1. 1 Outline 1. Why do we need statistics? 2. Descriptive statistics 3. Inferential statistics 4. Measurement scales 5. Frequency distributions 6. Z scores 7. The standard normal distribution 8. Norms

2. 2 Why do we need statistics?  Every test result is a product of both random influences and systematic influences  Statistical analysis helps us separate these two types of influence on behavior

3. 3 Why do we need statistics?  Basic idea of measurement theory: O = T + e  “Observed score = True score + error” T = systematic part of a score e = random error of measurement

4. 4 Why do we need statistics?  Consider example on next two slides  S1, S2, etc = systematic influences on Jamie’s score  R1, R2, etc = random influences

5. 5 Why do we need statistics?  S1 = IQ (120)  S2 = 10 hours studying  S3 = Motivation is high  R1 = Disturbed while studying text pages 180-184  R2 = Friend buys Jamie coffee before exam

6. S3 S2 S1 R1 R2 Observed Score % Observed score reflects a variety of influences: O = T + e

7. 7 Descriptive Statistics  Measures of central tendency  Mean – arithmetic average  Median – score with half of observations above and half below  Mode – most frequent score

8. 8 Descriptive Statistics  Measures of central tendency  Measures of variability  Range  Variance & standard deviation  Standard error of measurement

9. Inferential Statistics Population Sample Drawing a sample Making an inference

10. 10 Measurement scales A. Nominal Labels; not really numbers B. Ordinal Ranks C. Interval Equal intervals; no true zero D. Ratio Equal intervals; true zero

11. 11 Frequency distributions  A frequency distribution is a graph  It shows how often scores fall in various ranges  X-axis = scores on some dimension  Y-axis = frequency of those scores in a given data set

12. 12 Frequency distributions  The “Normal Curve” is a frequency distribution  Average scores are most common  Curve is symmetric

13. 13 Z scores  The Z score measures distance between a given score and the mean Z = x – X s

14. µ Z = 1.0 34.13% of scores fall in this region Area under the curve gives probability of obtaining a score in that region (see Z table)

15. 15 Norms  Z score is a measure of relative standing  How does one person do relative to the group they belong to?  Norms are also comparative scores  Express test performance in terms of a defined group or a defined capability

16. 16 Norms  Age-referenced norms reference group is defined by age compare one person to others  Criterion- referenced norms describes skills, tasks, knowledge a test-taker possesses not used to compare test- takers