611 – Using Data Sets, Technology, and Activities to Teach Statistics
Developing a Test of Normality in the Classroom
Robert Jernigan
American University
Many basic statistics textbooks assess normality with QQ plots with this advice: a quantile plot close to a straight line, indicates normality. But “how close to a straight line� is not addressed. As a review of hypothesis testing in a second semester undergrad course in statistics, we develop, in class, the test of normality due to Filliben (1975), using the correlation coefficient of the QQ plot. The development starts with the data set of MacDonald and Schwing (1973) demonstrating a variety of histogram and QQ plot shapes. First, students classify histograms and QQ plots based on their intuition of normality as requiring symmetric and bell-shaped histograms or a straight line QQ plot. Next, they examine the correlation coefficients of the QQ plots to determine how low a correlation best matches their intuition of normal or not. Then, students randomly generate samples from the standard normal distribution and calculate the QQ plot correlation to generate its sampling distribution. For these data their intuition about normality closely matches both their simulated lower percentage points and the more extensive simulations of Filliben (1975). The importance of looking at the data, an analyst’s intuition and experience in modeling, sampling distributions, hypothesis testing, power, QQ plots, and correlation are all reviewed and reinforced.
