732 |
1.306 |
2.344 |
2.435 |
2.579 |
2.488 |
1.555 |
1.811 |
1.488 |
1.548 |
1.689 |
2.218 |
2.187 |
2.12 |
1.84 |
1.522 |
1.574 |
1.136 |
2.225 |
1.667 |
2.526 |
2.112 |
2.373 |
2.699 |
2.352 |
2.902 |
2.706 |
0.782 |
0.505 |
1.847 |
0.392 |
1.139 |
1.139 |
1.177 |
1.945 |
2.864 |
1.809 |
1.124 |
2.842 |
2.864 |
2.493 |
2.955 |
1.388 |
1.275 |
0.967 |
0.371 |
1.313 |
1.019 |
1.419 |
1.644 |
2.261 |
2.404 |
2.05 |
2.653 |
2.239 |
2.478 |
2.103 |
1.962 |
-1.95 |
0.73 |
-0.074 |
0.024 |
2.488 |
2.397 |
2.299 |
2.737 |
2.12 |
1.433 |
1.789 |
2.105 |
1.9 |
2.533 |
2.17 |
1.667 |
2.639 |
2.856 |
2.895 |
2.842 |
-1.452 |
-0.199 |
1.146 |
-1.964 |
0.943 |
2.646 |
2.632 |
2.127 |
2.653 |
1.591 |
1.237 |
2.45 |
1.297 |
0.739 |
1.938 |
1.538 |
2.05 |
1.371 |
1.486 |
1.756 |
2.646 |
0.907 |
2.579 |
2.684 |
0.397 |
1.604 |
1.199 |
1.122 |
2.383 |
2.022 |
2.172 |
2.014 |
Let's do a 4-sample ANOVA for comparing the means of the 4 samples of data (assumed independent as they're all collected at different times separated by a month).
The hypothesis test is:
H0: All the means are equal, i.e. marital satisfaction stays the same over time
Ha: Marital satisfaction changes over time
Carrying out Single Factor ANOVA in Excel with alpha=0.05 (go to Data tab -> Data Analysis -> Single Factor ANOVA), we get the following output:
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 0.06661652 | 3 | 0.02220551 | 0.02528605 | 0.99453818 | 2.67769903 |
Within Groups | 108.893374 | 124 | 0.87817237 | |||
Total | 108.959991 | 127 |
The p-value of 0.9945 >> 0.01, hence we cannot reject the null hypothesis that the marital satisfaction stays the same over time. Hence, the marital satisfaction stays the same over time at the 0.01 significance level.