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Comprehensive Guide to Organizing and Analyzing Educational Research Data

This resource presents detailed methodologies for organizing and analyzing educational research data, specifically focusing on frequency distributions, cumulative frequency, mean, mode, median, and measures of variability. It includes practical examples using weights and quiz scores to illustrate standard statistical calculations such as summation, deviation scores, and the calculation of z-scores and T-scores. Ideal for educators and researchers, this guide simplifies complex statistical concepts for effective data analysis in educational settings.

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Comprehensive Guide to Organizing and Analyzing Educational Research Data

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  1. STATISTICS EXERCISE • EDUCATIONAL RESEARCH

  2. Organizing Data: An Array 19 23 71 56 17 32 95 23 17 • 95 • 71 • 56 • 32 • 23 • 23 • 19 • 17 • 17

  3. Array: Quiz Scores • 14.75 12 11.5 13.5 14.75 14.75 13 12.5 13.5 • 14.75 • 14.75 • 14.75 • 13.50 • 13.50 • 13.00 • 12.50 • 12.00 • 11.50

  4. 2. Frequency (f) - • Cumulative frequency (cf) -

  5. Frequency Example 1: Weights • X Tallies f cf • 95 1 1 9 • 71 1 1 8 • 56 1 1 7 • 32 1 1 6 • 23 1 1 2 5 • 19 1 1 3 • 17 1 1 2 2

  6. Frequency Example 2: Quiz scores • X Tallies f cf • 14.75 1 1 1 3 9 • 13.50 1 1 2 6 • 13.00 1 1 4 • 12.50 1 1 3 • 12.00 1 1 2 • 11.5 1 1 1

  7. SUMMATION • Weights Quiz scores • 95 14.75 • 71 14.75 • 56 14.75 • 32 13.50 • 23 13.50 • 23 13.00 • 19 12.50 • 17 12.00 • 17 11.50 • 353 120.25

  8. Putting it All Together Weights • X f cf fx • 95 1 9 95 • 71 1 8 71 • 56 1 7 56 • 32 1 6 32 • 23 2 5 46 • 19 1 3 19 • 17 2 2 34 • n = 9 = 353

  9. Putting it All Together Quiz scores • X f cf fx • 14.75 3 9 44.25 • 13.50 2 6 27.00 • 13.00 1 4 13.00 • 12.50 1 3 12.50 • 12.00 1 2 12.00 • 11.50 1 1 11.50 • n = 9 = 120.25

  10. Mean Weights • = 353 / 9 • = 39.22 • Mean Quiz Scores • = 120.25 / 9 • = 13.36

  11. Mode (Mo) Weights • 95 • 71 • 56 • 32 • 23 • 23 • 19 • 17 • 17 • Mo = 17 & 23 -- bimodal

  12. Mode Quiz Scores • 14.75 • 14.75 • 14.75 • 13.50 • 13.50 • 13.00 • 12.50 • 12.00 • 11.50 • Mo = 14.75

  13. 3. Median (Mdn) • Group A Group B • X X • 7 50 • 6 6 • 5 5 • 4 -- Mdn 4 -- Mdn • 3 3 • 2 2 • 1 0

  14. Situations where calculating the median will NOT be so easy. Consider: • 7 7 7 8 8 8 9 9 10 10 • Mdn = L +[ ( n / 2 - cfb) / fw) } i • 7.5 + { ( 10 / 2 - 3 ) / 3 } 1 • = 7.5 + (5 - 3) / 3} 1 • = 7.5 + (2 / 3) 1 • = 8.17

  15. E. Measures of Variability • 1. Range • R = Xh - Xl • Example 1: Weights • R = 95 - 17 = 78 • Example 2: Quiz Scores • R = 14.75 - 11.5 = 3.25

  16. Deviation Scores • x (little x) = X (test score) - Mean • Example 1: Weights

  17. Score X X - Mean x2 • 95 55.78 3111.41 • 71 31.78 1009.97 • 56 16.78 281.57 • 32 -7.22 52.13 • 23 -16.22 263.09 • 23 -16.22 263.09 • 19 -20.22 408.85 • 17 -22.22 493.73 • 17 -22.22 493.73 • n = 9 x2=6377.57 • Sum = 353 Mean = 39.22

  18. Example 2: Quiz Scores • X X - Mean x2 • 14.75 1.39 1.93 • 14.75 1.39 1.93 • 14.75 1.39 1.93 • 13.50 0.14 0.02 • 13.50 0.14 0.02 • 13.00 -0.36 0.13 • 12.50 -0.86 0.74 • 12.00 -1.36 1.85 • 11.50 -1.86 3.46 • n = 9 = 0 x2 = 12.01 • Mean = 13.36

  19. Example 1: Weights • sigma 2 = 6377.63 / 9 • = 708.63 • Example 2: Quiz Scores • sigma 2 = 12.01 / 9 • = 1.33

  20. Example 1: Weights • sigma = square root { 63377.63 / 9} • = square root {708. 63} • = 26.62 • Example 2: Quiz Scores • sigma = square root {1.33} • = 1.15

  21. Standard Scores • z-scores • Mean = 0 Standard Deviation = 1 • Equation: z = (X - Mean) / sigma • Mean of raw score distribution • sigma = SD of raw score distribution

  22. b. T-scores • Mean = 50 SD = 10 • Equation: T = 50 + 10 (z) • Example: Let's suppose that a teacher wants to compare the results of an English and of an Algebra test: • Test Score Mean Highest SD • English 84 110 180 26 • Algebra 40 47 60 5

  23. English z-score = ( 84 - 110) / 26 • = - 26 / 26 • z = - 1.00 • Algebra z-score = ( 40 - 47) / 5 • = -7 / 5 • z = -1.4

  24. English T-score = 50 + 10 (-1.00) • T = 50 + -10 • T = 40.00 • Algebra T-score = 50 + 10 (-1.4) • T = 50 + -14.00 • T = 36.00

  25. FINISHED--DONE--COMPLETED • AT LONG, LONG LAST

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