The other day I caught myself singing “it’s just one of those myths…” to the well-known song by Cole Porter which actually goes “it’s just one those things”. I wondered whether it had been a Freudian slip, until I realised it had to do with the many ‘myths’ which we, at Age UK, have set about to demolish and are charging against daily. ‘Older people this’, ‘population ageing that’. One of these myths is that the age of voters is, by and large, related with their political preferences.

It is usually voiced that it’s the relatively older voters who tip the balance in the General Elections in the UK, for the turnout among those over 55 is bigger than that of under-25s. Whereas this is true, the relation between age and voting intentions is often overlooked – it is simply accepted as a matter of ‘fact’ that such a relation exists: “older voters tend to go for the Conservatives”, for example.

Obviously, we don’t actually know how people finally vote, but we do know what they said they intended to vote shortly before each election –thanks to Ipsos-Mori, which has been collecting these data over the last 30 years. And thus I could test whether there has been any statistical association between age and voting intentions for the three main political parties (plus a fourth catch-all category, ‘other’) since the 1987 General Election – for previous years, the breakdown of the data by age varies. For this purpose I used a fairly common statistical test: the chi-square test of independence, which I’m sure you either know a lot about or do not want to know anything of right now, so I’m going to omit any details here.

The data come broken down into six age groups and for each one of these the percentage of respondents who said that would vote Conservative, Labour, Liberal Democrat (or the SDP- Liberal Alliance in 1987) or another political party is recorded. The following is the table for the 2010 General Election:

Age | Conservative | Labour | Liberal Democrat | Other |

18-24 | 29.5% | 31.3% | 29.8% | 9.4% |

25-34 | 34.5% | 30.4% | 28.5% | 6.6% |

35-44 | 34.3% | 30.6% | 26.1% | 8.9% |

45-54 | 34.3% | 28.0% | 25.6% | 12.1% |

55-64 | 37.9% | 27.8% | 22.6% | 11.6% |

65+ | 43.9% | 31.0% | 16.0% | 9.1% |

Obviously, some may say, age and intentions go hand in hand, after noting that 43.9% of voters aged 65 and over intended to vote Conservative against 29.5% of the under 24 whilst a mere 16% of the 65 plus said they were voting the Lib-Dems, against almost 30% of the youngest voters.

But what did I find? Not a trace of association. Ever. (Well, in the six General Elections since 1987). That’s why statistical tests have been developed (and why we rely on them): because eyeballing data may, and often is, very deceitful indeed. However it seems that many a commentator is keen on leaving the surface of reality completely unscathed, thus perpetuating this myth – and many others.

You can’t do a chi-square test on proportions or percentages, you need the actual hard numbers.

Dear Jody,

Thanks for your comment (and for reading Age UK’s blogs).

Actually you can run a chi sq test even if you don’t know the sample sizes; you need to assume probabilities against which you run the test. (This is known as the chi sq test for given probabilities).

In our case, the data included proportions by age group for four parties (Con, Lab, LibDem, and Others). For example, for 18-24 year olds in 2010 we have (see table in text)

Con Lab LD Oth

0.295 0.313 0.298 0.094

And so on for the other age groups and years.

I tested the hypothesis that the proportions for each group did not significantly differ from 25% for each party (ie, that one quarter of the votes of each age group would go to each party). And I could not reject this null in any of the six years:

x.sq parameter p.value

1987 294 299 0.5707609

1992 594 599 0.5499701

1997 138 143 0.6024231

2001 474 479 0.5558866

2005 570 575 0.5510033

2010 1074 1079 0.5372239

Hope this helps

Happy to discuss! Kind regards,

José

The below chi squared tests are on data all with exactly the same proportions, but differing counts:

> # proportions vs counts

>

> props

> props1 props2 props3 props4

> props1

Con Lab Lib Other

1 29.5 31.3 29.8 9.4

2 34.5 30.4 28.5 6.6

3 34.3 30.6 26.1 8.9

4 34.3 28.0 25.6 12.1

5 37.9 27.8 22.6 11.6

6 43.9 31.0 16.0 9.1

> chisq.test(props1)

Pearson’s Chi-squared test

data: props1

X-squared = 10.7001, df = 15, p-value = 0.7735

> props2

Con Lab Lib Other

1 59.0 62.6 59.6 18.8

2 69.0 60.8 57.0 13.2

3 68.6 61.2 52.2 17.8

4 68.6 56.0 51.2 24.2

5 75.8 55.6 45.2 23.2

6 87.8 62.0 32.0 18.2

> chisq.test(props2)

Pearson’s Chi-squared test

data: props2

X-squared = 21.4002, df = 15, p-value = 0.1245

> props3

Con Lab Lib Other

1 73.75 78.25 74.50 23.50

2 86.25 76.00 71.25 16.50

3 85.75 76.50 65.25 22.25

4 85.75 70.00 64.00 30.25

5 94.75 69.50 56.50 29.00

6 109.75 77.50 40.00 22.75

> chisq.test(props3)

Pearson’s Chi-squared test

data: props3

X-squared = 26.7503, df = 15, p-value = 0.03084

> props4

Con Lab Lib Other

1 88.5 93.9 89.4 28.2

2 103.5 91.2 85.5 19.8

3 102.9 91.8 78.3 26.7

4 102.9 84.0 76.8 36.3

5 113.7 83.4 67.8 34.8

6 131.7 93.0 48.0 27.3

> chisq.test(props4)

Pearson’s Chi-squared test

data: props4

X-squared = 32.1004, df = 15, p-value = 0.006239

>

Jody

The chi squared test for given probabilities to which you refer still compares counts (expected vs actual), as reflected in the R code here –

> chisq.test(props1[1,],p=c(0.4,0.3,0.2,0.1))$expected

[1] 40 30 20 10

>

And again significance depends on the counts not the proportions:

Chi-squared test for given probabilities

data: props1[1, ]

X-squared = 7.6506, df = 3, p-value = 0.05381

> chisq.test(props2[1,],p=c(0.4,0.3,0.2,0.1))

Chi-squared test for given probabilities

data: props2[1, ]

X-squared = 15.3012, df = 3, p-value = 0.001577

>