1. Psychology 202a Advanced Psychological Statistics
August 31, 2017

2. The show so far Last time we talked about: variables distributions
grouping
ways of understanding the shape of a distribution

3. Peabody Distribution Values Frequency 55 – 59 1 60 – 64 2 65 – 69 5
70 – 74
75 – 79 4
80 – 84 8
85 – 89 6
90 – 94
95 – 99 3
100 – 104

4. Lower and upper real limits
What we say
What we mean
55 – 59
54.5 – 59.5
60 – 64
59.5 – 64.5
65 – 69
64.5 – 69.5
70 – 74
69.5 – 74.5
75 – 79
74.5 – 79.5
80 – 84
79.5 – 84.5
85 – 89
84.5 – 89.5
90 – 94
89.5 – 94.5
95 – 99
94.5 – 99.5
100 – 104
99.5 – 104.5

5. Relative frequency distribution
Peabody Values
Relative Frequency
55 – 59
.025
60 – 64
.050
65 – 69
.125
70 – 74
75 – 79
.100
80 – 84
.200
85 – 89
.150
90 – 94
95 – 99
.075
100 – 104

6. Histograms A histogram is a picture of the frequency distribution:
group the data (7 to 15 intervals)‏
identify real limits and midpoints of intervals
draw “histobars” over the intervals
use informative labels
example by hand

7. Histograms in R hist(Peabody) R has done an OK job:
informative labels
reasonable number of intervals
but the limits R chose for the intervals are a little strange
help(hist)

8. Ways of understanding shape
Graphics.
Descriptive statistics.

9. 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.

10. Aspects of shape
Those points correspond to the basic aspects of shape:
central tendency
modality
variability
symmetry or skew
kurtosis

11. Numerical Methods descriptive statistics measures of central tendency:
mean
median
mode
others
central tendency in R:
mean(Peabody)‏
median(Peabody)‏

12. 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

13. Descriptive Statistics for Variability
The measure of variability is generally determined by the measure of central tendency.
median  interquartile range
mean  standard deviation