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--- stats_concepts [2017/03/20 11:38]
steveclarke [Skewness and Kurtosis]
+++ stats_concepts [2018/04/10 09:12] (current)
72.38.112.148
@@ Line 60: / Line 60: @@
 STDEVP is used when the group of numbers being evaluated is complete - it's the entire population of values. In this case, the 1 is NOT subtracted and the denominator for dividing the sum of squared deviations is simply N itself, the number of observations (a count of items in the data set). Technically, this is referred to as "biased." Remembering that the P in STDEVP stands for "population" may be helpful. Since the data set is not a mere sample, but constituted of ALL the actual values, this standard deviation function can return a more precise result.
 ==== Reliability ====
-We have included a Reliability.xlsx spreadsheet that shows examples of how we calculate various reliability metrics as well as biserials.
+Reliability in statistics and psychometrics is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions.
+We have included a {{:Reliability.xlsx|Reliability}} spreadsheet that shows examples of how we calculate various reliability metrics as well as biserials.
 ==== Skewness and Kurtosis ====
-We have included a Skewness and Kurtosis.xlsx spreadsheet that shows examples of how we calculate Skewness and Kurtosis.
+Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.
+Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or lack of outliers.
+We have included a {{:Skewness.xlsx|Skewness} and {{:Kurtosis.xlsx|Kurtosis} spreadsheet that shows examples of how we calculate Skewness and Kurtosis.
 ==== Adverse Impact ====
 Steps for calculating Adverse Impact.
-.	At each score, calculate the pass rate percentage for each subgroup. (divide the number of persons in each group (ethnicity subgroups and gender subgroups - that had that score by the total number of people in that subgroup)
+  - At each score, calculate the pass rate percentage for each subgroup. (divide the number of persons in each group (ethnicity subgroups and gender subgroups - that had that score by the total number of people in that subgroup)
-.	Identify the highest percentage
+  - Identify the highest percentage
-.	Divide each of the other percentages by the higher percentage – if it is less than 80% than that group is adversely impacted.
+  - Divide each of the other percentages by the higher percentage – if it is less than 80% than that group is adversely impacted.
@@ Line 76: / Line 82: @@
 If you were to pretend that those were the only three groups – the 1.1% would be the highest percentage rate.
-.	If the passpoint were set at a score of 69.8, 0 Caucasian candidates out 16 Caucasian passed = 0%; 1/92 Black passed = 1.1%; 1/111 Hispanic passed = 0.9% passed.  (pretending those are the only 3 groups for demonstrative purposes)
+  - If the passpoint were set at a score of 69.8, 0 Caucasian candidates out 16 Caucasian passed = 0%; 1/92 Black passed = 1.1%; 1/111 Hispanic passed = 0.9% passed.  (pretending those are the only 3 groups for demonstrative purposes)
-.	The highest is 1.1% for Blacks
+  - The highest is 1.1% for Blacks
-.	Calculate the pass rates:
+  - Calculate the pass rates:
-a.	Caucasian 0/1.1 = 0% - less than 80% so there is Adverse Impact (thus the * next to it)
+    * Caucasian 0/1.1 = 0% - less than 80% so there is Adverse Impact (thus the * next to it)
-b.	Hispanic 0.9/1.1 = 81.8% - more than 80% so there is no Adverse impact (therefore no * next to it)
+    * Hispanic 0.9/1.1 = 81.8% - more than 80% so there is no Adverse impact (therefore no * next to it)
 A second example:
-.	For the score of 66.1 – 3/16 Caucasian passed = 18.75%; 6 out 92 Black passed = 6.52%; 5 out of 111 Hispanic passed = 4.50%
+  - For the score of 66.1 – 3/16 Caucasian passed = 18.75%; 6 out 92 Black passed = 6.52%; 5 out of 111 Hispanic passed = 4.50%
-.	 Highest percentage is 18.75% for Caucasian
+  - Highest percentage is 18.75% for Caucasian
-.	Calculate the pass rates
+  - Calculate the pass rates
-a.	Black = 6.52/18.75 = 34.8% - Less than 80%, so there is Adverse Impact
+    * Black = 6.52/18.75 = 34.8% - Less than 80%, so there is Adverse Impact
-b.	Hispanci = 4.5/18.75 = 24% - less than 80%, so there is Adverse Impact
+    * Hispanic = 4.5/18.75 = 24% - less than 80%, so there is Adverse Impact
-These files are calculating this for every single score.
+{{:adverseimpact.png?600|}}
 ==== Alternate Scores ====
@@ Line 107: / Line 112: @@
 We have the following systems loaded with values:
 ^System^AlternateBase^AlternateMean^AlternateStDev^
-|rue (Default)|?|-|-|
+|True (Default)|?|-|-|
 |Custom|?|0 or Calculated|0 or Calculated|
 |Z Scores|?|0|1|
@@ Line 165: / Line 170: @@
 |d|{{:stat_biserialcorrected_d.png?|}} \\ **ABS** function returns the **absolute value** (i.e. the modulus) of any supplied number. The syntax of the function is: ABS(number). where the number argument is the numeric value that you want the modulus of.|
 |Ordinal|{{:stat_biserialcorrected_d.png?|}} \\ **EXP** function in Excel **calculates** for the value of “e” raise to certain power of **integer**. “e” is a constant number which is equal to 2.71828182845904, the **natural logarithm** base. When it comes to the value of e, Excel uses a value of 2.718282.|
-||{{:stat_biserialcorrected.png?|}}|
+||{{:stat_biserialcorrected.png?200|}}|