Introduction to Behavioral Statistics Standard Scores, Centiles and some other Odds & Ends

Some Additional Measures of Dispersion (Variability) Coefficient of Variation - A relative measure of dispersion Used to compare distributions with different distributions. Useful for comparing standard deviations of variables that involve different units of measurement. The larger the CV, the larger the dispersion relative to the Mean.

Some Additional Measures of Dispersion (Variability) Index of Dispersion A measure of dispersion of qualitative variables. Based on distinguishability of observations Which one of these things is not like the others? Read over the procedures for doing this on page 124-125 in the Text Book.

Centiles & Test Norms Introduction - Knowing that you received a score of 70 on a test, provides you with no information about how well you did. Knowing Rank Order helps, but there are problems. Knowing the Mean provides still more information. The centile provides an easy means to locate any given score in a distribution of scores and gets around the limitations of rank order.,

Centiles & Test Norms Centiles - Introduction Computation If we know a score falls at the 20th percentile, we know that it is better than 20% of the scores and lower than 80% of the scores. It is the point on the scale of measurement above which 80% of the scores fall and below which 20% of the scores fall. Computation

Centiles & Test Norms A way to give meaning to a score. Makes the distribution rectangular Since the Centile Rank is an Ordinal level measurement, they cannot be averaged. Useful only for group computed on.

Standard Scores A standard score is a raw score expressed in terms of standard deviation units from the mean. This gives us a score which has a mean of 0 (zero) and a SD of 1 (one). We then know how many SDs any given score falls from the Mean. Converting to standard score leaves skewness, kurtosis & rank order unchanged.

Standard Scores Other systems of Standard Scores Navy system has mean of 50 and S.D. of 10 Air Force system has mean=70 and SD=10

Standard Scores Summary of Standard Score Unlike Centile Scores - standard scores can be averaged

Next: Probability & the Normal Curve Press Here to Return to Class Page Next: Probability & the Normal Curve We aren't going to spend a lot of time on this, but there are a few things you should be aware of.