Question

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

Answer 1

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

H_a: 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.