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Intro to Stats

Intro to Stats. Variability. Variability. Reflects the degree to which scores differ from one another Usually in reference to the mean value A measure of the central tendency and variability give an efficient overview of a set of data. Range. Most general measure of variability

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Intro to Stats

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  1. Intro to Stats Variability

  2. Variability • Reflects the degree to which scores differ from one another • Usually in reference to the mean value • A measure of the central tendency and variability give an efficient overview of a set of data

  3. Range • Most general measure of variability • Imprecise and VERY sensitive to extreme scores • Subtract lowest score from highest score • r = (H – L)

  4. Practice • Data: 1, 5, 2, 1, 2, 12, 3, 2, 4 • r = (h – l)

  5. Standard Deviation (SD) • The average variability in a set of scores • (the average distance from mean) • s = Σ(X-X)2 (also known as the sum of squares) n – 1 X = each individual score X = mean of all scores n = sample size

  6. Practice • s = Σ(X-X)2 (also known as the sum of squares) n – 1 Data: 1, 5, 2, 1, 2, 12, 3, 2, 4; Mean = 3.56

  7. Why n – 1? • It’s more conservative • Forces the denominator to be smaller and to estimate more variability • When we run inferential analyses, this means we are less likely to think there is a difference between 2 groups when there actually isn’t • The difference based on using n or n-1 decreases as the sample gets bigger (and more similar to the population)

  8. Standard Deviation (SD) • The larger the SD, the more different your scores are from one another • The SD is sensitive to extreme scores, just like the mean • Can be used to identify scores that are unusually far from the mean

  9. Variance • Square of the standard deviation • s2 = Σ(X-X)2 n – 1 X = each individual score X = mean of all scores n = sample size

  10. SD vs. Variance • SD is in the original units; variance is in units squared • Squared units are typically difficult to interpret meaningfully (much less communicate) • Variance is important for later inferential statistics though!

  11. The importance of variability • Without variability, everyone is the same • So there’s nothing to explain! • Can be caused by poor methods • Show up in descriptive statistics • Truncated ranges • Small standard deviations

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