4
$\begingroup$

What is the best way to represent the following data graphically? Can I use a histogram

Year    Output per Person       Capital Employed
2010    16.3 units/annum        £40,000 p.p
2011    15.1 units/annum        £38,000 p.p
2012    14.4 units /annum       £35,000 p.p
2013    11.7 units per annum    £33,000 p.p
2014    10.8 units per annum    £30,000 p.p
$\endgroup$
  • 3
    $\begingroup$ You have three variables (year, output, capital). Are you interested in the relationship between output and capital, or is it their individual behaviour over time you care about -- or something else? What aspects of the information matter for you? (Is this for some subject or is it a real issue you face?) $\endgroup$ – Glen_b Aug 28 '14 at 5:01
  • $\begingroup$ @Glen_b I'm interested in the relationship between output and the capital? I want to show that when capital employed is decreased, output also decreased $\endgroup$ – chamzzey Aug 28 '14 at 5:36
7
$\begingroup$

I see two main alternatives, the scatterplot (see Stephan's post, or a slightly different version below which is sometimes worth trying with time series), and superimposed time series (see the second plot below), though there are a number of other possibilities.

However, beware of interpreting the appearance of correlation as meaningful. Specifically, since both your quantities are both "per person, per annum", you have a classical situation where you expect spurious correlation in the original sense of the term.

enter image description here

enter image description here

$\endgroup$
  • $\begingroup$ One comment: double-axis plots are often discouraged and may be easily misleading so should be used with caution. $\endgroup$ – Tim Apr 22 '17 at 8:14
  • $\begingroup$ @Tim I agree they can be misleading, which is why the axes were color-coded to match the lines -- looking at it, do you really think this one is misleading? $\endgroup$ – Glen_b Apr 22 '17 at 9:27
  • 1
    $\begingroup$ No I don't :) I'm just saying it is worth mentioning that this particular kind of plot should be used with caution. $\endgroup$ – Tim Apr 22 '17 at 10:30
  • 1
    $\begingroup$ @Tim - It'd be helpful to hear in what way and in what circumstances they can mislead. $\endgroup$ – rolando2 Apr 22 '17 at 12:15
6
$\begingroup$

Probably best to do a simple scatterplot. Using R:

foo <- data.frame(year=2010:2014,output=c(16.3,15.1,14.4,11.7,10.8),
  capital=c(40,38,35,33,30)*1000)
with(foo,plot(capital,output,xlab="Capital Employed",ylab="Output per Person",pch=19))

scatterplot

Or also plot the years:

with(foo,plot(capital,output,xlab="Capital Employed",ylab="Output per Person",pch=NA))
with(foo,text(capital,output,year))

scatterplot with years

However, note that both capital and output decline over time. So either output is driven by capital... or both are independently driven by some time-dependent trend (or something in between). Be careful when interpreting correlations, especially over time.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.