Transcript 09/10/2015

Psychology 202a
Advanced Psychological
Statistics
September 10, 2015
The plan for today
• Continuing the discussion of standard
deviation.
• Descriptive statistics for skew and
kurtosis.
• Linear transformations.
• Models.
• Conditional distributions.
The standard deviation (cont.)
• The conceptual formula for the sample
variance is
2
N
s 
2
i 1
X i  M  .
N 1
• The standard deviation is just the square root of
the variance.
Numerical assessment of skew
• ordering of mean and median
• skewness indices
– Pearson proposed 3*(mean-median)/s
– third moment:
N
3
X  M 
3 
( N  1)( N  2) s
– comment on (lack of) utility of third moment
Numerical assessment of kurtosis
• fourth moment:
N ( N  1)

4
( N  1)( N  2)( N  3) s
 X  M 
4
3( N  1) 2

( N  2)( N  3)
• bad idea except in very large data sets