The Meaning of Test Scores

1. The Meaning of Test Scores Schroeder PSY/SPED 572

2. Background Statistics Scales of Measurement Nominal LD, ED, OHI Ordinal 89, 85, 70, 69, 50 Interval Ratio

3. Describing Data Distributions Graphs of scores used to represent how scores relate to each other Histograms, Frequency Polygons, Curves

4. Histogram

5. Frequency Polygon

6. Curve

7. Homework #1 As a follow-up to the "Everyday Psychometrics" section on graphing data, please bring in graphs published in newspapers or magazines. We will discuss whether the graphs aid in interpreting the data or serve to misrepresent the data.

8. Symbols ? X N f X S2 S Sum Score Number of cases Frequency Mean Variance Standard Deviation

9. Raw Scores Based on number of items answered correctly Provides basis for all other scores (is absolutely necessary) Not used in test interpretation because it depends on number and difficulty of test items

10. Measures of Central Tendency 95, 87, 86, 86, 78, 73 Mean (average) Median (score that cuts distribution in half) Mode (most frequently occurring score) X = ?X / N

11. Measures of Variability 95, 87, 86, 86, 78, 73 Range Highest Score � Lowest Score Quartiles (p. 79) Standard Deviation Get from variance

12. Homework #2 Review the evening newspaper and/or weekly news magazines and look for news articles or advertisements that include references to the statistics discussed in this chapter. Bring in the articles to discuss during the next class session, focusing on the type of statistics utilized and whether the appropriate one was chosen.

13. Skewness Describes how scores are distributed � not bad or abnormal Positive skew Negative skew

14. Question� You are the union negotiator for a company that has a number of very high paid workers who have been with the company for a very long time. You are trying to negotiate for a substantial raise for next year. Which statistic would you want to use to summarize the average salary of your workers, the mean or median? Why?

15. Discuss the types of distributions of data you would expect for the following: a) IQ test scores from all pupils enrolled in Illinois schools b) IQ test scores from all pupils enrolled in Bayonne, New Jersey schools c) test scores from a very difficult test d) a series of 1,000 rolls of the die e) college professors' salaries in an university department in which all of the professors have tenure and have been teaching for more than 20 years e) test scores from a very easy test.

16. Why norms are important� Allow us to compare an individual�s test score to those of others who took the test Norms determine percentiles, standard scores, grade equivalents, etc.

17. Norms Standardization Norm-referenced Sampling

18. Within-Group Norms Age norms (equivalents) Grade norms (equivalents) Percentiles (not Percentage Correct) 86th percentile = ? Standard Scores z-scores t-scores Stanines (p. 88) Deviation IQ

19. Relativity of Test Norms Normative Sample National Anchor Norms Specific Norms Fixed Reference Group

20. Domain-referenced score interpretation Compare individual�s performance to a set standard (or criterion) Best used for testing basic skills, not more complex processes Create specific objectives and probes for those objectives Reports what skills a person has Need to determine cutoff score

21. The Normal Curve Many traits are �normally distributed� in the population See p. 84 for examples Few very extreme, most clustered around average Understanding the normal curve Shows how scores relate to one another Value is in knowing how may cases fall between two scores What psychological traits would you not expect to be normally distributed?

23. What is a good test? Reliability Validity Other considerations

24. Standards activity Standards introduction Identify main points of introduction Standard 11 & Standard 5 Summarize your standard in everyday language and give an example of where it might apply