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Statistics

Statistics. Descriptive Statistics Inferential Statistics. Descriptive statistics Used to describe a set of data Inferential statistics Used to draw inferences about a population based on data obtained from a sample. Parameter Statistic. Scales of Measurement.

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Statistics

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  1. Statistics

  2. Descriptive Statistics Inferential Statistics

  3. Descriptive statistics Used to describe a set of data Inferential statistics Used to draw inferences about a population based on data obtained from a sample. Parameter Statistic

  4. Scales of Measurement Nominal scales (Categorical data) Ordinal scales Interval scales Ratio scales

  5. Distributions IQ Scores 113, 117, 84, 103, 105, 108, 115, 126, 103, 112, 106, 111, 113, 90, 107, 76, 109, 97, 103, 97, 89, 101, 93, 99, 115, 94, 94, 94, 108, 97, 95, 87, 107, 97, 88, 99, 97, 82, 112, 91, 107, 93, 83, 99, 100, 92, 102, 93, 100, 83, 125, 96, 84, 113, 113, 96, 97, 88, 100, 95, 86, 77, 80, 125, 110, 114, 121, 102, 90, 103, 91, 103, 109, 104, 79, 100, 85, 76, 115, 105, 95, 88, 93, 111, 107, 108, 98, 84, 123, 107, 118, 93, 101, 92, 99, 92, 136, 121, 97, 101, 102, 114, 103, 81, 71, 104, 85, 106, 120, 108, 112, 131, 94, 104, 121, 123, 91, 103, 93, 102 N = 120

  6. IQ Scores - Ranked 71, 76, 76, 77, 79, 80, 81, 82, 83, 83, 84, 84, 84, 85, 85, 86, 87, 88, 88, 88, 89, 90, 90, 91, 91, 91, 92, 92, 92, 93, 93, 93, 93, 93, 93, 94, 94, 94, 94, 95, 95, 95, 96, 96, 97, 97, 97, 97, 97, 97, 97, 98, 99, 99, 99, 99, 100, 100, 100, 100, 101, 101, 101, 102, 102, 102, 102, 103, 103, 103, 103, 103, 103, 103, 104, 104, 104, 105, 105, 106, 106, 107, 107, 107, 107, 107, 108, 108, 108, 108, 109, 109, 110, 111, 111, 112, 112, 112, 113, 113, 113, 113, 114, 114, 115, 115, 115, 117, 118, 120, 121, 121, 121, 123, 123, 125, 125, 126, 131, 136 N = 120

  7. Frequency distribution of IQ scores Cumulative Value Frequency Percent Percent 71 .8 1 .8 76 2 1.7 2.5 77 1 .8 3.3 79 .8 1 4.2 80 .8 5.0 1 81 1 .8 5.8 82 1 .8 6.7 83 1.7 2 8.3 84 3 2.5 10.8 85 2 1.7 12.5 86 1 .8 13.3 87 1 .8 14.2 88 3 2.5 16.7 89 1 .8 17.5 90 2 1.7 19.2 91 3 2.5 21.7 . . . . 136 1 .8 100.0 Total 120 100

  8. Grouped Frequency Distribution of IQ scores Mid- Cumulative Value F Percent point Percent 72 1 .8 .8 70 - 74 4 3 .3 4 75 -79 77 .2 82 8 6 .6 10 .8 80 - 84 8 6 .6 85 - 89 87 17 .5 92 18 15 .0 32 .5 90 - 95 95 - 99 97 17 14 .2 46 .7 102 21 17 .5 64 .2 100 -104 107 15 12 .5 76 .7 105 - 109 12 10 .0 86 .7 110 - 114 112 117 5 4 .2 90 .8 115 - 119 6 5 .0 95 .8 120 - 124 122 127 3 2 .5 98 .3 125 - 129 1 .8 .2 130 - 134 132 99 137 1 .8 100 .0 135 - 139 N 120

  9. Measures of Central Tendency Mode The most common score

  10. Grouped Frequency Distribution of IQ scores Mid- Cumulative Value F Percent point Percent 70 - 74 72 1 .8 .8 77 4 3 .3 4 .2 75 -79 8 6 .6 80 - 84 82 10 .8 8 6 .6 85 - 89 87 17 .5 92 18 15 .0 32 .5 90 - 95 97 17 14 .2 46 .7 95 - 99 102 21 17 .5 64 .2 100 -104 107 15 12 .5 76 .7 105 - 109 112 12 10 .0 86 .7 110 - 114 117 5 4 .2 90 .8 115 - 119 122 6 5 .0 95 .8 120 - 124 127 3 2 .5 98 .3 125 - 129 132 1 .8 99 .2 130 - 134 1 .8 .0 137 100 135 - 139 N 120

  11. Measures of Central Tendency Median (Mdn) The score that corresponds to the point at or below which 50% of the scores fall. (The 50th percentile.)

