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stats_section [2017/02/13 11:43]
steveclarke 		stats_section [2017/06/07 09:52] (current)
72.38.112.148
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 |ValueMedian|Median (middle) ValueTotal for all Candidates for this Section| |ValueMedian|Median (middle) ValueTotal for all Candidates for this Section|
 |ValueMode|Mode (most frequent) ValueTotal for all Candidates for this Section| |ValueMode|Mode (most frequent) ValueTotal for all Candidates for this Section|
- +|KuderRichardson20|k = Count of Items in Section ​\\ Total Section Variance = Variance of Candidate Raw Scores for Section ​\\ Sum of p*q = sum of all items p (difficulty) * q (1-p) for all items in Section ​\\ \\ {{:​stat_kr20.png|}}| 
- +|StandardErrorMean|s = StDev of QtyCorrect for Section \\ n = Count of Candidates ​\\ {{:​stat_stderr.png|}}| 
- +|StandardErrorMeasurement|s = StDev of QtyCorrect for Section \\ n = Count of Candidates \\ kr20 = Kuder Richardson 20 \\ {{:​stat_stderrmeasurement.png|}}| 
-KuderRichardson20 k = Count of Items in Section +|Skewness|n = Count of Candidates ​\\ xi = QtyCorrect for each Candidate ​in Section ​\\ x  = Mean of QtyCorrect ​in Section ​\\ s = StDev of QtyCorrect ​in Section ​\\ \\ {{:​stat_skewness_1.png|}} \\ \\ Calculate Population Skewness using Sample Skewness ​\\ \\ {{:​stat_skewness_2.png|}}| 
-Total Section Variance = Variance of Candidate Raw Scores for Section +|Kurtosis|n = Count of Candidates ​\\ xi = QtyCorrect for each Candidate ​in Section ​\\ x  = Mean of QtyCorrect for Section ​\\ s = StDev of QtyCorrect for Section ​\\ \\ Calculate Sample Kurtosis ​{{:​stat_kurtosis_1.png|}} \\ \\ Calculate Population Kurtosis using Sample Kurtosis ​\\ \\ {{:​stat_kurtosis_2.png|}}|
-Sum of p*q = sum of all items p (difficulty) * q (1-p) for all items in Section +
- +
-k/​((k-1))*((Total Section Variance- ∑▒〖(p*q)〗))/​(Total Section Variance) +
- +
- +
- +
-StandardError s = StDev of QtyCorrect for Exam +
-n = Count of Candidates +
-s/√n +
- +
- +
- +
-Skewness n = Count of Candidates +
-xi = QtyCorrect for each Candidate ​on Section +
-x ̅ = Mean of QtyCorrect ​for Section +
-s = StDev of QtyCorrect ​for Section +
- +
-Calculate Sample Skewness SkewS +
-n/​((n-1)(n-2)) ​ ∑▒((x_i- x ̅)/s) ^3 +
- +
-Calculate Population Skewness using Sample Skewness +
- +
-(SkewS*(n-2))/​√(n* (n-1)) +
- +
- +
- +
-Kurtosis n = Count of Candidates +
-xi = QtyCorrect for each Candidate ​on Section +
-x ̅ = Mean of QtyCorrect for Section +
-s = StDev of QtyCorrect for Section +
- +
-Calculate Sample Kurtosis ​KurtS +
-(n(n+1) ​ ∑▒(x_i- x ̅ ) ^4)/​((n-1)(n-2)(n-3) s^4 )  -  (3〖(n-1)〗^2)/​(n-2)(n-3)  +
- +
-Calculate Population Kurtosis using Sample Kurtosis +
- +
-((KurtS*(n-2)*(n-3))/​((n-1))-6)/​((n+1)) +