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Statistics Basics
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Total Error = Sum of Deviances
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SUM(x
i
– mean)
•
Example: 10
8
8
9
5
mean = 8
10 – 8 =2
8 – 8 = 0
8 – 8 = 0
9 – 8 = 1
5 – 8 =  3
SUM = 0
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Sum of deviances is always equal to 0
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Since this is not a good measure of variability, must do sum of squared errors
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Sum of Squared Errors
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Also referred to as SS
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SUM(x
i
– mean)
2
•
example: using same numbers
10 – 8 = 2
2
= 4
8 – 8 = 0
2
= 0
8 – 8 =0
2
= 0
9 – 8 =1
2
= 1
5 – 8 = 3
2
=9
SUM = 14
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good measure of accuracy, but it is dependent upon the size of the data set
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must control for size of data set
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Variance
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SS/ (N1)
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Example:
14/4 = 3.5 units squared
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Gives answer in units squared
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(N1) = degrees of freedom
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Standard Deviation
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SQUARE ROOT(variance) = SQUARE ROOT(SS/(N1)
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Example:
SQUARE ROOT(3.5) = 1.87
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Defines the measure of variation in a given data set
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The smaller the standard deviation, the more accurate the mean is
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 Spring '08
 Hoffman
 Statistics, Normal Distribution, Standard Deviation

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