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stats_exam [2017/02/10 11:25]
steveclarke 		stats_exam [2017/06/07 09:53] (current)
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 |QtySkipped|Total of all QtySkipped for all Items on the Exam| |QtySkipped|Total of all QtySkipped for all Items on the Exam|
 |QtyIncorrect|Total of all QtyIncorrect for all Items on the Exam| |QtyIncorrect|Total of all QtyIncorrect for all Items on the Exam|
-|RawPercent|x = Count of Correct Items on Exam| +|RawPercent|x = Count of Correct Items on Exam \\ n = Count of Candidates on Exam \\ k = Count of Items on Exam \\ \\ {{:​stat_rawpercent.png|}}| 
- +|ValueCorrect|Total of all ValueCorrect for all Items on the Exam| 
- +|ValueSkipped|Total of all ValueSkipped for all Items on the Exam| 
-n = Count of Candidates on Exam +|ValueIncorrect|Total of all ValueIncorrect for all Items on the Exam| 
-k = Count of Items on Exam +|ValueTotal|(ValueCorrect + ValueSkipped + ValueIncorrect)| 
-x/​(n*k*100) +|ValuePercent|{{:​stat_valuepercent.png|}}| 
-ValueCorrect Total of all ValueCorrect for all Items on the Exam +|Difficulty|x = Count of Correct Items on Exam \\ n = Count of Candidates on Exam \\ k = Count of Items on Exam \\ \\ {{:​stat_difficulty.png|}}| 
-ValueSkipped Total of all ValueSkipped for all Items on the Exam +|RawHigh|Highest QtyCorrect achieved by a Candidate on the Exam| 
-ValueIncorrect Total of all ValueIncorrect for all Items on the Exam +|RawLow|Lowest QtyCorrect achieved by a Candidate on the Exam| 
-ValueTotal (ValueCorrect + ValueSkipped + ValueIncorrect) +|RawMean|Mean (average) QtyCorrect achieved by a Candidate on the Exam| 
-ValuePercent ValueTotal/​(ValueMax*100) +|RawVariance|Variance of QtyCorrect for all Candidates on the Exam| 
-Difficulty x = Count of Correct Items on Exam +|RawStdev|Standard Deviation of QtyCorrect for all Candidates on the Exam| 
-n = Count of Candidates on Exam +|ValueHigh|Highest ValueTotal achieved by a Candidate on the Exam| 
-k = Count of Items on Exam +|ValueLow|Lowest ValueTotal achieved by a Candidate on the Exam| 
-x/(n*k) +|ValueMean|Mean (average) ValueTotal achieved by a Candidate on the Exam| 
-RawHigh Highest QtyCorrect achieved by a Candidate on the Exam +|ValueVariance|Variance of ValueTotal for all Candidates on the Exam| 
-RawLow Lowest QtyCorrect achieved by a Candidate on the Exam +|ValueStdev|Standard Deviation of ValueTotal for all Candidates on the Exam| 
-RawMean Mean (average) QtyCorrect achieved by a Candidate on the Exam +|ValueMedian|Median (middle) ValueTotal for all Candidates on the Exam| 
-RawVariance Variance of QtyCorrect for all Candidates on the Exam +|ValueMode|Mode (most frequent) ValueTotal for all Candidates on the Exam| 
-RawStdev Standard Deviation of QtyCorrect for all Candidates on the Exam +|PercentDistribution|Text field which holds a summary of the score distributions. ​ Not a statistic, but used in reporting| 
-ValueHigh Highest ValueTotal achieved by a Candidate on the Exam +|QtyPassExam|Count of Candidates that passed Exam.  See [[stats_candidate|Registrant ​Statistics]]| 
-ValueLow Lowest ValueTotal achieved by a Candidate on the Exam +|SpearmanRank|n = Number of Candidates \\ RankOdd = Candidates Ranking on Odd Items only compared to all other Candidates on Exam \\ RankEven = Candidates Ranking on Odd Items only compared to all other Candidates on Exam \\ \\ {{:​stat_spearmanrank.png|}}| 
-ValueMean Mean (average) ValueTotal achieved by a Candidate on the Exam +|SpearmanBrown|{{:​stat_spearmanbrown.png|}}| 
-ValueVariance Variance of ValueTotal for all Candidates on the Exam +|KuderRichardson20|k = Count of Items on Exam \\ Total Test Variance = Variance of Candidate Raw Scores ​\\ Sum of p*q = sum of all items p (difficulty) * q (1-p) for all items in Exam \\ \\ {{:​stat_kr20.png|}}| 
-ValueStdev Standard Deviation of ValueTotal for all Candidates on the Exam +|KuderRichardson21|qtyX = Count Items answered correctly on Exam \\ x ̅ = Mean of QtyCorrect for each Candidate on Exam \\ s = StDev of Raw Scores of all Candidates on Exam \\ \\ {{:​stat_kr21.png|}}| 
-ValueMedian Median (middle) ValueTotal for all Candidates on the Exam +|StandardError|s = StDev of QtyCorrect for Exam \\ n = Count of Candidates ​\\ {{:​stat_stderr.png|}}| 
