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When calculating the 3 month rolling average, the system processes the over 50% vendors based on the values in the state business rules USECOSTCONTAINMENTOFOVER50VENDORS and DAYTOCALCULATEOVER50VENDORPRICES in the STATEBUSINESSRULES table. Refer to the Over 50% Vendor Report topic for more information.
Sum the paid amounts from FIs redeemed over the last twelve weeks (current system date minus twelve weeks).
Caveats: The goal is to include all WIC approved food benefits issued on the FI into the calculation. The clients are instructed to select least expensive items and the vendors are trained accordingly. At one standard deviation, the paper FI Type food items really need to be grouped on a single FI in a manner such that the items are habitually redeemed in full more often than not. If more than half of clients choose to redeem less than the full amount of fish, fruits/vegetables, and beans, then it is possible that a FI's maximum price would be less than the redeemed amount for a client who redeems the full set of food benefits on the same FI type.
We may need to provide a variable allowing the user to choose a 1, 2, or 3 standard deviations to apply. By mathematical convention, applying one standard deviation of its average, 68.3% of the data set is generally included. At two standard deviations, 95.4% within plus/minus these two standard deviations of your average is generally included. At three standard deviations, 99.7% of your price data is generally included.
Sum the paid amounts from EBTs (FICs) redeemed over the last twelve weeks (current system date minus twelve weeks).
Caveats: The goal is to include all WIC approved food benefits into the calculation. The clients are instructed to select least expensive items and the vendors are trained accordingly. One standard deviation may well cover the prices at the food item level. It depends upon how disparate the price variance is in the WIC approved manufacturers products, the generic milk and juice compared to the WIC approved name brands.
We may need to provide a variable allowing the user to choose a 1, 2, or 3 standard deviations to apply. By mathematical convention, applying one standard deviation of its average, 68.3% of the data set is generally included. At two standard deviations, 95.4% within plus/minus these two standard deviations of your average is generally included. At three standard deviations, 99.7% of your price data is generally included.
This process is run each time EOD is run.
Average Price = Mean Redemption Amount over twelve weeks
Maximum Price = Redemption Amount over twelve weeks plus one standard deviation
A normal distribution of data means that most of the examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other.
A measure describing how close members of a data set are in relation to each other. The standard deviation is kind of the "mean of the mean" (average variance of an average), and often can help you find a pattern in the data. The standard deviation can be found by taking the square root of the variance. If the variance is 25, the standard deviation is 5.
One of two equal factors of a given number. For example, 5 is a square root of 25 because 5*5 = 25. Another square root of 25 is -5 because (-5)*(-5) = 25. The +5 is called the principle square root of 25.
Biased variance and standard deviation
Unbiased variance and standard deviation
Biased or Unbiased Variance Method:
For the Unbiased Method = Divide the result by the count of items in the set of data minus 1 item (standard variance value)
For the Biased Method = Divide the result by the count of items in the set of data (forcing a result of a lower variance value or a deviated variance)
The Unbiased Variance method provides a common deviation value. You should use the Unbiased Method, because it is the standard default method, unless there is a business reason to understand and use a deviated variance
In both variance method examples in the document, you begin with all three items in the data set count to produce the mean or average value.
To determine the biased variance value, use the full count of the items in the data set that were used to calculate the mean (average). Because the Biased Variance Method results in a lower variance value (a deviated rate below the standard variance), the data set count is not reduced by one.
X = One value in the set of data
(The redeemed amount)
Avg(X) = The average of all the values x in your set of data, the mean
Paper FIs: (the sum of the redeemed amounts for the last twelve weeks by peer group and food instrument type)
EBT: (the sum of the redeemed amounts for the last twelve weeks by peer group and food item)
n = the number of values (item count) in the set of data
Business Rule:
A State business rule defines the number of standard deviation to apply to the mean. If the State business rule EOD_3MONTH_ROLLING_AVG_NBR_STD_DEVIATIONS = "1" then one standard deviation is applied.
A State business rule defines the variance method use when calculating the standard deviation. If the State business rule EOD_3MONTH_ROLLING_AVG_VARIANCE_METHOD = "B" then the biased variance method is applied.
Count the number of items in the set of data for the beginning value of n.
Find the average value of all items in the set of data. Average Price = Mean Redemption Amount over twelve weeks
For each value x, subtract the overall avg (x) from each x. When result is negative it means that x is below the mean.
Multiply that result by itself (otherwise known as determining the square of that value). The result is positive.
Sum up all those positive squared values.
For the Biased Method = Divide that result by (n).
For the Unbiased Method = Divide that result by (n-1).
Find the square root of that last number, the variance, for the value of the standard deviation of your set of data. The standard deviation is the positive square root of the variance, the mean of the mean.
Maximum Price = Average Price plus one standard deviation.
For the data set example {1, 2, 3} there are a total of three items in the set of data, therefore the value of n begins at 3
n=3 for the total of three items in the set of data
1+2+3 = 6 for the total of the value of all items in the set of data 6 / 3 = 2 to find the average value of the set of data
1-2 = -1; 2-2 = 0; 3-2 = 1
-1 * -1 = 1; 0 * 0 = 0; 1 * 1 = 1
1 + 0 + 1 = 2
Biased Method: 2 / 3 =.666666666 or.667
Unbiased Method: 2 / 2 = 1
Biased Method: the square root of.667 is.8168 rounded to 82 cents Unbiased Method: the square root of 1 is 1
Biased Method: 2 +.82 = 2.82 (results in a lower variance value) Unbiased Method: 2 + 1 = 3 (results in a standard variance value)
The biased variance is:
(1-2)2 + (2-2)2 + (3-2)2
¾¾¾¾¾¾¾¾¾¾¾ =.666666666 or.667
(3)
The standard deviation is the square root of the biased variance, which equals:
_____
Ö 0.667 =.8168
The mean plus one standard deviation for the biased variance equals:
2 +.8168
The unbiased variance is:
(1-2)2 + (2-2)2 + (3-2)2
¾¾¾¾¾¾¾¾¾¾¾ = 1
(3-1)
The standard deviation is the square root of the unbiased variance, which equals:
_____
Ö 1 = 1
The mean plus one standard deviation for the unbiased variance equals:
2 + 1
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Software Version: 2.40.00