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Variability. Chapter 4. What is it?. How much difference there is from person to person How spread out scores are No variability = all scores are the same. Why do we care?. Less variability = more know about the population based on the sample

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Variability l.jpg

Variability

Chapter 4


What is it l.jpg
What is it?

  • How much difference there is from person to person

  • How spread out scores are

  • No variability = all scores are the same


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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


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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


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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 we’d 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


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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


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