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# Z score

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standard distribution based scoring technique and implementation

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### Z score

1. 1. Z-Score Standard distribution based scoring technique and implementation on scoring SMA BU Gading 2007 Prepared by febru354@yahoo.com 1
2. 2. Standard Deviation • The standard deviation is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. – If many data points are close to the mean, then the standard deviation is small; – if many data points are far from the mean, then the standard deviation is large. – If all the data values are equal, then the standard deviation is zero. SMA BU Gading 2007 Prepared by febru354@yahoo.com 2
3. 3. Which the better one ? SMA BU Gading 2007 Prepared by febru354@yahoo.com 3
4. 4. Standard probability SMA BU Gading 2007 Prepared by febru354@yahoo.com 4
5. 5. Z-Score • In statistics, the standard score, also called the z-score or normal score, is a dimensionless quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing. • The standard score indicates how many standard deviations an observation is above or below the mean. It allows comparison of observations from different normal distributions, which is done frequently in research. • The standard score is not the same as the z-factor used in the analysis of high-throughput screening data, but is sometimes confused with it. SMA BU Gading 2007 Prepared by febru354@yahoo.com 5
6. 6. Z-Score Cont’d • The quantity z represents the distance between the raw score and the population mean in units of the standard deviation. z is negative when the raw score is below the mean, positive when above. SMA BU Gading 2007 Prepared by febru354@yahoo.com 6
7. 7. Z-Score Cont’d Sample / small data / part of population Total population / global SMA BU Gading 2007 Prepared by febru354@yahoo.com 7
8. 8. Z-Score Scenario • Raw  Z-Score  Z- Std  SUM • Raw  Z-Score ======== Global Expected Mean • One Parameter Only : • Expected upgrade >= 95% X (Max raw + Mean) Matured Scores SMA BU Gading 2007 Prepared by febru354@yahoo.com 8
9. 9. Step 1 + 2 SMA BU Gading 2007 Prepared by febru354@yahoo.com 9
10. 10. Step 3 + 4 SMA BU Gading 2007 Prepared by febru354@yahoo.com 10
11. 11. Z-Score Effect • Distribution is unchanged but its translated in order to be centered on the value 0. • Proofed : SUM ( Z-Score ) = 0 SMA BU Gading 2007 Prepared by febru354@yahoo.com 11
12. 12. SMA BU Gading 2007 Prepared by febru354@yahoo.com 12
13. 13. That’s all Thanks for your attentions febru@soluvas.com febru.soluvas.com SMA BU Gading 2007 Prepared by febru354@yahoo.com 13