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stats_exam [2017/01/10 15:21] 127.0.0.1 external edit |
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| - | ====== Calculations ====== | + | ====== Exam Statistics and Results ====== |
| - | ==== Scaled Scoring ==== | + | Table: **ceStatsExam** |
| - | Item Writing tracks two types of Candidate scores: raw scores and scaled scores. A raw score is a score without any sort of adjustment or transformation, such as the simple number of Items answered correctly. A scaled score is the results of some transformation applied to the raw score. The purpose of scaled scores is to report scores for all Candidates on a consistent scale. | + | |
| - | Th scaled score is calculated using two different formulas based on the raw score. One formula is used if the Candidate is at or above the raw cut score. The other formula is used if the Candidate raw score is blow the raw cut score. | + | Aggregation of all [[Stats_Item|Item Stats]] for the Exam. |
| - | ** At or Above Raw Cut Score** | + | ^Field^Description^ |
| + | |StatsID|Unique Identifier for this set of Statistics| | ||
| + | |QtyQuestions|Count of all Items on the Exam| | ||
| + | |QtyCandidates|Count of all Candidates taking the Exam| | ||
| + | |QtyCompetencies|Count of distinct Competencies from all Items on the Exam| | ||
| + | |QtySections|Count of Sections on the Exam| | ||
| + | |ValueMax|Maximum achievable points for Exam, from sum of all Value Max of Items on the Exam| | ||
| + | |QtyCorrect|Total of all QtyCorrect 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| | ||
| + | |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| | ||
| + | |ValueIncorrect|Total of all ValueIncorrect for all Items on the Exam| | ||
| + | |ValueTotal|(ValueCorrect + ValueSkipped + ValueIncorrect)| | ||
| + | |ValuePercent|{{:stat_valuepercent.png|}}| | ||
| + | |Difficulty|x = Count of Correct Items on Exam \\ n = Count of Candidates on Exam \\ k = Count of Items on Exam \\ \\ {{:stat_difficulty.png|}}| | ||
| + | |RawHigh|Highest QtyCorrect achieved by a Candidate on the Exam| | ||
| + | |RawLow|Lowest QtyCorrect achieved by a Candidate on the Exam| | ||
| + | |RawMean|Mean (average) QtyCorrect achieved by a Candidate on the Exam| | ||
| + | |RawVariance|Variance of QtyCorrect for all Candidates on the Exam| | ||
| + | |RawStdev|Standard Deviation of QtyCorrect for all Candidates on the Exam| | ||
| + | |ValueHigh|Highest ValueTotal achieved by a Candidate on the Exam| | ||
| + | |ValueLow|Lowest ValueTotal achieved by a Candidate on the Exam| | ||
| + | |ValueMean|Mean (average) ValueTotal achieved by a Candidate on the Exam| | ||
| + | |ValueVariance|Variance of ValueTotal for all Candidates on the Exam| | ||
| + | |ValueStdev|Standard Deviation of ValueTotal for all Candidates on the Exam| | ||
| + | |ValueMedian|Median (middle) ValueTotal for all Candidates on the Exam| | ||
| + | |ValueMode|Mode (most frequent) ValueTotal for all Candidates on the Exam| | ||
| + | |PercentDistribution|Text field which holds a summary of the score distributions. Not a statistic, but used in reporting| | ||
| + | |QtyPassExam|Count of Candidates that passed Exam. See [[stats_candidate|Registrant Statistics]]| | ||
| + | |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|}}| | ||
| + | |SpearmanBrown|{{:stat_spearmanbrown.png|}}| | ||
| + | |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|}}| | ||
| + | |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|}}| | ||
| + | |StandardError|s = StDev of QtyCorrect for Exam \\ n = Count of Candidates \\ {{:stat_stderr.png|}}| | ||
| + | |StandardErrorMeasurement|s = StDev of QtyCorrect for Exam \\ n = Count of Candidates \\ kr20 = Kuder Richardson 20 \\ {{:stat_stderrmeasurement.png|}}| | ||
| + | |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|}}| | ||
| + | |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|}}| | ||
| + | |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|}}| | ||
| + | |AlternateSystem|Stores Alternate Value used for Calculation (True, Custom, ZScore, TScore,…) see [[stats_concepts#Alternate Scores|Alternate Scores]]| | ||
| + | |AlternateBase|Alternate used in Alternate Calculations see [[stats_concepts#Alternate Scores|Alternate Scores]]| | ||
| + | |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]]| | ||
| + | |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| | ||
| - | (CandidateRaw - RawCut) * ( (ScaledMax - ScaledCut) / (RawMax - RawCut) ) + ScaledCut | ||
| - | |||
| - | ** Below Raw Cut Score** | ||
| - | |||
| - | (ScaledCut-1) - ( ( (RawCut-1) - CandidateRaw) * ( ( (ScaledCut-1) - ScaledMin) / ( (RawCut-1)- RawMinScore) ) ) | ||
| - | |||
| - | {{:scaledscore.png?200|}} | ||
