Measures of Spread 1. Range: the distance from the lowest to the highest score * Problem of clustering differences ** Problem of outliers.

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Presentation transcript:

Measures of Spread 1. Range: the distance from the lowest to the highest score * Problem of clustering differences ** Problem of outliers

2. Interquartile Range *omits the upper and lower 25% of scores *eliminates the effect of extreme scores *trimmed samples *loss of information Data Set I: 8, 8, 9, 10, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14,14, 15, 15, 16, 17 Range = 9 Interquartile Range = 3 Data Set II: 1, 2, 3, 10, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14,14, 15, 21, 25, 30 Range = 29 Interquartile Range = 3

Average Deviations: y: 2, 3, 4, 3, 4, 1, 4 = 3 The average deviation will always be zero! Read: The sum of - y minus the mean of y, divided by n example data set: = = 0

Variance: Standard Deviation: These are here defined as descriptive statistics. average of the summed, squared-deviations about the mean the square root of the average of the summed squared deviations about the mean

As inferential statistics See the difference

Influence of extreme scores on variance. Note: d = difference score the difference between a given score and the mean. Y: 1, 2, 19, 5, 8, 7 A score of 7 (d squared = 0) contributes no units to the variance. A score of 5 contributes 4 units to the variance. A score of 2 contributes 25 units to the variance. A score of 19 contributes 144 units to the variance. Extreme scores contribute disproportionately more. Watch out for OUTLIERS!