The document discusses z-scores and standardization. A z-score is a statistic that indicates how many standard deviations an observation is above or below the mean. It is calculated by subtracting the population mean from an individual raw score and dividing by the population standard deviation. This process converts raw scores to standardized z-scores that allow comparison across different data sets and distributions. The document provides examples of calculating z-scores and discusses how standardization keeps the distribution unchanged but centers it on a value of 0.

1. Z-Score
Standard distribution based
scoring technique and
implementation on scoring
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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.
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3. Which the better one ?
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4. Standard probability
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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.
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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.
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7. Z-Score Cont’d
Sample / small data / part of population
Total population / global
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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
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9. Step 1 + 2
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10. Step 3 + 4
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11. Z-Score Effect
• Distribution is unchanged but its translated
in order to be centered on the value 0.
• Proofed : SUM ( Z-Score ) = 0
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13. That’s all
Thanks for your attentions
febru@soluvas.com
febru.soluvas.com
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