Statistical Analysis for Education and Psychology Researchers

Displaying Data Distributions

Charts, data plots and tables are the most common ways of displaying data. Charts and
data plots in particular are an excellent means of data visualization, and a way of
identifying particular features and patterns of variation in data.

Example 3.4

Educational researchers were interested in the relationship between university students’
A-level achievements and their degree performance. Part of a data set obtained from a
study of university entrants is shown in Table 3.2. All students who entered a UK
university in 1988 were included in the study, but the data shown is only for those
students, in four separate disciplines, who graduated with a first class honours degree.

In Table 3.2 data is listed for 8 cases. There are 7 variables in the data set and a
description is as follows:
Variable Description
SUB Subject studied at university
SEX Gender of candidate
CASENO Unique ID of candidate
DEGP Degree class obtained (Ist class only, coded as I/5)
ASCORE1 Total A-level points score (A=5, B=4, C=3 etc)
NUMV Number of A-levels obtained
AGEY Age in yrs of candidate at start of course

The full data set is presented in Table 1, Appendix A1.
You may recall that when beginning an analysis with data like that presented in Table
3.2, preliminary considerations should include clear identification of what variables have
been observed or measured, the level of measurement of each variable and whether there
is any variation in the values of each variable. Depending upon the level of measurement
of the variables there are a number of options for displaying visually data distributions.

Table 3.2: Details of first class honours graduates

OBS SUB SEX CASENO DEGP ASCORE1 NUMV AGEY

1 Phys.Sci/5 F 302 I/5 7 3 18.7500

2 Phys.Sci/5 M 303 I/5 14 3 18.7500

3 Phys. Sci/5 M 320 I/5 15 3 18.2500

4 Phys.Sci/5 M 321 I/5 12 3 20.3333

5 Phys.Sci/5 M 329 I/5 11 3 19.0000

6 Phys.Sci/5 M 330 I/5 9 4 18.7500

7 Phys.Sci/5 M 331 I/5 14 4 19.0833

8 Phys.Sci/5 M 367 I/5 20 4 18.6667

Bar charts, stem and leaf plots, relative frequency tables and pie charts are most often
used to depict categorical data and quantitative discrete (count) data. Grouped relative

Statistical analysis for education and psychology researchers 50