Descriptive Statistics


When comparing two or more groups, it is generally a good idea to start by creating some form of side-by side boxplots or quantile plots. These plots reveal important information about the location, spread, and shape of the distribution of scores in each group. In the quantile plot shown below, the upper and lower bars represent the 90th and 10th percentiles respectively. The red bar in the middle of each box represents the median. The box extends from the 25th to the 75th percentile. The filled blue circle is the mean with lines extending one standard error of the mean in each direction. The dotted line is the mean averaging across all groups.

The plot shows that the false smile led to the greatest leniency and the neutral expression led to the least. The median leniency for the false smile is higher than the 75th percentile leniency score for the neutral expression. The distributions do not appear to have much skew: the mean and medians are about the same and the medians are about half way between the 25th and 75th percentiles.




How this was done

Which facial condition led to the greatest leniency?
false smile
felt smile
miserable smile
neutral expression
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True or False: The median leniency for the false smile is lower than the 75th percentile leniency score for the neutral expression.
True
False
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The box plots shown below are character based rather than graphical. They convey pretty much the same information, although they do not show the medians.



SAS Univariate Procedure 

                              Schematic Plots

Variable=LENIENCY

         10 +
            |            |           |
            |            |           |
          8 +            |           |           0           |
            |            |           |           |           |
            |         +-----+        |           |           |
          6 +         |     |     +-----+        |           |
            |         *--+--*     |     |     +-----+     +-----+
            |         |     |     *--+--*     *--+--*     |     |
          4 +         |     |     |     |     +-----+     *--+--*
            |         +-----+     +-----+        |        +-----+
            |            |           |           |           |
          2 +                                                |
             ------------+-----------+-----------+-----------+-----------
       COND             false        felt    miserable     neutral


How this was done

A table of descriptive statistics is shown below.

leniency By Condition

Means and Std Deviations

Level     N     Mean     Std Dev   Std Err of Mean 
false     34   5.36765   1.82700     0.31333
felt      34   4.91176   1.68087     0.28827
miserable 34   4.91176   1.45368     0.24930
neutral   34   4.11765   1.52285     0.26117

How this was done



The standard error of the mean is computed by:
Dividing the mean by the standard deviation
Dividing the mean by N
Dividing the mean by the square root of N
Dividing the standard deviation by the square root of N
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