A marriage counselor conducted a study of couples, categorizing each of the couples as "communicative" or "non-communicative." Among other things, the counselor wanted to see whether the percentage of communicative couples whose marriage ended in separation or divorce was the same as the percentage of non-communicative couples whose marriage ended in separation or divorce. Which hypothesis test would be most appropriate for this study?
Test of two proportions
To determine which hypothesis test would be most appropriate for this study, we need to consider the characteristics of the study design and the type of data being analyzed.
In this case, the marriage counselor wants to compare the percentage of communicative couples whose marriage ended in separation or divorce to the percentage of non-communicative couples whose marriage ended in separation or divorce. The counselor is interested in determining whether these percentages are the same or different.
Since we are examining categorical data (i.e., whether the marriages ended in separation or divorce), the most appropriate hypothesis test would be the chi-square test for independence. This test is used to analyze associations between two categorical variables.
The null hypothesis for this study would assume that there is no association between couple communication (communicative vs. non-communicative) and marriage outcome (separation or divorce). The alternative hypothesis would suggest that there is an association between these variables.
To perform the chi-square test for independence, you would need to construct a contingency table that includes the counts or frequencies of communicative and non-communicative couples whose marriages ended in separation or divorce. From this table, you would calculate the expected cell frequencies under the assumption of independence, and then calculate the chi-square test statistic.
Finally, you would compare the calculated chi-square test statistic to the critical value from the chi-square distribution or calculate the p-value associated with the test statistic. If the p-value is less than the chosen significance level (e.g., 0.05), you would reject the null hypothesis and conclude that there is evidence of an association between couple communication and marriage outcome.
In summary, the most appropriate hypothesis test for this study would be the chi-square test for independence, which can determine if there is an association between communication style and the marriage outcome.