Variability

1
Variability

• Chapter 4

2
What is it?

• How much difference there is from person to
  person
• How spread out scores are
• No variability all scores are the same

3
Why do we care?

• Less variability more know about the population
  based on the sample
• Less variability more any one person can tell
  you about the group that he or she is from

4
To keep in mind

• Two groups of scores can have the same mean, but
  different amounts of variability
• Two groups of scores can have different means,
  but the same amount of variability
• ? mean and variability measure two different
  things

5
Quantifying variability

• Range number of scores between the highest and
  lowest scores
• Problem only the highest and lowest scores
  matter
• Outlier ? high range
• Can use interquartile range instead, which just
  addresses number of scores between highest and
  lowest, once top and bottom 25 have been lopped
  off
• Still not as good of a measure as wed like to use

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Standard Deviation

• Ideal measure of variability
• Tells about average distance of scores from mean
• i.e., how much do scores deviate from the mean of
  the group
• Keep in mind standard deviation tells about all
  the scores

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Calculating standard deviation

• Most straightforward
• Take each score, subtract the mean
• Take the mean of those difference scores
• Problem always get zero

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To avoid zero

• First calculate variance (average squared
  distance of each score from the mean)
• 1. take each score, subtract the mean
• 2. square that difference
• 3. add up across all scores
• ? sum of squares (sum of the squared difference
  between each score and the mean, SS)
• 4. divide

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Divide by what?

• Depends on who you have information from
• If you have information from all the people you
  care about, divide by the total number of scores
  you have (n)
• ? s2 variance
• If you have information from a sample, but want
  to estimate variability for the population,
  divide by one less than the total number of
  scores you have (n-1)
• n-1 df degrees of freedom
• ? s2 or SD2 variance

10
What about standard deviation?

• To get from variance to standard deviation, want
  to get from average squared distance between each
  score and the mean to the average distance
  between each score and the mean
• ? regardless of whether using formula for
  population or for sample, take the square root
• ? s or s (or SD)

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What is s, or SD, exactly?

• Estimate of how much variability there is in the
  population, based on how much variability there
  is in the sample
• Will not be exactly the same, but will give a
  good estimate

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Be sure to keep in mind

• What, in English, are
• Sum of squares
• Variance
• Standard deviation
• How to calculate, for population, and to estimate
  in a population based on the sample
• Symbols
• What it all means