Topic_4.1___Descriptive_Statistics___Examples

Topic_4.1___Descriptive_Statistics___Examples - Descriptive...

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Descriptive Statistics - Examples Ash Genaidy
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Case Study Most cases of lower back pain are mild and transient, requiring temporary activity modification. About 5% of the cases become chronic and disabling. When conservative measures fail, surgeons may recommend a spinal fusion in an effort to relieve pain in selected cases.
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Case Study A study was conducted to examine the efficacy of anterior lumbar fusion in relieving lower back pain. Thirty-five patients participated in the study. A prospective design was employed where the pain level was measured in the lower back and leg regions at baseline (right before the surgery), 3-month, 1-yr and 2- yr intervals.
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Case Study Analog scale for measuring pain: I____________________________I 0 10 no worst pain imaginable pain
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Case Study Descriptive statistics for: Age Level of back pain at baseline
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AGE DATA I N ASCENDI NG ORDER Obs AGE 1 28 2 30 3 31 4 33 5 34 6 36 7 37 8 37 9 38 10 39 11 39 12 39 13 40 14 40 15 41 16 41 17 43 18 43 19 43 20 43 21 44 22 44 23 45 24 46 25 49 26 49 27 50 28 50 29 50 30 50 31 52 32 52 33 53 34 68 35 71
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Measures of Central Tendency Mean = =(28 + 30 + … + 53 + 68 +71)/35 = 43.66 Median = 43 ordered value, n is odd; average of & ordered values, n is even; n Y Y n i i = = 1 th n ) 2 1 ( + th n ) 2 ( th n ) 1 2 ( +
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Measures of Central Tendency Lower quartile = 38.5 median of the smallest n/2 obs, n is even; median of the smallest (n+1)/2 obs, n is odd; Upper quartile = 49.5 median of the largest n/2 obs, n is even; median of the largest (n+1)/2 obs, n is odd; Interquartile range = 11 (Upper quartile – Lower quartile)
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Measures of Central Tendency the most commonly occurring value (s); Outlier(s) = 71 and 68 falls more than 1.5 interquartile range (16.5 yrs) above the upper quartile (i.e., 50 yr) or more than 1.5 interquartile range (16.5 yrs) below the lower quartile (ie., 38 yr).
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Measures of variation Variance = 84.64 = [(28 – 43.66) 2 + (30-43.66) 2 + … + (68-43.66) 2 + (71- 43.66) 2 ] / (35-1) Standard Deviation = 9.2 - - = ) 1 /( ) ( 2 2 n Y Y S i
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SAS Output: Measures of Central Tendency and Variation Basi c St at i st i cal Measur es Locat i on Var i abi l i t y Mean 43. 65714 St d Devi at i on 9. 20020 Medi an 43. 00000 Var i ance 84. 64370 Mode 43. 00000 Range 43. 00000 I nt er quar t i l e Range 12. 00000
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SAS Output: Percentiles Quant i l e Est i mat e 100% Max 71 99% 71 95% 68 90% 52 75% Q3 50 50% Medi an 43 25% Q1 38 10% 33 5% 30 1% 28 0% Mi n 28
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Topic_4.1___Descriptive_Statistics___Examples - Descriptive...

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