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Ch 5: Variability (skip p. 151-162)

Ch 5: Variability (skip p. 151-162). Wed, Feb 18 th , 2004. Variability . Describes spread/diversity of the scores in distribution Options: range, interquartile range, standard deviation, variance Range: difference betw highest & lowest scores.

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Ch 5: Variability (skip p. 151-162)

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  1. Ch 5: Variability(skip p. 151-162) Wed, Feb 18th, 2004

  2. Variability • Describes spread/diversity of the scores in distribution • Options: range, interquartile range, standard deviation, variance • Range: difference betw highest & lowest scores. • Interquartile Range (IQR): width of middle 50% of distribution

  3. (cont.) • IQR: Q1 is 25% percentile (score for which 25% scores fall below it); Q3 is 75% percentile • IQR = Q3 – Q1 • Less affected by outliers than range • Box plot (in book) graphs the range, 25%, median, & 75% scores

  4. Variance & SD • Variance – average of squared deviations from the mean • Based on deviation scores, y-ybar, then square, and take average • Unit is squared original unit, so hard to interpret • Standard deviation – average deviation from mean (square root of variance) • Based on deviation scores  averaged • SD calculated in original unit, so easier to interpret

  5. Calculating Variance, SD • 1) Start by finding “Sum of Squares” (SS) SS =  (y-ybar)2 That is, sum up each scores’ (y) squared deviation from the mean (ybar). Example: (8, 12, 35, 17, 22, 11), N = 6 Ybar (mean) = 17.5 SS = (8-17.5)2 + (12-17.5)2 + (35-17.5)2 + (17-17.5)2 + (22-17.5)2 + (11-17.5)2 = 489.5 • Note – must square the deviations, otherwise they would sum to 0

  6. (cont.) • 2) After finding SS, find variance: S2y = SS / N-1 (for sample variance, for population variance, use N as denom) Here, S2y = 489.5 / 6-1= 97.9 • 3) Find standard deviation: Sy = sqrt (SS / N-1) …or sqrt(S2y ) Here, Sy = sqrt (489.5 / 6-1) = 9.89

  7. Properties of Standard Dev • 1) Add/subtract a constant from each score  doesn’t change the standard deviation • The mean will change by that constant, but the spread of the scores won’t change • 2) Mult/divide each score by constant & standard dev changes by the same constant • Because the mean will change by that constant, your deviation scores will change consistently too

  8. Notes on Lab 10 • SPSS: follow step-by-step instructions for using menus…note: • To add constant to each score in data, use “Compute” function • Transform  Compute Window pops up…under “Target variable” come up w/new variable name (addthree), for “Numeric Expression” – choose original variable from list (e.g., age) then type in transformation you want (e.g., age +3), hit OK SPSS will add a new column in dataset with this new transformed variable

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