1. Review of Basics

2. REVIEW OF BASICS PART I Measurement Descriptive Statistics Frequency Distributions

3. MEASUREMENT CONCEPTS Measured vs. True Scores Statistical Models Measurement Scales

4. Measured Scores Any measured score represents: True underlying score Measurement error Lower measurement error means higher reliability

5. Statistical Models A statistical model is a way to represent the data Outcome i = model i + error i Most statistical methods are based on a linear model outcome i = (slope)x i + y-intercept

6. MEASUREMENT SCALES What assumptions can you make about a score? Many statistics require a certain measurement scale. The measurement scale is a property of the data.

7. 1. Nominal Scale Numbers classify into groups. Math, other than counting, is not meaningful.

8. 2. Ordinal Scale Numbers are rank orders. Math, other than counting, is not meaningful.

9. 3. Interval Scale Numbers represent amounts, with equal intervals between numbers. Math, other than ratio comparisons, is meaningful.

10. 4. Ratio Scale Numbers represent amounts, with equal intervals and a true zero true zero: score of zero represents a complete absence Math, including ratios, is meaningful.

11. Why You Can’t do Ratios on an Interval Scale

12. The Same Temperatures on Another Interval Scale

13. The Same Temperatures on a Ratio Scale (Rankine = F + 459.6)

14. The Same Temperatures on a Ratio Scale (Kelvin = C + 273.15)

15. DESCRIPTIVE STATISTICS Central Tendency Variability Frequency Distributions z-Scores

16. Central Tendency – Typical Score mean: arithmetic average median: middle score mode: most frequent score

17. Variability – Spread of Scores deviation: difference between observed score and model (e.g., mean) sum of squares(SS): sum of squared differences from the mean

18. Variability variance: average squared difference from the mean standard deviation: average unsquared difference from the mean

19. FREQUENCY DISTRIBUTIONS frequency: number of times a score occurs in a distribution frequency distribution: list of scores with the frequency of each score indicated

20. Normal Distributions symmetrical equal mean, median, and mode bell-shaped

21. Why Be Normal? Many variables are affected by many random factors. Effects of random factors tend to balance out.

22. Skewness Extent to which scores are piled more on one end of the distribution than the other positive skew negative skew

23. Skewness Skewness = 0 for a normal distribution Skewness < 0 for a negatively skewed distribution Skewness > 0 for a positively skewed distribution

24. Kurtosis Measure of the steepness of the curve Platykurtic: flat Leptokurtic: steep

25. Kurtosis Kurtosis = 0 for a normal distribution Kurtosis < 0 when the distribution is flatter than a normal Kurtosis > 0 when the distribution is steeper than a normal

26. Take-Home Points Measurement is always open to error Take into account what assumptions you can reasonably make about the data Central tendency and variability go together