1. EPE/EDP 557 Key Concepts / Terms –Empirical vs. Normative Questions Empirical Questions Normative Questions –Statistics Descriptive Statistics Inferential Statistics –Populations & Samples Population –Parameter Sample –Statistic –Hypothesis: statement positing a relationship among variables Null-hypothesis Research-hypothesis (or working hypothesis)

2. EPE/EDP 557 Key Concepts / Terms –Variable: concept, characteristic, or state of being that can vary from one observation to another Nominal: attributes Ordinal: ranks or orders Interval: consistent numeric scale with arbitrary zero Ratio: consistent numeric scale with meaningful zero –Distribution: arrangement/listing of a set of scores in order of magnitude –Frequency Distribution: listing of achieved scores in order of magnitude & corresponding listing of the number of occurrences of each score

3. EPE/EDP 557 Distribution 100 90 80 70 60 50 Frequency Distribution Xf 1001 902 801 703 601 502

4. EPE/EDP 557 Central Tendency –Mean ( M): simple average e.g. 3, 4, 4, 5, 9 ΣX = 3 + 4 + 4 + 5 + 9 = 25 N = 5 25 ÷ 5 = 5 –Median (Mdn.): middle score If N is odd, use middle score If N is even, take average of 2 middle scores –Mode (Mo.): most frequent score(s)

5. EPE/EDP 557 Central Tendency –Skewed Distribution: distribution unbalanced by extreme scores in one direction

6. EPE/EDP 557 Central Tendency –Skewed Distribution:

7. EPE/EDP 557 Bar Graphs, Histograms, & Frequency Polygons –Bar Graph:

8. EPE/EDP 557 Bar Graphs, Histograms, & Frequency Polygons –Histogram:

9. EPE/EDP 557 Bar Graphs, Histograms, & Frequency Polygons –Frequency Polygon:

10. EPE/EDP 557 Variability: –describe the degree to which scores are spread out / dispersed –provide information about how scores differ (vary) –3 major measures of variability: Range (R) Variance (V) Standard Deviation (SD)

11. EPE/EDP 557 Measures of Variability: –Range: Simplest measure of variability Range = highest score – lowest score Fractiles: –Used to locate specific points in a distribution –Not actual measures of variability, but…

12. EPE/EDP 557 Measures of Variability: –Standard Deviation: The “Heart & Soul” of the concept of variability Provides information on the average deviation of scores from the mean in a distribution Sample Standard Deviation: or

13. EPE/EDP 557 SD Deviation Method

14. EPE/EDP 557 SD Computational Method

15. EPE/EDP 557 Variability (Dispersion) –Variance: Provides information on how far all of the scores in a distribution deviate from the mean

16. EPE/EDP 557 Variability: –Kurtosis: the degree of curvature of a unimodal distribution of scores Flat = Platykurtic (below left) Peaked = Leptokurtic (below right)