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PPA 415 – Research Methods in Public Administration. Lecture 4 – Measures of Dispersion. Introduction. By themselves, measures of central tendency cannot summarize data completely.
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PPA 415 – Research Methods in Public Administration Lecture 4 – Measures of Dispersion
Introduction • By themselves, measures of central tendency cannot summarize data completely. • For a full description of a distribution of scores, measures of central tendency must be paired with measures of dispersion. • Measures of dispersion assess the variability of the data. This is true even if the distributions being compared have the same measures of central tendency.
Introduction • Measures of dispersion discussed. • Index of qualitative variation (IQV). • The range and interquartile range. • Standard deviation and variance.
Index of Qualitative Variation • Used primarily for nominal variables, but can be used with any variable with a frequency distribution. • Ratio of amount of variation actually observed in a distribution of scores to the maximum variation that could exist in that distribution.
Index of Qualitative Variation • Maximum variation in a frequency distribution occurs when all cases are evenly distributed across all categories. • The measure gives you information on how homogeneous or heterogeneous a distribution is.
Range and Interquartile Range • Range: the distance between the highest and lowest scores. • Only uses two scores. • Can be misleading if there are extreme values. • Interquartile range: Only examines the middle 50% of the distribution. Formally, it is the difference between the value at the 75% percentile minus the value at the 25th percentile.
Range and Interquartile Range • Problems: only based on two scores. Ignores remaining cases in the distribution.
The Standard Deviation • The basic limitation of both the range and the IQR is their failure to use all the scores in the distribution • A good measure of dispersion should • Use all the scores in the distribution. • Describe the average or typical deviation of the scores. • Increase in value as the distribution of scores becomes more heterogeneous.
The Standard Deviation • One way to do this is to start with the distances between every point and some central value like the mean. • The distances between the scores are the mean (Xi-Mean X) are called deviation scores. • The greater the variability, the greater the deviation score.
The Standard Deviation • One course of action is to sum the deviations and divide by the number of cases, but the sum of the deviations is always equal to zero. • The next solution is to make all deviations positive. • Absolute value – average deviation. • Squared deviations – standard deviation.
