Assessing Normality

Definition Normal Probability Plot = a graph that plots observed data versus normal scores. A normal score is the expected z-score of the data value, assuming that the distribution of the random variable is normal.

Drawing a Normal Probability Plot Arrange the data in ascending order Compute , where i is the position in the list and n is the number of observations. Find the z-score corresponding to fi from the Standard Normal Distribution table. Plot the observed values on the horizontal axis and the corresponding expected z-scores on the vertical axis.

Guidelines Reject normality if more than one outlier is present Reject normality if the normal quantile plot does not follow a linear pattern (more or less)

Summary Population is not approximately normal if any of the following are true: Sample contains an outlier Sample exhibits a large degree of skewness Sample is multimodal; in other words, it has more than one distinct mode

Example: Normal Probability Plot

Example: Normal Probability Plot

1. Draw a normal probability plot (By Hand) 30 32.1 35.7 40 43.2 44.5

Normal Quantile Plot (TI-83/84) Enter data in L1 “2nd” button, “y=“ button, “enter” button Enter the following parameters: Choose ON Type: Last One Data: L1 (2nd – 1) Data Axis: x Mark: + “Zoom” button, Choose ZoomStat, “Enter” button

2. Draw a normal probability plot (By TI-83/84) 30 32.1 35.7 40 43.2 44.5

3. Draw a normal probability plot (By TI-83/84) 30 32.7 40 53 500 200