Psychology 202a
Advanced Psychological
Statistics
September 8, 2015
What can we say about the
Peabody distribution?
• The Peabody distribution is centered in the
80s and 90s.
• The distribution tends to pile up in one
place.
• There is substantial variation in the scores.
• The distribution is not symmetric: there
may be some negative skew.
• Extreme low and high scores are much
less frequent than central scores.
Aspects of shape
• Those points correspond to the basic
aspects of shape:
– central tendency
– modality
– variability
– symmetry or skew
– kurtosis
Numerical Methods
• descriptive statistics
• measures of central tendency:
– mean
– median
– mode
• central tendency in R:
– mean(Peabody)
– median(Peabody)
Choosing measures of central
tendency
• geometric interpretations
– mean = balance point
– median = halfway point
• your purpose may govern choice
– cereal box example
• principle of “resistance” may govern
choice
Stem and Leaf Plot of Peabody
5|7
6|14
6|55799
7|12
7|6679
8|01113444
8|566799
9|00112234
9|556
10|0
Descriptive Statistics for Variability
• skipping over modality (why?)
• The measure of variability is pretty much
determined by the measure of central
tendency.
• median  interquartile range
• mean  standard deviation
The interquartile range
• Considerations that make the median a
reasonable choice for central tendency
(e.g., resistance) may apply just as well to
measuring variability.
• Interquartile range = the difference
between the median of the upper half of
the data and the median of the lower half.
• These “medians” are actually quartiles.
Stem and Leaf Plot of Peabody
5|7
6|14
6|55799
7|12
7|6679
8|01113444
8|566799
9|00112234
9|556
10|0
The standard deviation
• When the mean is the chosen measure of
central tendency, a measure of variability
that is something like average distance
from the mean is a reasonable way of
describing variability.
• Digression in R.
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.
Simple descriptive statistics in
SAS
• proc univariate
• proc means
Extending R
• Writing a simple function.
• An IQR function that does what we want it
to do.