Topical Statistics – To be decided

First post-election analysis

Posted on May 11, 2015May 11, 2015 by dtoher

The aftermath of the General Election has led to much discussion about the reliability of the pre-election polls.

One thing that is yet unknown is the potential influence the opinion polls themselves had on how people voted in relatively close contests. Were potential UKIP voters more likely to stick with Conservative candidates in constituencies that could turn Labour? How much did the “fear of SNP” holding the balance of power affect previous Liberal Democrat voters in England? Who stayed away from polls: could this have dramatically have influenced the weightings that should have been given in pre-election polling?

Having sourced results data from the BBC website [by constituency, based on AP reporting of results] and also electorate sizes from the AP website I decided to look at aspects of election voting that have not (as yet) been widely discussed. There are still some minor issues with the data – where the turnout (as reported by the BBC) is not the same as that based on AP figures for the electorate size (9 constituencies in total).

I have decided to put the mapping data to one side at the moment – lots of maps (of both winners and runners-up) abound at the moment, and detailed spatial analysis will wait until I confirm the data about electorate sizes.

Turnout in Scotland did indicate that in the post-referendum climate, increased voter engagement and participation has continued. Compare the graph above with that of 2010 and the difference in Scottish engagement is evident.

Now looking at the margins of victory – by region and by victor.

So, what is striking about this image? Some Labour MPs had a huge margin of victory. Really a margin of victory of greater than 20% of voters is inefficient distribution of votes. Otherwise, the main talking points are the high turnout in many Scottish constituencies and the fact that the SNPs didn’t have the complete landslide of votes that their return of seats (almost 95% of Scottish seats) suggested and also that there was a much higher turnout in Conservative seats than in Labour seats.

Of the 2,909,882 valid votes cast in Scotland, the SNP polled 1,454,439 (49.98%), with Labour on 24.06%; 15.16% for the Conservatives and 7.55% for the Liberal Democrats. However, due to the First Past the Post system, the return on votes for the SNP resulted in them winning all but 3 of the 59 Scottish seats.

In Wales: Conservatives 27.25% [11 out of 40 (27.5%) seats]; Labour 36.86% [25 (62.5%) of seats]; UKIP 13.63% [0 seats]; Liberal Democrats 6.52% [1 seat]; Plaid Cymru 12.12% [3 (7.5%) of seats].

Wales is therefore a prime example of how UKIP failed spectacularly in converting votes into seats.

Before the election, there was speculation about how the UKIP vote would affect the main parties. UKIP did poll relatively well in “safe” Conservative seats – building their vote share with no direct return. The effect on the Labour vote was more direct – UKIP polled slightly better in areas that could have been marginal Labour victories [in the 15000-20000 Labour votes; the Conservatives won 61 seats, Labour won 91 seats, the Liberal Democrats 1 seat and the SNP won 18 seats] than they did in the equivalent Conservative seats. Therefore, UKIP voters had more of an influence in potential Labour gains over Conservatives than was perhaps expected.

Other than the unfortunate problem of lack of proportionality created by FPTP voting, another issue is caused by the discrepancy in the sizes of the electorate. Welsh constituencies, in particular, are unusually small and may be subject to boundary changes in the future: the very small Scottish constituencies are islands which don’t lend themselves to easy mergers with parts of the mainland.

All discussions about changing the electoral system should first consider fixing the current system: the size of the constituencies is too variable to be considered equitable.

Thus the size of the margin matters in terms of the number of potential (not just actual) voters.

So who had “important” votes? Those in the bottom left of this graph: relatively small electorates in close contests. The two extremes (left and right) of this graph represent island constituencies [Na h-Eileanan an Iar is the smallest constituency, while the Isle of Wight is the largest constituency].

Looking at the constituencies where the margin of victory was less than 5% of those who voted by the size of the constituencies. Four out of the Liberal Democrats eight seats were on margins of less than 5% of valid votes. Turnout in these close seats were (on average) higher than in the seats with a closer margin: so a close race does help to encourage turnout. A “safe seat” is not a helpful thing for voter engagement.

		2015
		Cons.	Green	La bour	LibDems.	PlaidCy.	SNP	UKIP	Speaker
2010	Cons.	295	0	10	0	0	0	1	0
	Green	0	1	0	0	0	0	0	0
	Labour	9	0	209	0	0	40	0	0
	LibDems.	27	0	12	8	0	10	0	0
	PlaidCy.	0	0	0	0	3	0	0	0
	SNP	0	0	0	0	0	6	0	0
	UKIP	0	0	0	0	0	0	0	0
	Speaker	0	0	0	0	0	0	0	1

The main unexpected outcome of the election was not the collapse of the Liberal Democrat vote but the extent to which Liberal Democrat seats were won by Conservative rather than Labour votes. However, this should not have been surprising, as 38 of the Liberal Democrats had a Conservative runner up in 2010. But only 17 Liberal Democrat seats had a Labour runner up in 2010.

