Chapter 5: Measures of Variability

Question 1

Variability (Dispersion)

Answer 1

• Degree to which an individual data point is distributed around the mean
• Statistics attempts to sort out what the ‘causes’ of variability in behaviour are

Question 2

Range: median

Answer 2

• Distance from lowest –> highest score
• -Influenced by outliers
• -(Xf - Xi)
• Not a good measure of spread b/c extremes (high/ low) can have big effect

Question 3

Interquartile Range (IQR): median

Answer 3

• 2 inner quartiles/ center most 50% of population
• -Range is taken w these groups to eliminate outliers
• Is a trimmed stat b/c it is a stat calculated based on a trimmed sample
• Goal = eliminate outliers that are due to measurement errors

Advantage
-Based on middle 50%, less influenced by extreme values

Disadvantage

• Discards too much data
• -Creates a very trimmed sample

Question 4

Trimmed Sample

Answer 4

Samples with a % of extreme scores removed

Question 5

Trimmed Statistics

Answer 5

Statistics calculated based on trimmed samples

Question 6

Sample Variance (s^2): mean

Answer 6

Sum of squared about the mean, divided by (N-1)

-Is bias unless calculated correctly

Question 7

Population Variance

Answer 7

Variance of a population is usually estimated, rarely computed
-A difference in variance reflects the differences in distribution

Question 8

Standard Deviation: mean

Answer 8

• +’ve square root of the variance
• Measure of average of the deviations of each score from the mean
• -How much, on average, scores differ from the mean

Question 9

Bias

Answer 9

-Proportion of statistic whose range average isn’t a parameter it estimates

Question 10

Degrees of Freedom (df)

Answer 10

# of independent pieces of information remaining after estimating 1+ populations
-(N-1) = df

Question 11

Expected Value (E)

Answer 11

Long-range average of a statistic over repeated samples

Question 12

Boxplot: median

Answer 12

• Graphical representation of the dispersion of a sample & extreme scores
• Hinges: scores cutting off top & bottom 1/4
• H-spread: range b/w hinges (Hf - Hi)
• Median: line inside the box
• Whiskers: line indication = 1.5xH-spread
• -If biggest/ smallest score = less than a whisker, the whisker line should only extend to that value
• Outliers: any score beyond the whisker

Question 13

Quartile Location

Answer 13

[ (Median Location +1) / 2 ]

-Location of the quartile in an ordered series

Question 14

Whisker

Answer 14

Line from top & bottom of the box to the farthest point that’s no more than 1.5X the IQR from the box

Question 15

Winsorized Variance

Answer 15

Variance of a Windsor sample

-Take out ie. greatest & lowest 20% & replace with the lowest/ highest values remaining

Question 16

Winsorized Standard Deviation

Answer 16

Standard deviation of a winsorized sample

Question 17

Average Deviation

Answer 17

• Sum of the difference b/w scores & mean
• We don;t use this b/c the -ve #s cancel out
• -Therefore we square it, get rid of -ve deviations & obtain variance
• -We then sqr root variance & obtain standard deviation
• –> v = s^2