Part II Sigma Freud and Descriptive Statistics Chapter 3 Vive La Différence: Understanding Variability

Why Variability Is Important How different scores are from one particular score (usually the mean)? – Spread – Dispersion

Measures of Variability Three types of variability – Range – Standard Deviation – Variance Typically reported together – Average – Variability

Computing the Range Most general estimate of variability Two types: – Exclusive Range r = h - l – Inclusive Range r = h – l + 1

Computing the Range Data: 98, 86, 77, 56, 48 h 98highest score - l- 48lowest score r 50range

Types of Range-Like Things Range Mid-range – midpoint of range Interquartile range – range between 1 st & 3 rd quartiles Semi-interquartile range – midpoint of interquartile range Studentized range – range expressed in standard deviations

Computing Standard Deviation Standard deviation (s or SD) - most frequently reported measure of variability s or SD = average amount of variability in a set of scores

Computing Standard Deviation by Hand 1. List each score

Computing Standard Deviation by Hand 2. Compute the Mean

Computing Standard Deviation by Hand 3. Subtract the mean from each score 88 – 6 = – 6 = – 6 = – 6 = – 6 = – 3 = -3 Sum0

Computing Standard Deviation by Hand 4./5. Square each individual difference and sum 88 – 6 = +2+2 x +2 = – 6 = +2+2 x +2 = – 6 = +2+2 x +2 = – 6 = +1+1 x +1 = – 6 = 00 x 0 = 0 66 – 6 = 00 x 0 = 0 55 – 6 = -1-1 x -1 = – 6 = -1-1 x -1 = – 6 = -2-2 x -2 = – 3 = -3+3 x +3 = +9 Sum028

Computing Standard Deviation by Hand 6. Divide the sum by n – 1 7. Compute the square root of 3.11

Using Excel’s STDEV.S Function

The Computation of the Standard Deviation Using the STDEV.S Function Using Excel’s STDEV Function

Why n – 1? The standard deviation is intended to be an estimate of the POPULATION standard deviation – We want it to be an unbiased estimate – Subtracting 1 from n artificially increases the SD A conservative estimate of the population

Comparing the STDEV.S and STDEV.P Functions

Things to Remember… Standard deviation is the average distance from the mean The larger the standard deviation, the greater the variability Standard deviation is sensitive to extreme scores (it is just an Average after all)

Computing Variance Variance = standard deviation squared

Using Excel’s VAR.S Function

Comparing the VAR.S and VAR.P Functions

Standard Deviation or Variance Standard deviation is stated in original units Variance is stated in units that are squared Which is easier to interpret???

 Measures of variability help understand what a distribution of data points looks like.  Use to distinguish distributions from one another and describe a collection of data points. Summary