A researcher is interested in the relationship between socio-economic status (SES) and domestic violence. She believes that there is a greater incidence of domestic violence in households below the poverty line. To assess this relationship, she surveys a random sample of American adults and asks two questions. First participants are asked to estimate their household income. Later in the survey participants are asked if there has been any physical violence between members of their household (Yes or No). How could the researcher determine whether there is a relationship between SES and incidence of domestic violence?

#### One-way ANOVA

Possibly correct, but not the best answer.

One-way ANOVA can be used to test hypotheses regarding the equality of means for multiple groups. While it is generally used for three or more groups, it can be applied to two groups as we have here.

A better choice is a test that is designed specifically to compare two group means.

#### Correlation

Possibly correct, but not the best answer.

Correlation is usually used to assess the relationship between two continuous variables. It can be used to measure and test the relationship between a continuous variable and a dichotomous variable, as we have here.

However, another test would generally be the best choice for this example.

#### t-test for independent samples

Correct!

The null hypothesis that there is no difference in household income for households that reported violence and those that didn’t.

The data are from two groups (those who reported domestic violence and those who did not) and we have household income (SES) for everyone. If the null hypothesis is true, the mean SES for these two populations is the same. The t-test for independent groups is appropriate to compare the two groups on SES.

Of course, the first step is to verify that we have reasonably well satisfied the assumptions of normal distributions within each population and equal variances. When reporting findings, it is important to focus on the means and the precision of estimates. This can be done nicely with confidence intervals.

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#### t-test for paired data

Incorrect.

The paired t-test is used when the data are paired scores on a continuous variable, such as SES estimates for each of two spouses in each household. In the current example there is only one measure from each household, so the data are not paired.

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#### The Expert says…

The null hypothesis is that there is no difference in household income for households that reported violence and those that didn’t.

The data come from two groups (those who reported domestic violence and those who did not) and we have household income (SES) for everyone. If the null hypothesis is true, the mean SES for the populations represented by these two samples is the same. The t-test for independent groups is appropriate to compare the two groups on a continuous variable like SES.

Of course, the first step is to verify that the assumptions of normal distributions within each population and equal variances are reasonably well satisfied. When reporting the findings, it is important to focus on the means and the precision of estimates. This can be done nicely with confidence intervals.