Types of Scores & Types of Standard Scores

A requirement in MAED(Guidance & Counseling): Psychological Testing

1. TYPES OF SCORES MR. CRISALDO H. CORDURA TYPES OF STANDARD SCORES

2. WHAT IS A TEST SCORE? A test score is a piece of information, usually a number, that conveys the performance of an examinee on a test . One formal definition is that it is "a summary of the evidence contained in an examinee's responses to the items of a test that are related to the construct or constructs being measured."

3. Types of scores Raw Scores Percentage Scores Derived Scores Developmental Scores Scores of Relative Standing

4. WHAT IS A RAW SCORE? The raw score is the number of items a student answers correctly without adjustment for guessing. For example, if there are 15 problems on an arithmetic test, and a student answers 11 correctly, then the raw score is 11. Raw scores, however, do not provide us with enough information to describe student performance.

5. Percentage Scores A percentage score is the percent of test items answered correctly. These scores can be useful when describing a student's performance on a teacher-made test or on a criterion-referenced test. However, percentage scores have a major disadvantage: We have no way of comparing the percentage correct on one test with the percentage correct on another test. Suppose a child earned a score of 85 percent correct on one test and 55 percent correct on another test. The interpretation of the score is related to the difficulty level of the test items on each test. Because each test has a different or unique level of difficulty, we have no common way to interpret these scores; there is no frame of reference.

6. Derived Scores Derived scores are a family of scores that allow us to make comparisons between test scores. Raw scores are transformed to derived scores. Developmental scores and scores of relative standing are two types of derived scores. Scores of relative standing include percentiles, standard scores, and stanines.

7. Developmental Scores Sometimes called age and grade equivalents, developmental scores are scores that have been transformed from raw scores and reflect the average performance at age and grade levels. Thus, the student's raw score (number of items correct) is the same as the average raw score for students of a specific age or grade. Age equivalents are written with a hyphen between years and months (e.g., 12–4 means that the age equivalent is 12 years, 4 months old). A decimal point is used between the grade and month in grade equivalents (e.g., 1.2 is the first grade, second month).

8. Scores of Relative Standing Percentile Ranks   A percentile rank is the point in a distribution at or below which the scores of a given percentage of students fall. Percentiles provide information about the relative standing of students when compared with the standardization sample. Look at the following test scores and their corresponding percentile ranks.

9. Standard Scores   

10. What is a Standard Score? Standard score is the name given to a group or category of scores. Each specific type of standard score within this group has the same mean and the same standard deviation.

11. The different types of Standard Scores: Z-Scores T-Scores Deviation IQ Scores Normal Curves Equivalents Stanines Percentile Ranks

12. Z-Scores Have a mean of 0 and a standard deviation of 1.

13. Calculating Z-Scores z = – Example: raw score = 31, mean =27, S = 6. z = = 4/6 or .67   Interpretation The person scored .67 standard deviations above the mean .

14. How to Identify Z-Scores? Positive and Negative Z-Scores Some z-scores will be positive whereas others will be negative. If a z-score is positive, its’ corresponding raw score is above (greater than) the mean. If a z-score is negative, its’ corresponding raw score is below (less than) the mean. http://statistics-help-for-students.com/How_do_I_interpret_Z_score_data_in_SPSS.htm#.W1I4vbgRXIU

15. T-Scores A t score is one form of a standardized test statistic (the other you’ll come across in elementary statistics is the z-score ). The t score formula enables you to take an individual score and transform it into a standardized form>one which helps you to compare scores. http://www.statisticshowto.com/probability-and-statistics/t-distribution/t-score-formula/ have a mean of 50 and a standard deviation of 10 .

16. Formula for T-Scores: If you have only one item in your sample , the square root in the denominator becomes √1. This means the formula becomes:

17. Sample question: A law school claims it’s graduates earn an average of $300 per hour. A sample of 15 graduates is selected and found to have a mean salary of $280 with a sample standard deviation of $50. Assuming the school’s claim is true, what is the probability that the mean salary of graduates will be no more than $280?

18. Step 1: Plug the information into the formula and solve: x̄ = sample mean = 280 μ = population mean = 300 s = sample standard deviation = 50 n = sample size = 15

19. t = (280 – 300)/ (50/√15) = -20 / 12.909945 = -1.549. Step 2: Subtract 1 from the sample size to get the degrees of freedom: 15 – 1 = 14. The degrees of freedom lets you know which form of the t distribution to use (there are many, but you can solve these problems without knowing that fact!).

20. Step 3: Use a calculator to find the probability using your degrees of freedom (8). You have several options, including the TI-83 (see How to find a t distribution on a TI 83 ) and this online calculator . Here’s the result from that calculator. Note that I selected the radio button under the left tail, as we’re looking for a result that’s no more than $280: https://surfstat.anu.edu.au/surfstat-home/tables/t.php

21. Converting Z-score to T-score http://www.statisticshowto.com/probability-and-statistics/t-distribution/t-score-formula/

22. Deviation IQ scores: have a mean of 100 and a standard deviation of 15 or 16.

23. Deviation IQ scores are frequently used to report the performance of students on norm-referenced standardized tests. The deviation scores of the Wechsler Intelligence Scale for Children–III and the Wechsler Individual Achievement Test–II have a mean of 100 and a standard deviation of 15, while the Stanford-Binet Intelligence Scale–IV has a mean of 100 and a standard deviation of 16. Many test manuals provide tables that allow conversion of raw scores to deviation IQ scores.

24. Normal curve equivalents: Have a mean of 50 and a standard deviation of 21.06.

25. Normal curve equivalents (NCEs) a type of standard score with a mean of 50 and a standard deviation of 21.06. When the baseline of the normal curve is divided into 99 equal units, the percentile ranks of 1, 50, and 99 are the same as NCE units (Lyman, 1986). One test that does report NCEs is the Developmental Inventory-2.However, NCEs are not reported for some tests.

26. Stanines Standard score bands divide a distribution of scores into nine parts.

27. Stanines are bands of standard scores that have a mean of 5 and a standard deviation of 2. Stanines range from 1 to 9. Despite their relative ease of interpretation, stanines have several disadvantages. A change in just a few raw score points can move a student from one stanine to another. Also, because stanines are a general way of interpreting test performance, caution is necessary when making classification and placement decisions. As an aid in interpreting stanines, evaluators can assign descriptors to each of the 9 values:

28. 9—very superior 8—superior 7—very good 6—good 5—average 4—below average 3—considerably below average 2—poor 1—very poor

29. Percentile ranks Point in a distribution at or below which the scores of a given percentage of students fall.

30. References: Excerpt from Assessment of Children & Youth with Special Needs, by L.G. Cohen, L.J. Spenciner , 2007 edition, p. 57-62 http://www.statisticshowto.com/probability-and-statistics/t-distribution/t-score-formula/ https://surfstat.anu.edu.au/surfstat-home/tables/t.php