-ValueMode Mode (most frequent) ValueTotal for all Candidates on the Exam +|StandardErrorMeasurement|s = StDev of QtyCorrect for Exam \\ n = Count of Candidates \\ kr20 = Kuder Richardson 20 \\ {{:​stat_stderrmeasurement.png|}}| 
-PercentDistribution Text field which holds a summary of the score distributions. ​ Not a statistic, but used in reporting +|AlphaCoefficient|k = Count of Items on Exam \\ Total Test Variance = Variance of Candidate Raw Scores ​\\ Sum of Item Variance = Sum of all item variances on Exam \\ \\ {{:​stat_alphacoefficient.png|}}| 
-QtyPassExam Count of Candidates that passed Exam.  See Candidate ​Statistics ​(PassExam) +|Skewness|n = Count of Candidates ​\\ xi = QtyCorrect for each Candidate on Exam \\ x ̅ = Mean of QtyCorrect on Exam \\ s = StDev of QtyCorrect on Exam \\ \\ {{:​stat_skewness_1.png|}} \\ \\ Calculate Population Skewness using Sample Skewness ​\\ \\ {{:​stat_skewness_2.png|}}| 
-SpearmanBrown (2*SpearmanRank)/​((1+SpreamanRank)) +|Kurtosis|n = Count of Candidates ​\\ xi = QtyCorrect for each Candidate on Exam \\ x ̅ = Mean of QtyCorrect for Exam \\ s = StDev of QtyCorrect for Exam \\ \\ Calculate Sample Kurtosis ​{{:​stat_kurtosis_1.png|}} \\ \\ Calculate Population Kurtosis using Sample Kurtosis ​\\ \\ {{:​stat_kurtosis_2.png|}}| 
-KuderRichardson20 k = Count of Items on Exam +|AlternateSystem|Stores Alternate Value used for Calculation (True, Custom, ZScore, TScore,​…) ​ see [[stats_concepts#​Alternate Scores|Alternate Scores]]| 
-Total Test Variance = Variance of Candidate Raw Scores +|AlternateBase|Alternate used in Alternate Calculations see [[stats_concepts#​Alternate Scores|Alternate Scores]]| 
-Sum of p*q = sum of all items p (difficulty) * q (1-p) for all items in Exam +|AlternateMean|Alternate Mean used in Alternate Calculations see [[stats_concepts#​Alternate Scores|Alternate Scores]]| 
- +|AlternateStDev|Alternate Standard Deviation used in Alternate Calculations see [[stats_concepts#​Alternate Scores|Alternate Scores]]| 
-k/​((k-1))*((Total Test Variance- ∑▒〖(p*q)〗))/​(Total Test Variance) +|QuestionLogitSum|Future use| 
-KuderRichardson21 qtyX = Count Items answered correctly on Exam +|QuestionLogitMean|Future use| 
-x ̅ = Mean of QtyCorrect for each Candidate on Exam +|QuestionLogitVariance|Future use| 
-s = StDev of Raw Scores of all Candidates on Exam +|QuestionLogitSquaredSum|Future use| 
- +|QuestionSpreadExpansion|Future use| 
-qtyX/​((qtyX-1))* ​ ((1-x ̅*(qtyX-x ̅)))/​((qtyX*s)) +|CandidateLogitSum|Future use| 
-StandardError s = StDev of QtyCorrect for Exam +|CandidateLogitMean|Future use| 
-n = Count of Candidates +|CandidateLogitVariance|Future use| 
-s/√n +|CandidateLogitSquaredSum|Future use| 
-AlphaCoefficient k = Count of Items on Exam +|CandidateSpreadExpansion|Future use|
-Total Test Variance = Variance of Candidate Raw Scores +
-Sum of Item Variance = Sum of all item variances on Exam +
- +
-k/​((k-1))*((Total Test Variance- ∑▒〖Item Variance〗))/​(Total Test Variance) +
-SpearmanRank n = Number of Candidates +
-RankOdd = Candidates Ranking on Odd Items only compared to all other Candidates on Exam +
-RankEven = Candidates Ranking on Odd Items only compared to all other Candidates on Exam +
- +
-1-  (6*∑▒(RankOdd-RankEven)^2 )/​(n*(n^2-1)) +
-Skewness n = Count of Candidates +
-xi = QtyCorrect for each Candidate on Exam +
-x ̅ = Mean of QtyCorrect on Exam +
-s = StDev of QtyCorrect on Exam +
-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 Exam +
-x ̅ = Mean of QtyCorrect for Exam +
-s = StDev of QtyCorrect for Exam +
- +
-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)) +
- +
-AlternateSystem Stores Alternate Value used for Calculation (True, Custom, ZScore, TScore,​…) ​ see Alternate Scores +
- +
-AlternateBase Alternate ​Base used in Alternate Calculations see Alternate Scores +
- +
-AlternateMean Alternate Mean used in Alternate Calculations see Alternate Scores +
- +
-AlternateStDev Alternate Standard Deviation used in Alternate Calculations see Alternate Scores +
- +
-QuestionLogitSum Future use +
-QuestionLogitMean Future use +
-QuestionLogitVariance Future use +
-QuestionLogitSquaredSum Future use +
-QuestionSpreadExpansion Future use +
-CandidateLogitSum Future use +
-CandidateLogitMean Future use +
-CandidateLogitVariance Future use +
-CandidateLogitSquaredSum Future use +
-CandidateSpreadExpansion Future use+