A psychologist wants to investigate the relationship between stress and mental health during the first year of college. The researcher developed scales that measure 1) the frequency of stressful events, 2) the perceived importance of these events, 3) the desirability of such events, and 4) the impact of these events of the student. The researcher had 150 first year college students fill out this questionnaire as well as a Symptom Checklist, which is designed to assess the presence or absence of psychological disorders. What statistical procedure would help this researcher discover if psychological disorders can be predicted from the different aspects of stress that have been measured?

#### Multiple Regression

Correct.

The null hypothesis is that mental health cannot be predicted by the three measures of stress.

Multiple regression analysis can be used to derive an equation to predict scores on one variable (e.g., mental health) based on scores on one or more variables (e.g., three mental health scales).

Of course, we should verify that assumptions of the analysis have been met, including normal distributions of errors around the regression model with equal variances for all values of the predictor. The model may not be appropriate for nonlinear relationships. The multiple correlation is a measure of the effect size.

#### One-way ANOVA

Incorrect.

One-way ANOVA can be used to test hypotheses regarding the equality of means for three or more groups. One-way ANOVA is appropriate for research situations in which we have one continuous DV and three or more categorical levels of a single independent variable.

#### Chi-square test of independence

Incorrect.

Chi-square is used to assess relationships between categorical variables using frequency counts (e.g., number of ‘yes’ responses vs. ‘no’ responses).

In this example we have continuous variables, not categorical variables.

#### Correlation (r)

Incorrect.

Correlation can be used to measure the relationship between two continuous measures. Here we are interested in predicting one continuous measure using three other continuous measures.

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#### The Expert says…

We are interested in testing whether the three measures of stress together can predict the measure of mental health. To test whether one variable can predict another variable, we could use simple regression. With more than one predictor, we can use multiple regression.

The statistical test requires the assumptions that residuals from the model are normally distributed with equal variance for all values of the predictors. The model does not describe relationships well if the relationships are nonlinear.

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