The Normal Curve Z Scores, T Scores, and Skewness

The Normal Curve We learned how to calculate the SD –But what does it mean? We understand more about the SD once we understand the normal curve

Z Scores Z score - raw score expressed in standard deviation units If we know the mean and SD we can calculate the Z score

Z Scores and the Percentage of Area Under the Curve Percentage of area under curve between mean and any Z score is known and constant

Converting Z Scores to Percentile Scores Using table A we can determine the percentile value of the raw score from the Z score Standard scores

Areas Under the Normal Curve What if we want to know the area between 2 scores? Take Z scores for each Determine area below each Z score –p 1 -p 2

T Scores Standard score Typically used in education settings Mean = 50; SD =10 T=10z+50 Created for general population –Not used much in statistical analysis

Calculating Skewness Skewness - measure of bilateral symmetry of the data Use Z scores to determine distribution of raw scores around the mean –Z = normal curve –Z 3 - (+) = positive skew –Z 3 - (-) = negative skew