Scaling Z-scores T-scores C-scores
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This document discusses various types of scaling scores used in educational testing and assessment. It begins by defining raw scores and derived scores. It then discusses three main types of derived scores: Z-scores (standard scores), T-scores (transformed scores), and C-scores. For each score type, it provides the meaning, calculation method, and examples of calculating the scores from raw scores. It concludes by discussing the utilities of each score type and providing some example problems for practice.
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REFERENCES:
1] Asthana,B.(2015) Measurement and evaluation in
psychology and evaluation,Agarwal Publication, Agra.
2] Garrett, H.E.(1952) Statistics in psychology and education,
Longmans, Green & Co., London.
3] Gupta, S.C. & Kapoor, V.K.(2011) Fundamentals of
Mathematics Statistics, Sultan Chand & Sons, New Delhi.](https://image.slidesharecdn.com/surbhisharmascalingzscorestscorescscores-200325175237/85/Scaling-Z-scores-T-scores-C-scores-35-320.jpg)
Scaling Z-scores T-scores C-scores
- 1. SCALING: Z- SCORES (Standard Scores) T- SCORES (Transformed Scores) C- Scores SURBHI SHARMA Department of Education UNIVERSITY OF LUCKNOW 25/03/2020 1
- 2. 25/03/2020 2 • What are SCORES? • What are RAW SCORES? • Meaning of Derived/Converted/ Standard Scores. 1. Z-Scores 1.1 Meaning of Z- Scores 1.2 Calculation of Z- Scores 1.3 Utility of Z- Scores 2. T- Scores 2.1 Meaning of T- Scores 2.2 Calculation of T- Scores 2.3 Utility of T- Scores 3. C- Scores 3.1 Meaning of C- Scores 3.2 Calculation of C- Scores 3.3 Utility of C- Scores • Problem Sums • References
- 3. 25/03/2020 3 What are Scores? According to Ross – “A score on any test is simply a numerical description of an individual’s performance on that task.”
- 4. 25/03/2020 4 What are RAW Scores? According to Smith – “Raw Scores are direct counts of the number of items a specified event has occurred, such as - • the number of test items answered correctly, • the number of books read, • the number of errors made in solving a problem, • the number of statements endorsed on a questionnaire, etc.”
- 5. 25/03/2020 5 I scored 60 in English & 60 in Mathematics. Are my scores in both subjects significantly meaning the same?
- 6. What should I do now? 25/03/2020 6
- 7. 25/03/2020 7 Derived Scores / Converted Scores / Standard Scores Meaning: The scores which have a definite reference point or norm, and this norm is the Mean (M) of the scale. Besides, it has a definite standard deviation (). …contd.
- 8. 25/03/2020 8 Derived Scores / Converted Scores / Standard Scores Types of Derived Scores: • Z- Scores • T- Scores • C-Scores • Stanine Scores • Hull Scores , etc.
- 9. 25/03/2020 9 In midterm exam, Ram has obtained a score of 55 in mathematics. The Maximum Marks can be scored is 85 for the class The Mean is 50 for the class SITUATION A SITUATION B
- 10. 25/03/2020 10 1. Z-Scores (Standard Scores): Meaning of Z- Scores: It tells how many standard deviations someone is above or below the mean. Mean(M) = 0 Standard Deviation () = 1 Its value is generally from -3 to +3 The unit of Z-Score is similar to the standard deviation ()
- 11. 25/03/2020 11 Calculation of Z- Scores/ Sigma-scores (Standard Scores) Where, Z= Z-Score or sigma-score X= Raw Score M= Mean = Standard Deviation
- 12. 25/03/2020 12 Ques. 1. The marks obtained by student A in the Mathematics and Language tests of maximum marks 100, each are 80 and 70 respectively. If the mean (M) of mathematics scores of the class students is 60 and standard deviation () 8, and in the language test 40 and 10 respectively; then find out in which subject the student A is more able as compared to other students?
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- 15. 25/03/2020 15 Analysis: Because student A’s Z-score in language is more than that of mathematics, so he is more able in language in the class as compared to mathematics.
- 16. 25/03/2020 16 Utility of Z-Scores: In Education for meaningful analysis of scores of a students, etc.
- 17. 25/03/2020 17 2. T-Scores (Transformed Scores): Meaning of T- Scores: T-scores are those converted scores of raw scores of which- Mean(M) = 50 Standard Deviation () = 10 Distribution is Normal.
- 18. 25/03/2020 18 Calculation of T- Scores: Where, T= T-Score X= Raw Score M= Mean = Standard Deviation
- 19. 25/03/2020 19 Calculation of T- Scores: Where, T= T-Score Z= Z-Score
- 20. 25/03/2020 20 Ques. 2. In Ques. 1 The score in mathematics of student A=80 and Z-Score= 2.5; and the score in language= 70 and Z-Score= 3. Convert these scores into T-Scores.
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- 23. 25/03/2020 23 Row Scores Standard Scores ( Z-Scores) T-Scores 80 2.5 75 70 3 80 Tabulation of Scores :
- 24. 25/03/2020 24 Utility of T-Scores: If the range of general distribution is taken to be 100, then range of T-Scale becomes from 0 to 100 as a result, therefore the measurement of scores can be done more accurately.
- 25. 25/03/2020 25 Comparison of Z- Scores & T- Scores
- 26. 25/03/2020 26 3. C-Scores : Meaning of C- Scores: C-scores are those converted scores of raw scores of which- Mean(M) = 5 Standard Deviation () = 2 Range of Raw Score is displayed on a 11- point scale from 0 to 10.
- 27. 25/03/2020 27 Calculation of C- Scores: Where, C= C-Score Z= Z-Score Method 1: Using Z-Score
- 28. 25/03/2020 28 Calculation of C- Scores: Method 2: Using Percentile Rank, that is, a raw score into C-Score by first changing raw scores into percentile rank and then into C-Scores by using the following table:
- 29. 25/03/2020 29 Utility of C-Scores: In Education, the use of C-Scores is more useful than the use of Z-Scores and T-Scores. However, • C-Score has demerit of being awarding 0- Score. •Also, there comes much difference in % if C-Score goes up/down by even 1- point.
- 30. 25/03/2020 30 Sums For Practice:
- 31. 25/03/2020 31 Ques. A. In a testing survey of class X students with N=500, their mean was observed as 80 and standard deviation as 8. Assuming normality of distribution of their scores, how many students would be below the score of a student getting 88? (UGC-Net, 2019) a) 171 b) 421 c) 84 d) 16
- 32. 25/03/2020 32 Ques. B. A researcher gives two tests-one in English language and another in mathematics. He/She finds the mean & standard deviation of each of the two groups n=100, as follows: Assuming the curve for the two distributions overlapping, how many students in English language are below the mean of those in mathematics? a) 34 b) 84 c) 16 d) 32 English Mathematics Mean(M) 50 60 Standard Deviation() 10 12
- 33. 25/03/2020 33 Answers : Ques. A 421 Ques. B 34
- 35. 25/03/2020 35 REFERENCES: 1] Asthana,B.(2015) Measurement and evaluation in psychology and evaluation,Agarwal Publication, Agra. 2] Garrett, H.E.(1952) Statistics in psychology and education, Longmans, Green & Co., London. 3] Gupta, S.C. & Kapoor, V.K.(2011) Fundamentals of Mathematics Statistics, Sultan Chand & Sons, New Delhi.
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