Assessing Normality Definition Normal Probability Plot a graph

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 1. Arrange the data in ascending order 2. Compute , where i is the position in the list and n is the number of observations. 3. Find the z-score corresponding to fi from the Standard Normal Distribution table. 4. 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)

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) 1. Enter data in L 1 2. “ 2 nd” button, “y=“ button, “enter” button 3. Enter the following parameters: Choose ON Type: Last One Data: L 1 (2 nd – 1) Data Axis: x Mark: + “Zoom” button, Choose Zoom. Stat, “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