Measures of Variability
Variability Measure of the spread or dispersion of a set of data 4 main measures of variability –Range –Interquartile range –Variance –Standard deviation
Range Difference between high and low scores Provides estimate of variability Very unstable –Changes radically if extreme scores are present in the data set
Interquartile Range (IQR) Difference between the raw scores at the 75th and 25th percentile points –IQR = Q 3 - Q 1 More interested in the middle scores than in the extreme scores –Only considers middle half of data set –Not affected by scores at extreme ends
Variance Determines the distance of each raw score from the mean of the data Deviation –d
Variance Average of the squared deviations
Standard Deviation Squaring of deviation scores can cause problems Need to bring variance into line with other variability measures Standard deviation –A measure of the spread of the values in a parametric data set standardized to the scale of the unit of measurement of the data –Square root of the average of the squared deviations from the mean
Standard Deviation
Standard Deviation of a Population Definition method Can be cumbersome and lengthy procedure –Especially when N is large –Increased probability of mathematical error
Raw Score Method Algebraic manipulation of definition method to allow for the use of raw scores Simpler to apply –Squaring and summing of raw scores
Calculating Standard Deviation for a Sample Sample is drawn from the population –Sample smaller than population –Sample should be representative of the population Variability of sample is rarely as large as that of the population Correction factor needed in equation is needed to estimate the SD for the population from the sample
Calculating Standard Deviation for a Sample Equations already presented assume entire population has been sampled –Error occurs when using these equations for a sample Degrees of freedom –Number of values in a data set that are free to vary –Correction factor N-1
Equations Definition formula Raw score method