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Understanding and Interpreting Statistics in Assessments Clare Trott and Hilary Maddocks

Understanding and Interpreting Statistics in Assessments Clare Trott and Hilary Maddocks. This Session. Why use statistics in assessments ? “Averages”, Standard Deviation, variance, Standard Error Normal distribution, confidence intervals Scales Overlapping confidence intervals.

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Understanding and Interpreting Statistics in Assessments Clare Trott and Hilary Maddocks

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  1. Understanding and Interpreting Statistics in Assessments Clare Trottand Hilary Maddocks

  2. This Session • Why use statistics in assessments? • “Averages”, Standard Deviation, variance, Standard Error • Normal distribution, confidence intervals • Scales • Overlapping confidence intervals

  3. Why use statistics in assessments? • What are the assumptions made?

  4. Feedback

  5. Central Tendency • Which is better? When? Spread • What is • Standard Deviation? • Variance? • Standard Error?

  6. Feedback

  7. MODE Means Make Everyone Add Numbers (and) Share MOST OFTEN D E MEDIAN MED IAN

  8. Standard Deviation 2, 3, 6, 9, 10 Mean = 6, SD = 3.16 2, 2, 6, 10, 10 Mean = 6, SD = 3.58 • Measures the average amount by which all the data values deviate from the mean • Measured in the same units as the data

  9. Variance and Standard Deviation Standard deviation = σ = Variance = Mean ()

  10. Standard Error This is the variance per person

  11. Normal Distribution Confidence Intervals What are Confidence Intervals? Why are they important? • What is Normal Distribution? • Why is it useful?

  12. Feedback

  13. Normal Distribution Number of standard deviations from the mean

  14. Confidence Intervals TRUE SCORE The wider the range the more confident we can be that the true score lies in this range C I 99% Confidence Interval 95% Confidence Interval Due to inherent error in measurement it is better to quote a 95% confidence interval

  15. Confidence Intervals 1.645 -1.645 -1.96 1.96 -2.575 2.575 90% Confidence Interval 95% Confidence Interval 99% Confidence Interval

  16. 95% Confidence Intervals True Score • True score lies inside CI 95% of occasions • 1 in 20 (5%) will not include the true score

  17. Scales • What scales are used in reporting? • How are they defined? • Why are standardised scores preferred?

  18. Feedback

  19. Scaled scores 4 6 8 10 12 14 16 Percentiles 70 80 90 100 110 120 130 Standardised scores 2 10 25 50 75 90 98 Very low low Low average average High average high Very high

  20. Simplified Table

  21. Scale to Standardised • 1 to 5 ratio • 10 scaled 100 standardised • 9 scaled 95 standardised • 11 scaled 105 standardised • 15 scaled 125 standardised • 6scaled 80 standardised

  22. Standardised scores against standard deviations mean -1sd 1sd -2sd 2sd 3sd -3sd 70 80 90 100 110 120 130 Very low low Low average average High average high Very high

  23. Percentiles against standard deviations mean -1sd 1sd -2sd 2sd Low average Very high -3sd high 3sd 2 10 25 50 75 90 98 Very low low average High average

  24. Scaled scores against standard deviations mean -1sd 1sd -2sd 2sd Low average Very high high -3sd 3sd 4 6 8 10 12 14 16 Very low low average High average

  25. Differences in Class Intervals Suppose we have the class intervals for two tests which could be linked, and we wish to find whether there is a significant difference between the two sets. Test 1 95% Confidence Interval 102 ± 15.8, standard error 2.96 Test 2 95% Confidence Interval 118 ± 23, standard error 6.63 86.2 102 117.8 105 118 131 There appears to be no significant difference as there is a distinct overlap.

  26. H0 : There is no significant difference in the two Confidence Intervals (the new confidence interval contains zero) H1 : There is a significant difference in the two Confidence Intervals (the new CI does not contain zero Formula Difference in scores =(118 – 102) = 16 ± 14 New CI 2 16 30 This does not contain zero so we reject H0 and so there is a significant difference in the two tests.

  27. Test 1 95% Confidence Interval 95 ± 6, standard error 3.06 88 95 102 Test 2 95% Confidence Interval 106 ± 10, standard error 5.102 96 106 116 There appears to be no significant difference as there is a distinct overlap.

  28. H0 : There is no significant difference in the two Confidence Intervals (the new confidence interval contains zero) H1 : There is a significant difference in the two Confidence Intervals (the new CI does not contain zero Difference in scores =(106 – 95) = 11 ± 11.6 New CI -0.6 11 22.6 This does contain zero so we accept H0 and so there is no significant difference in the two tests.

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