1 / 19

Chapter 5

Chapter 5. Statistical Concepts: Creating New Scores to Interpret Test Data. Norm-referenced Vs. Criterion Referenced Testing. Norm-referencing Comparing each person’s score to the average score of peer or “norm” group Criterion-Referencing

issac
Download Presentation

Chapter 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 5 Statistical Concepts: Creating New Scores to Interpret Test Data

  2. Norm-referenced Vs. Criterion Referenced Testing • Norm-referencing • Comparing each person’s score to the average score of peer or “norm” group • Criterion-Referencing • Compares test scores to a predetermined value or a set of criterion. • See Table 5.1, p. 83

  3. Derived or Converted Scores • Ways of making sense out of normal curve • Types of derived scores: • percentiles • standard scores • developmental norms

  4. Derived or Converted Scores: Percentiles • The percentage of people falling below the obtained percentile and range from 1 to 99, with 50 being the mean. • Do not to confuse percentile scores with the term “percentage correct.” • See Figure 5.1, p. 85.

  5. Derived or Converted Scores: Standard Scores • Z scores • T scores • Deviation IQs • Stanines • Sten scores • Normal Curve Equivalents (NCE) Scores • College and graduate school entrance exam scores (e.g., SATs, GREs, and ACTs), and • Publisher type scores

  6. Derived or Converted Scores: Developmental Norms • Grade equivalents • Age norms

  7. Determining and Understanding Standard Scores • z scores • A standard score that helps us understand where an individual falls on the normal curve. • Practically speaking, z scores run from -4.0 to plus 4.0 (rarely get a z score that’s higher or lower) • To find a z score: (X – M)/SD

  8. Converting z Scores to Other Types of Scores • Percentiles: Find your z score, then either approximate percentile or look at Appendix D for conversion of z scores to percentiles. • Converting to Standard Scores • 1. Get your z score • 2. Plug your z score into the following conversion formula • z-score (SD of desired score) + mean of desired score

  9. Converting z Scores to Other Types of Standard Scores • Use your conversion formula by plugging in the means and standard deviations for each of the respective standard scores that follow: • T scores (M = 50, SD = 10) used for personality tests mostly. • DIQ scores (M = 100, SD = 15). Mostly used for tests of intelligence. • Stanines (M = 5, SD = 2, round or to nearest whole number). Mostly used for achievement testing.

  10. Converting z Scores to Other Types of Standard Scores • Sten scores (M = 5.5, SD = 2, round to nearest whole number). Used with personality inventories and questionnaires. • NCEs (M of 50, SD of 21.06). Like percentiles in that they basically range from 0 – 100 but evenly distributed. (Percentiles, bunch up around mean). Used for educational tests usually.

  11. Converting z Scores to Standard Scores (Cont’d) • SATs/GREs (M = 500, SD = 100). • ACTs (M = 21, SD = 5) • Publisher Type Scores: Mean and standard deviations arbitrarily set by publisher.

  12. Developmental Norms: Age Comparisons • When you are being compared to others at your same age. • Often done for physical attributes: • My 10 year old weighs 78 lbs, what percentile is she as compared to others her age • Can use z scores to determine: • E.g., [78 – 80 (mean)]/8 (SD) = -.25 z or a percentile of about 40 (p = 40).

  13. Developmental Norms: Grade Equivalents • Grade Equivalents: Compares the child’s score to his or her grade level. • E.g., Child in 5.6 grade and gets at mean compared to peer group. GE = 5.6 • GE over 5.6 means that he or she is doing better than his or her peer group • GE below 5.6 means that he or she is doing worse than his or her peer group • Usually, not a statement about how much better or how much worse (a child who is in 5.6 and gets GE of 7.5 is not necessarily at 7.5 grade level).

  14. Rule Number 3:z Scores Are Golden • z scores help us see where an individual’s raw score falls on a normal curve and are helpful for converting a raw score to other kinds of derived scores. That is why we like to keep in mind that z scores are golden and can often be used to help us understand the meaning of scores.

  15. Standard Error of Measurement • Based on reliability of test • Tells you how much error there is in the test and ultimately how much any individual’s score might fluctuate do to this error. • Formula = SEM = SD 1 – r • Multiply the standard deviation of the score you are using (e.g., for T score, SD = 10, for DIQ SD = 15) times the square root of 1 minus the reliability of the test. • Work practice problem, Box 5.5, p. 98.

  16. Rule Number 4: Don’t Mix Apples and Oranges • As you practice various formulas in class, it’s easy to use the wrong raw score, mean or standard deviation. • In determining the SEM for Latisha (p. 95), we used Latisha’s DIQ score of 120 and figured out the SEM using the DIQ standard deviation of 15. • However, if we had been asked to figure out the SEM of her raw score, we would use her raw score and the standard deviation of raw scores. • Whenever asked to figure out a problem, remember to use the correct set of numbers (don’t mix apples and oranges), otherwise your answer will be incorrect.

  17. Scales of Measurement • In assessment, we measure characteristics in quantifiable terms: but “quantifiable” can be defined differently • E.g., gender is measured as either male or female • E.g. achievement can be measured on a scale that has a large range of scores • Four different scales of measurement help us define “quantifiable” • Type of scale you use helps to determine type of instrument that is used to measure what you are measuring.

  18. Scales of Measurement • Four scales to identify how to measure a quality include: • 1. Nominal scale. Numbers are arbitrarily assigned to represent different categories. E.g., race might be: • = Asian • = Latino • = African American • = Caucasian, etc. • 2. Ordinal scale. Magnitude or rank order is implied. E.g., Rating scale: “The counseling I received was helpful in obtaining the goals I came in for.” • = Strongly Disagree • = Somewhat Agree • = Neutral • = Somewhat Agree • = Strongly Agree

  19. Scales of Measurement • 3. Interval scale. Establishes equal distances between measurements but has no absolute zero reference point. • E.g., A 600 on the GRE is better than a 550 but not twice as better as a 300. • 4. Ratio scale. has a meaningful zero point and equal intervals. • If I weigh 200, I weigh twice as much as someone who weighs 100.

More Related