STATISTICAL APPLICATIONS FOR PATIENT ORIENTED PRIMARY HEALTHCARE RESEARCH
|Concepts of Variance|
In Quantitative Methods we are interested in the spatial
relationship between responses within a set of numbers.
In Quantitative Methods we measure the distance between any individual's score from the estimated mean (average score as a measure of central tendency), as demonstrated in the following example.
The term variability is used to describe the differences between observed scores and measures of central tendency within a distribution of scores.
Figure 4.2 Formula to compute variance for a population
The formula to compute variance for a sample is
shown in Figure 4.3 below:
Figure 4.3 Formula to compute variance for a sample
In a general sense, variance is computed by:
The term variance can best be described as the average of the squared deviations of observations from the mean.
Figure 4.4 (i) Formula to compute standard deviation for a population
Figure 4.4 (ii) Formula to compute standard deviation for a sample
In Quantitative Methods we often consider the spreads of distributions and the shape of
distributions. Estimates of difference between an individual's score and the measure of
central tendency, the shape of the distribution, and the size of the distribution, are all elements of
Figure 4.5 Formula to compute Skewness
A negative skewness score indicates a negatively skewed distribution, while a positive skewness score indicates a positively skewed distribution. Examples of skewed distributions are shown in Figures 4.6, 4.7 and 4.8 below.
Figure 4.6 Illustration of negative skewness
Notice the tailing off of the distribution toward negative infinity
Figure 4.7 Illustration of a normal distribution (no skewness)
Notice the symmetry of the distribution, there is no tailing-off toward either negative or positive infinity
Figure 4.8 Illustration of positive skewness
Notice the tailing off of the distribution toward positive infinity
In most applications, the raw skewness is not used. Rather the reader is directed to the "standardized skewness" as shown in the formula below.
Figure 4.9 Formula to compute kurtosis
Examples of kurtosis are shown in
Figures 4.10, 4.11 and 4.12 below.
Figure 4.10 Illustration of a platykurtic distribution
Notice the flatness of the distribution (remember the term platy refers to flat). In order to achieve a platykurtic distribution, all scores within the distribution are unique.
Figure 4.11 Illustration of a mesokurtic distribution
Figure 4.12 Illustration of a leptokurtic distribution
Notice the Peakedness of the distribution (remember the term lepto refers to leaping). In order to achieve a leptokurtic distribution, all scores within the distribution are located close to the mean. There is very little deviation of scores from the measure of central tendency within the distribution.
In most applications, the raw kurotsis is not used. Rather the reader is directed to the "standardized kurtosis" as shown in the formula below.
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Professor William J. Montelpare, Ph.D.,