Handout Week 9b: Standardization

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12 Terms

1
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How does standard deviation act as a ruler?

Finding the z-score (take the point, subtract mean, & divide by standard deiviation)

  • tells us how unusual the data point is

  • how many standard deiviations the point is from the mean

  • negative z-score: below the mean

  • positive z-score: above the mean

2
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What is standardizing?

Comparing individual data values to their mean, relative to their standard deviation

  • using the z (z-score) formula → the result is called standardized values

  • unitless → allows for comparison

  • z = 0.6 (not unusual)

  • z = 4.5 (very unusual)

<p>Comparing individual data values to their mean, relative to their standard deviation</p><ul><li><p>using the z (z-score) formula → the result is called standardized values</p></li><li><p>unitless → allows for comparison</p></li><li><p>z = 0.6 (not unusual)</p></li><li><p>z = 4.5 (very unusual)</p></li></ul><p></p>
3
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What happens to values when you standardize them (convert to z)?

There is no change in shape

  • standardizing shifts the mean to 0

  • rescales standard deviation to 1

<p>There is no change in shape</p><ul><li><p>standardizing shifts the mean to 0</p></li><li><p>rescales standard deviation to 1</p></li></ul><p></p>
4
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What happens if you add a constant to each value?

Location: all shifts by the same amount

Spread: ± a constant → no impact on spread

5
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What happens if you multiple or divide all the data values by a constant?

Location & spread: are divided/multiplied by the same value → changes spread

6
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What is the correlation coefficient formula?

A numerical measurement of strength of the linear relationship between explanatory & response variables

  • sum of all z scores of x & y multiplied by eachother

  • divide by number of data points - 1

<p>A numerical measurement of strength of the linear relationship between explanatory &amp; response variables</p><ul><li><p>sum of all z scores of x &amp; y multiplied by eachother</p></li><li><p>divide by number of data points - 1</p></li></ul><p></p>
7
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What are the 3 conditions for correlation?

  1. Quantitative variables condition → not categorical

  2. Straight enough condition →can calculate a correlation coefficient for any pair of variables (but it is only meaningful for linear associations)

  3. Outlier condition → outliers can distort correlation (rxy) dramatically (can change the sign)

  • calculate correlation with & without outlier

8
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What are the properties of correlation?

  • Unaffected by standardization (shift/rescaling)

  • are only meaningful for linear associations

  • the sign of rxy gives the direction of the association

  • correlation is always between -1 & 1

  • correlation near 0 is a weak association

9
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What are correlation tables?

Common format for summarizing linear correlations among a set of variables

  • useful when you have more than 2 quantitative variables

<p>Common format for summarizing linear correlations among a set of variables</p><ul><li><p>useful when you have more than 2 quantitative variables</p></li></ul><p></p>
10
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What is a lurking variable?

A hidden variable that stands behind a relationship & is the true determinant by affecting both variables

11
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How do you calculate Xbar?

Sum of all possibilities x probabilities

  • same as finding expected value

<p>Sum of all possibilities x probabilities</p><ul><li><p>same as finding expected value</p></li></ul><p></p>
12
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What is the difference between a distribution & a model?

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