Another study investigates whether there is a linear relationship between sugar consumption and hyperactivity scores. Which test would be used?

Another study investigates whether there is a linear relationship between sugar consumption and hyperactivity scores. Which test would be used?

• A. 2-proportion z-test
• B. Chi-square goodness of fit
• C. Paired t-test
• D. Linear regression t-test

Answer: (D)

Testing for a linear relationship between two continuous variables is done with linear regression. Here, sugar consumption is the predictor and hyperactivity scores are the outcome. In simple linear regression, you estimate a slope that shows how much the hyperactivity score changes for each unit increase in sugar. The statistical test to determine if that slope is different from zero is a t-test on the regression coefficient. If the slope is significantly different from zero, there’s evidence of a linear association between sugar intake and hyperactivity. The other tests don’t fit this question: they’re for different situations (comparing proportions, checking distribution fit, or comparing means of paired measurements) and wouldn’t assess a relationship between two continuous variables.

Testing for a linear relationship between two continuous variables is done with linear regression. Here, sugar consumption is the predictor and hyperactivity scores are the outcome. In simple linear regression, you estimate a slope that shows how much the hyperactivity score changes for each unit increase in sugar. The statistical test to determine if that slope is different from zero is a t-test on the regression coefficient. If the slope is significantly different from zero, there’s evidence of a linear association between sugar intake and hyperactivity. The other tests don’t fit this question: they’re for different situations (comparing proportions, checking distribution fit, or comparing means of paired measurements) and wouldn’t assess a relationship between two continuous variables.