Monday

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Monday October 8 Deeper Understanding of
Standard Deviation Data Transformation
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Life Expectancy

• If you are male, your mean life expectancy at
  this time is 76.
• If you are female, your mean life expectancy is
  82.

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Life Expectancy

• If you are male, your mean life expectancy at
  this time is 76.
• If you are female, your mean life expectancy is
  82.
• Is this a small, medium, or big difference?

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Life Expectancy

• If you are male, your mean life expectancy at
  this time is 76.
• If you are female, your mean life expectancy is
  82.
• Is this a small, medium, or big difference?
• What is s6? s12? s18?

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Standard Deviation in Words

• The standard deviation is an expression of the
  average deviation of all the data points in the
  batch of data from the mean of the batch
  (expressed in the same unit of measurement as
  that for the mean)

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_
X
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Data Transformation Last week, we already saw
one kind of data transformation Percentile
Rank Converting scores to percentile ranks
allows comparison across measures with different
metrics. For example, you can ask if your
percentile rank in height (inches) predicts your
percentile rank in weight (pounds).
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Data Transformation Last week, we already saw
one kind of data transformation Percentile
Rank Converting scores to percentile ranks
allows comparison across measures with different
metrics. For example, you can ask if your
percentile rank in height (inches) predicts your
percentile rank in weight (pounds).
Transforming interval scores to ordinal
(percentile rank) scores lost information about
the shape of the distribution.
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Data Transformation Last week, we already saw
one kind of data transformation Percentile
Rank Converting scores to percentile ranks
allows comparison across measures with different
metrics. For example, you can ask if your
percentile rank in height (inches) predicts your
percentile rank in weight (pounds).
Transforming interval scores to ordinal
(percentile rank) scores lost information about
the shape of the distribution. The Z-score
transformation converts scores to a standard
format, with a mean of 0 and a standard deviation
of 1, while preserving the shape of the
distribution.
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Z-score transformation
_
Xi - X
Zi
?
Converts scores into the distance in standard
deviation units from the mean, with negative
values being below the mean and positive values
being above the mean.
_
Z 0, ?z1
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• Because z-scores are in standard units
• you can compare positions across different
  variables that use different units of measurement
  (you can compare apples with oranges!)
• you can quickly see if the position of an
  individual relative to the distribution is
  similar or different.

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T-Score converts Z by multiplying by 10 and
adding 50
T 10Z 50
This distribution has a mean of 50 and a standard
deviation of 10. This conversion helps those who
are frightened by negative numbers and decimal
points.
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SATs and GREs are transformed to have a mean of
500 and a standard deviation of 100. SAT
100Z 500
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