1. Central Tendency Mean: what most call “average”
Describes a distribution through numerical account of the centre of a distribution.
Mean: what most call “average”
> res<-c(21,18,12,31,23,31,44,7)
> mean(res)
[1]
SPSS: Analyze Menu, Descriptive Statisitcs

2. Central Tendency
Describes a distribution through numerical account of the centre of a distribution.
Median: the variate with the same number of variates both greater and less than it; the centre variate in an ordered array
> res<-c(21,18,12,31,23,31,44,7)
> median(res)
[1] 22
SPSS: Analyze Menu, Descriptive Statisitcs

3. Central Tendency
Describes a distribution through numerical account of the centre of a distribution.
Mode: the variable class with the greatest abundance or highest frequency
> res<-c(21,18,12,31,23,31,44,7)
> library(modeest)
> mfv(res)
[1] 31

4. Which Measure?
What best characterises the centre of the distribution? What measures are most affected by outliers?
Y=23.4, median=22, mode=31

5. Dispersion
Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency.

6. Dispersion Range: difference between largest and smallest variates
Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency.
Range: difference between largest and smallest variates
> res<-c(21,18,12,31,23,31,44,7)
> max(res)-min(res)
[1] 37

7. Dispersion
Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency.
Interquartile range: characterizes the middle 50% of a distribution by subtracting the 25th percentile from the 75th percentile.
1st quartile
2nd quartile
3rd quartile
Yi Sorted 7 18 12 21 23 31 44
> res<-c(21,18,12,31,23,31,44,7)
> IQR(res)

8. Dispersion
Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency.
Variance & Standard Deviation: provide a combined measure of every variates’ deviation from the mean (compare to spread between only two variates using range or IQR)

9. Dispersion
Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency.
Variance: think of “average” squared deviation from the mean
Variance is good for some kinds of distribution comparisons, but s2 not in original units
> res<-c(21,18,12,31,23,31,44,7)
> var(res)

10. Dispersion Standard Deviation: average deviation from the mean
Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency.
Standard Deviation: average deviation from the mean
> res<-c(21,18,12,31,23,31,44,7)
> sd(res)
[1]

11. Comparing Dispersions
Comparing s of distributions of different “sized” things not useful
The size of s is determined by value of variates.
Larger Ys (e.g., length of primate humeri) create larger s than smaller Xs (e.g., length of rat femurs)
Primate humeri & rat femurs

12. Comparing Dispersions
Coefficient of variation “standardizes” standard deviation by the mean
Comparisons must use same units
From: Pattern and Process in Cultural Evolution (2009), edited by S. Shennan, pp University of California Press.