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PSYC 2530 (16)

Ch. 4 - Variability

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PSYC 2530
Anne Russon

Ch. 4 - Variability Wednesday, September 19, 2013:06 PM Variability - Beyond typical value --> typical dispersion - Intuition: spread, range, spread, "more or less" - Problem: ○ Increase in variability =  Decrease in predictability  Decrease in homogeneity  Increase in Heterogeneity - Goal : measure spread of scores in a distribution - Descriptive : degree to which scores in a sample are spread out or clustered - Inferential : how accurately any one score or sample represents the population ○ Small V = scores clustered --> any score gives a good representation of the population ○ Large V = scores widely spread --> a few extreme scores can give a distorted picture of the general population MeasuringVariability - Variability can be measured by the ○ Range ○ Standard deviation & variance - Between scores, variability measures distance Range - Total distance spanned by sample scores - "rough" (approximation, unrefined) Only reflects extremes (typical = middle) ○ Only reflects extremes (typical = middle) ○ Unstable - Fast and easy to calculate - Value (e.g., winter temperature) StandardDeviation - "Normal", "common", "typical", dispersion ○ e.g., 7 +- 2, "more or less" - Try average distance between scores & mean Calculate"average"distance - Sum deviations for each score (value -- mean) Sum of squared deviationsscore to mean? Variance - Sum of Squares (SS): good measure of overall variability, but dependenton the number of scores - So, we calculate the average variability: SS/(n-1) 2 - This value is called the variance (s ) Note: N-1, not N StandardDeviation - Sample variance : s 2 - Population variance : σ 2 StandardDeviation:calculation StandardDeviation:calculation StandardDeviationProperties - Add constant to every score in a sample? ○ Standard deviation does not change ○ Visualize histogram: adding a constant moves every score, whole package just shifts - Multiply each score by a constant? ○ Standard deviation is multiplied by the same constant ○ This multiplies the distance between scores Usi
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