1. Variability Chapter 4

2. What is it? • How much difference there is from person to person • How spread out scores are • No variability = all scores are the same

3. Why do we care? • Less variability = more know about the population based on the sample • Less variability = more any one person can tell you about the group that he or she is from

4. To keep in mind • Two groups of scores can have the same mean, but different amounts of variability • Two groups of scores can have different means, but the same amount of variability •  mean and variability measure two different things

5. Quantifying variability • Range = number of scores between the highest and lowest scores • Problem = only the highest and lowest scores matter • Outlier high range • Can use interquartile range instead, which just addresses number of scores between highest and lowest, once top and bottom 25% have been lopped off • Still not as good of a measure as we’d like to use

6. Standard Deviation • Ideal measure of variability • Tells about average distance of scores from mean • i.e., how much do scores deviate from the mean of the group • Keep in mind: standard deviation tells about all the scores

7. Calculating standard deviation • Most straightforward: • Take each score, subtract the mean • Take the mean of those difference scores • Problem: always get zero

8. To avoid zero • First calculate variance (average squared distance of each score from the mean) • 1. take each score, subtract the mean • 2. square that difference • 3. add up across all scores •  sum of squares (sum of the squared difference between each score and the mean, SS) • 4. divide

9. Divide by what? • Depends on who you have information from • If you have information from all the people you care about, divide by the total number of scores you have (n) •  s2 = variance • If you have information from a sample, but want to estimate variability for the population, divide by one less than the total number of scores you have (n-1) • n-1 = df = degrees of freedom •  s2 or SD2 = variance

10. What about standard deviation? • To get from variance to standard deviation, want to get from average squared distance between each score and the mean to the average distance between each score and the mean •  regardless of whether using formula for population or for sample, take the square root •  s or s (or SD)

11. What is s, or SD, exactly? • Estimate of how much variability there is in the population, based on how much variability there is in the sample • Will not be exactly the same, but will give a good estimate

12. Be sure to keep in mind • What, in English, are: • Sum of squares • Variance • Standard deviation • How to calculate, for population, and to estimate in a population based on the sample • Symbols • What it all means