Testing for the Significance of b

Inferential Regression Analysis: Testing for the Significance of b

The most common use of regression analysis in criminal justice and criminology research is in the context of hypothesis testing. Just like the correlation coefficient r , the slope coefficient b does not itself determine whether the null hypothesis should be rejected. The slope coefficient b is also unstandardized. This means that it is presented in the DVs’ original units. This makes it impossible to figure out whether b is “large” or “small.” The measurement of the DV can have a dramatic impact on the slope coefficient. For instance, if a researcher trying to predict the length of prison sentences imposed on people convicted of burglary measures the DV (“sentence length”) in days and finds that gender (male or female) has a slope of b = 10, then the average difference between male and female offenders is only 10 days. By comparison, if sentence length is measured in months, and the researcher finds b = 5, then even though this slope is half the size of the previous one, the real-world meaning is substantial. A slope of b = 5 means there is a 5-month difference between men and women. This is a big discrepancy!

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We will first discuss the procedure for determining whether b is statistically significant. If it is not, there is no point converting it to a standardized metric. If it is, then a researcher would take the next step of standardizing it. To figure out whether b is significant, a five-step hypothesis test must be conducted. We will conduct this test on the b from above using ⍺ = .05.