  12. Sample A:26811141620 Mdn = 11.0 Sample B:2681114162051 Mdn = 12.5 2 N + 1 Median location =

  13. Grouped Frequency Distribution of IQ scores Mid- Cumulative Value F Percent point Percent 72 1 .8 .8 70 - 74 4 3 .3 4 75 -79 77 .2 82 8 6 .6 10 .8 80 - 84 8 6 .6 85 - 89 87 17 .5 92 18 15 .0 32 .5 90 - 95 95 - 99 97 17 14 .2 46 .7 102 21 17 .5 64 .2 100 -104 107 15 12 .5 76 .7 105 - 109 12 10 .0 86 .7 110 - 114 112 117 5 4 .2 90 .8 115 - 119 6 5 .0 95 .8 120 - 124 122 127 3 2 .5 98 .3 125 - 129 1 .8 .2 130 - 134 132 99 137 1 .8 100 .0 135 - 139 N 120

  14. Mean ( 0, :or M) The average score å X ( 3 = capital Sigma = add up all the numbers) X = N Sample A: 2 6 8 11 14 16 20 77 X = = 11 . 0 (Mdn= 11.0 ) A 7 Sample B 2 6 8 11 14 16 20 51 128 ( Mdn = 12.5 ) X = = 16 B 8 Outlier

  15. Properties of the mean 0 0 X X - X - 2 2 - 11 -9 6 -4 6 - 11 8 8 - 11 -3 11 0 11 - 11 14 3 14 - 11 16 4 16 - 11 9 9 20 20 - 11 0 0 ' ' X - X - = 0 = 0

  16. Scores 10 12 15 18 20 Sample A 2 8 15 22 28 Sample B 15 15 15 15 15 Sample C

  17. M Scores Mdn 10 12 15 18 20 15 15 Sample A 2 8 15 22 28 15 15 Sample B 15 15 15 15 15 15 15 Sample C

  18. Measures of Variability Range The scale distance between the largest and the smallest scores. Scores Mdn M 12 15 18 20 15 15 Sample A 10 2 8 15 22 28 15 15 Sample B 15 15 15 15 15 15 15 Sample C RangeA = 20 - 10 = 10 RangeB = 28 - 2 = 26 RangeC = 15 - 15 = 0

  19. Interquartile Range Is the distance between the score occuring at the 25th percentile and the score occuring at the 75th percentile.

  20. Mean (Average) Deviation å ( X - X ) N 0 0 X X - X - 2 2 - 11 -9 6 -4 6 - 11 8 -3 8 - 11 11 0 11 - 11 14 3 14 - 11 16 4 16 - 11 20 20 - 11 9 9 0 0 ' ' X - X - = 0 = 0

  21. Mean Absolute Deviation å X - X N 0 0 X X - * X - * 2 2 - 11 9 6 6 - 11 5 8 8 - 11 3 11 11 - 11 0 14 14 - 11 3 16 16 - 11 4 20 20 - 11 9 9 0 0 ' ' X - X - = 32 = 32

  22. Variance (for population) å 2 ( X - X ) 2 s = N 0 0 X Sample 2 ) X - (X - A -5 10 25 12 -3 9 0 0 15 18 3 9 20 5 25 G 0 = 65 68 0 15 = å 2 ( X - X ) 68 2 s = = = 13 . 60 N 5

  23. Standard Deviation (for population) å 2 ( X - X ) s = N 0 0 X Sample 2 ) X - (X - A 10 -5 25 12 -3 9 0 0 15 18 3 9 5 20 25 G 65 0 68 = 0 15 = å 2 ( X - X ) 68 s = = = 13 . 6 = 3 . 69 N 5

  24. Variance (for sample) å 2 ( X - X ) 2 s = N - 1 0 0 X Sample 2 ) X - (X - A 10 -5 25 12 -3 9 15 0 0 3 9 18 20 5 25 G = 65 0 68 0 15 = å 2 ( X - X ) 68 2 s = = = 17 . 00 N - 1 4

  25. Standard Deviation (for sample) å 2 ( X - X ) s = N - 1 0 0 X Sample 2 ) X - (X - A 10 -5 25 12 -3 9 15 0 0 3 9 18 5 20 25 G = 65 0 68 0 15 = å 2 ( X - X ) 68 s = = = 17 . 0 = 4 . 12 N - 1 4

  26. Degrees of freedom

  27. Boxplot of IQ Scores

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