1. Assessing Normality

2. 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.

3. 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.

4. 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)

5. 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

6. Example: Normal Probability Plot

7. Example: Normal Probability Plot

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

9. 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

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

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