		Runner Up 2010
Winner 2010		Cons.	Labour	LibDems.	PlaidCy.	SNP	Other
	Cons.	0	137	167	0	0	2
	Green	0	1	0	0	0	0
	Labour	147	0	76	5	28	2
	LibDems.	38	17	0	1	1	0
	PlaidCy.	1	2	0	0	0	0
	SNP	4	2	0	0	0	0
	Speaker	0	0	0	0	0	1

Only 109 out of 632 GB seats changed parties this election. These swing seats were mainly Liberal Democrat to Conservative (27) and Labour to SNP (40). Conservatives retained 295 of their 306 2010 seats; gaining 36 from Liberal Democrats and Labour. Labour retained only 209 of their 258 2010 seats; the SNP gained 50 seats from Labour and the Lib Dems. The SNP gains were particularly noticeable as they had come second in 29 constituencies in 2010 (having won 6). In 21 of their seats that they won this time round, the SNP came from at best a third place in 2010.

So – what have we learned from all of this. The election results were far messier than many had anticipated. There is a lot of analysis to be done and all of the soul-searching about the appropriateness and efficacy of opinion polls will no doubt be of interest to many statisticians. As no preferences are expressed under the FPTP system we will never really know the extent of tactical voting in UK elections.

Topical Statistics

A window of opportunity?

Posted on November 8, 2014 by dtoher

The study by UCL researchers published this week http://onlinelibrary.wiley.com/doi/10.1111/ecoj.12181/full was interesting in its approach… looking at a 10 year window (2001 – 2011); specifically “Over the period from 2001 to 2011, European immigrants from the EU-15 countries contributed 64% more in taxes than they received in benefits. Immigrants from the Central and East European ‘accession’ countries (the ‘A10’) contributed 12% more than they received.”

A major issue with this timeframe is that we cannot consider the conditions for the A10 countries to be approximately constant in terms of ease-of-access to the UK jobs market. The scale of the difference in the numbers of immigrants from the A10 is noteworthy: in 2001 it was 20,735, in 2005 this was 228,030 and in 2011 it was 892,984. The window really matters. Furthermore, in some of the analysis within the paper they look at the window 1995 – 2011. This inconsistency in the timeframes chosen does not lead to full confidence in the results. Just how reliant are the findings on the windows chosen? The robustness measures used within the paper do nothing to check this. The period before the A10 countries joined the EU was one in which the UK performed well economically; since then the economic crisis has hit. While the research supports the conclusions that even in the downturn the EU migrants still out-contributed others, whether that contribution was sufficient to be a net positive depends on the window used.

Many longitudinal analyses are weak in this aspect. A good robustness test will check to see how much of a difference a slight change in the time window selected would have on the overall conclusions as it prevents the criticism of cherry-picking of timeframes to suit a pre-determined outcome.

Topical Statistics

Consequences

Posted on October 27, 2014October 27, 2014 by dtoher

Having been landed with a rather large extra bill for the cost of E.U. membership of £1.7 billion [or about £27 per UK resident] due on the 1^st December, the consequences of changes in statistical methodology are prominent in the news.

The UK’s Office for National Statistics submits figures used to calculate the Gross National Income to Eurostat. These figures were agreed; they upwardly revised the estimate of the GNI. This upwards revision in the GNI is directly associated with the upwards revision in the bill. A guide to what general areas were under revision is here.

One interesting element that added to the upwards figure was the addition of illegal activities into the accounts. Included in this aspect was a calculation of £5.3 billion accounted for by prostitution. The breakdown of this figure is explained well by Jolyon here: [note that this was published well before the current payment demand was made public and it also links to a commentary about how the Irish Central Statistics Office approached the same problem.]… basically, it boils down to estimates being based on a biased rather than representative sample and no-one really stopping to think about what the total figure would mean.

The surprise shown by politicians about the state of affairs shows as obvious the lack of consideration given to the consequences of changes in statistical methodology. What can seem like minor adjustments can have major consequences.

Topical Statistics

Tooth decay in young children

Posted on October 1, 2014October 1, 2014 by dtoher

A striking feature of the coverage of the Public Health England report available here has been the lack of proper discussion about fluoridation of water.

Public Health England have themselves published the following water fluoridation health monitoring report (2014) that doesn’t seem to have been picked up on in relation to the dental health of three year olds in England.

Flouridation of water is done pretty standardly in Ireland, and has been been considered to be amongst the top ten achievements in public health: find out more here

Hmmm.

Topical Statistics

Scottish Referendum results

Posted on September 19, 2014September 19, 2014 by dtoher

I’ve been looking at the results in the Scottish independence referendum. The results will be the basis of a final year project, so further results will follow.

How each local authority area contributed to the overall NO majority

No majority (% of valid ballots counted) in each local authority area

One possible trend that I wanted to look at was how the pattern of inhabitants [based on 2011 Census] of the local authority areas was related to these voting patterns…

What percentage of people were born in England (based on 2011 Census).

A question asked in 2011 Census asked about identity. This map looks at the proportions in each Local Authority who claimed "Scottish" as their only identity. — A question asked in 2011 Census asked about identity. This map looks at the proportions in each Local Authority who claimed “Scottish” as their only identity.