Showing off your quantitative data

Tables

First stage might include some organising of your raw data.  You may have collected a list of times taken to complete a task or a list of numbers of words correctly recalled during a serial recall task.  Usually the simplest and quickest way to do this is with a table.  Often your table of raw data will be included in an appendix rather than in the main body of your report. 

Graphs and charts

Bar chart

Probably the graph you ever drew at primary school.  As we saw with levels of data, bar charts are the perfect way to illustrate any nominal data collected.  For example, the number of year 3 children in a primary school that can correctly complete Piaget’s three mountains task.  This could be compared to the number of year 5 children able to do the same. 

Importantly here the y axis considers amounts or percentages whilst the x axis carries the categories.  These categories can be in any order. 

Line graph

Tend to be seen as more complex but this needn’t be the case.  Yet again the y axis represents amounts, percentages, frequencies etc. but this time the x axis must also contain data that has a logical sequence and usually is numerical but could also be days of the week etc. that have a recognised set order. 

Line graphs are usually used for interval or ratio data.  One of the advantages is the ability to superimpose many lines on one graph (look left).  This makes comparison of different sets of data possible

Scattergrams and correlation coefficients

(Again)

Correlations are best illustrated using scattergrams

The two co-variables are plotted (one across the x axis and the other up the y).  Any link can immediately be seen.

A perfect positive correlation has a coefficient of + 1.0, no correlation has a coefficient of 0.

In the real world neither of these extremes usually exists.  Coefficients are lie somewhere between 0 and +1.0 for positive correlations and between 0 and -1.0 for negative.  The nearer 1.0 the higher the correlation. 

The board expect you to be able to guestimate a correlation coefficient.  Below I’ve included a few examples:

Curvilinear correlations

Correlations don’t always lie in a straight line.  For example when we looked at the effects of anxiety on recall we saw an inverted ‘U’ shaped correlation with low levels and high levels of anxiety resulting in lower levels of recall (the Yekes-Dodson law)

Beware of spurious correlations

Sales of ice cream are closely correlated to drownings in swimming pools and to the number of shark attacks!

According to QI, in the UK, in the 20th century hair length was closely correlated to performance on the Stock Market, as were lengths of women's skirts!

Clearly there is no obvious causal factors in any of these, rather third variables causing both.

Even reputable broadcasters report what at first glance may appear to be bona fide relationships such as the correlation between clumsiness in childhood and later, adult obesity.