Interpreting Test Scores
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The document discusses standard deviation tests and the interpretation of test scores relative to means and standard deviations. It explains the calculation of standard score metrics such as z-scores and stanine scores, along with their significance in educational assessments. Additionally, it emphasizes the importance of understanding the limitations and precision of standard score scales in evaluating student performance.
Interpreting Test Scores
- 1. ELTON JOHN B. EMBODO
- 2. Scores Standard Deviation Test 1: 8, 12, 14, 14, 16, 20 4.0 Test 2: 14, 16, 17, 17, 18, 20 2.0 Test 3: 20, 18, 17, 17, 16, 14 2.0 Test 4: 22, 20, 19, 19, 18, 16 2.0 Test 5: 44, 40, 38, 38, 36, 32 4.0
- 3. 68% ----- if the score falls either 1 standard deviation below the mean or 1 standard above the mean. 96%------if the scores falls either 2 standard deviation below the mean or 2 standard deviation above the mean. Almost 100%----if the score falls 3 standard deviation below the mean or 3 standard deviation above the mean.
- 4. If normally distributed test scores have a mean equal to 70 and a standard deviation equal to 10, what percentage of the their scores will be between? 1. 60 to 80 68% 2. 50 and 90 96% 3. 40 and 100? Almost 100%
- 5. Two students got scores 24 and 32 respectively and the mean and standard deviation of the obtained scores are 20.0 and 4.0 respectively. How many standard deviation units that the scores 24 and 32 fall from the mean score? Answer: 1 and 3 respectively. 32 is virtually above the all the scores on the test.
- 6. A student earned 12 out 20 points on a first test and 15 out 20 points on a second exam. Relative to the performance to the other students taking these tests, on which test did this student do best? Mean Sd Test1 10.0 2.0 Score 12 is 1 Sd above the mean Test2 14.0 2.0 Score 15 is 0.5 Sd above the mean The student scored higher than others on the first test.
- 7. Reading Math Science Number of Test Items 90 60 80 Mean of Scores 60 40 40 Standard Deviation 10 5 10 Use this information to determine whether each of the following statements is true or false. 1. Jenny scored 70 in reading and 60 in science. Relative to other students, she did better in reading than science. (False) 2. Paul scored 50 in both reading and math. Relative to other students, he did about the same in reading and math. (False) 3. Michael scored 40 in both math and science. Relative to other students, he did about the same in math science. (True)
- 8. where: x is the student’s test score μ is the mean of all the test scores σ is the standard deviation of the test scores x z µ σ − =
- 9. formula Where z is an arbitrary, the given of what standard deviation does a raw score falls from the mean 50 10T z= +
- 10. The term Stanine is an abbreviation of the words Standard NINE, and its value is limited to the range of 1 to 9 It has a mean equal to 5 and standard deviation equal to 2. A student whose raw score equals the test mean will obtain a stanine score of 5. A score that is 3 standard deviations above the mean is assigned a stanine of 9 not 11 because stanines are limited to a range of 1 to 9. Formula: 5 2( )STANINEScore z= +
- 11. Earlier intelligence tests derived a mental age score for a chid and compared that score to the individual’s chronological age. The ratio of the mental age to chronological age, when multiplied by 100, became the child’s intelligence quotient IQ. Analysis of scores of the then-dominant intelligence test indicated that the mean and the standard deviation of IQ’s were approximately 100 and 16 respectively.
- 12. Normal Curve Equivalent (NCE) scores are a standard score with a preset mean of 50 and standard deviation of 21.06 This is somewhat unusual value for standard deviation is used so that NCE scores will match percentile ranks at three points: 1. 50 and 99.
- 13. A standard score indicates how many standard deviations a student’s score is below or above the mean. Converting from a raw scores to standard scores does not change the meaning of the student's performance. (Just like converting the temperature from Celsius to Fahrenheit)
- 14. The interpretation of standard scores depends in part on the nature of the norm group. When comparing standard scores from different scores, one must also recognize that the abilities measured by the respective instruments are different. That’s why it is not surprising if a student obtains different scores in math and reading even if the tests use the same standard scores.
- 15. Standard scores divide differences in performance into equal intervals. For instance, performance represented by T-Scores of 40 of 50 to 55 represent approximately equal differences in whatever ability the test is measuring. This attribute of equal intervals is not shared in percentile rank Standard scores can be used to compare a student’s performance across. For percentile rank, they should be converted to b equal-interval scale before they can be added, subtracted, or averaged. Standard scores can be used to compare a student’s performance across tests. For example, if a student’s stanine scores in math and verbal skills are 4 and 2 respectively, one can conclude that the student performed better in math.
- 16. Many Standard-score scales imply a degree of precision that does not exist within educational tests. Differences of less than one-third standard deviation are usually not measurable. This means that differences less than 3 point on the 7-score and 5 point in deviation IQ’s are not meaningful. Both of these scales are too precise. They represent measures of relative standing as opposed to measures of growth. A student who progresses trough school in step with peers remains at the same number of standard deviations form the mean. The constant standard score may suggest (incorrectly) that growth is not occurring.