Transcript Chapter 5

Chapter 5
Measures of Variability
Golf Analogy: Which golfer is more consistent?
Each golfer hits 5
shots. The data are
distance from the
hole.
Mean
Variance
Beginner
Pro
-20
1
20
2
1
-2
-15
1
16
3
0.4
1
320.3
3.5
Variability
 Variability is the spread or dispersion of a set of
scores.
 Leptokurtic distribution has small dispersion.
 Platykurtic distribution has large dispersion.
 If the groups have a large amount of variance
the difference between the means will have to
be greater to find significance.
Interquartile Range
 Difference between the 75th and 25th
percentile.
Variance is the average squared
deviations from the mean.
The sum of the deviations is ZERO
Calculation of the Variance
Standard Deviation
 The SD is the square root of the variance.
 The variance is in squared units
 The SD is in original data units
 Sigma is the population statistic
Degrees of Freedom: The number
of things that are free to vary
 Assume that the mean of four values is 5
 Therefore the sum must equal 20
 Let 2, 3, and 7 be the first three numbers
 What must the 4th value be so sum = 20?
 It must be 8
 In this example the first 3 numbers are FREE
TO VARY
 The df for a single data set is (N-1)
[ see p 68 ]
DF and Sampling
 Samples rarely contain the extreme
values found in the population.
 A random sample of 100 university
men from a population of 15,000 is
unlikely to contain a subject with wt
350 or 100 although they exist in the
population.
 The variability of the sample is almost
never as large as the population.
 df is a correction factor so that a
statistic is not a biased estimate of the
parameter.
When N is large and the distribution is close to
normal there are 5-6 sds within the range
6 SDs