Question

It is common wisdom that death of a spouse can lead to health deterioration of the partner left behind. Is common wisdom right or wrong in this case? To investigate, Maddison and Viola (1968) measured the degree of health deterioration of 132 widows in the Boston area, all of whose husbands had died at the age of 45-60 within a fixed six-month period before the study. A total of 28 of the 132 widows had experienced a marked deterioration in health, 47 had seen a moderate deterioration, and 57 had seen no deterioration in health.Of 98 control women with similar characteristics who had not lost their husbands, 7 saw a marked deterioration in health over the same time period, 31 experienced a moderate deterioration of health, and 60 saw no deterioration.

1) Is this study observational or experimental?

2) State the null and alternative hypothesis

3) Which appropriate statistical test would be done for this experiment? Contingency analysis, t-test or goodness of fit?

Answer 1

Solution:-

1)

The study is observational.

2)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: The null hypothesis states that the proportion of deteriorated health in women with spouse died is identical to the proportion of deteriorated health in women with spouse.

Alternative hypothesis: At least one of the null hypothesis statements is false.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for homogeneity.

3)

Analyze sample data. Applying the chi-square test for homogeneity to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1)
D.F = 2
E_r,c = (n_r * n_c) / n

Χ² = 11.0

where DF is the degrees of freedom, r is the number of populations, c is the number of levels of the categorical variable, n_r is the number of observations from population r, n_c is the number of observations from level c of the categorical variable, n is the number of observations in the sample, E_r,c is the expected frequency count in population r for level c, and O_r,c is the observed frequency count in population r for level c.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 11.00.

We use the Chi-Square Distribution Calculator to find P(Χ² > 11) = 0.011.

Interpret results. Since the P-value (0.011) is less than the significance level (0.05), we reject the null hypothesis.