Statistical Analysis for Education and Psychology Researchers

the qualitative variable, NUMV or SUB. The number of graduates in each category is
proportional to the height or length of the bar. In the horizontal bar chart the category
variable, SUB, is shown here on the vertical axis. The length of each horizontal bar
corresponds to the number or frequency of graduates who obtained a first class degree in
a particular discipline of study. Here, simple visual inspection shows that a larger number
of graduates in physical sciences gained a first class degree compared with graduates in
education.
Closer scrutiny of the horizontal bar chart shows that approximately 25 per cent (29)
of graduates who obtained a first class degree graduated in engineering compared with
only 18 per cent (21) in the social sciences. The highest percentage of first class
graduates came from physical sciences (54 per cent, n=62). Note it is good practice,
whenever percentages are used, to provide the base figure on which the percentage is
based here 100 per cent=114. The width of the bars has no significance in a bar chart
(unlike in a histogram—see later).

Stem and Leaf Plot

A stem and leaf plot is a useful way of looking at the shape or pattern of a distribution as
all data values are shown for a variable.

Example 3.6

A stem and leaf plot for the variable ASCORE1 (A-level points score) from the student
A-level data set is shown in Figure 3.11. These plots can be drawn easily by hand. In the
example shown, the first two columns of figures form the stem and the adjacent row of
figures form the leaves. Look for example at the highest stem value of 20. Moving along
the leaf it can be seen that in this data set there are 17 values of 20 (17 zeros). Consider
another example at the other extreme end of the distribution, one student had a total A-
level score of only 7 points and two students had a score of 8 points. The plot in Figure
3.11 was produced by the SAS procedure UNIVARIATE using the option PLOT.
Appropriate SAS code would be:

proc univariate plot;

var ASCORE1;

run;

By default in SAS you multiply the stem and leaf value by 1 unless the output
indicates otherwise. This explains why the lowest value in the ASCORE1 distribution is

7. The stem value is 7 and the leaf value is 0 written as 7.0, this becomes (7.0×1)=7.

Stem Leaf #

20 00000000000000000 17

19 0000000000 10

18 00000000 8

17 000 3

Statistical analysis for education and psychology researchers 54