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Posts Tagged ‘Graphs’

A tale of two Graphs

May 3, 2016 2 comments

For the last two years I’ve collected some amazingly bad graphs from election material, both that has come through my door, and that other people have sent me (see this and this.) My own MP provided so many gems that Colin Beveridge  (@icecolbeveridge) started an Internet campaign to have people refer to these misleading election graphs as “Mulhollands” – after the man himself. This led to Colin and others tweeting him questions about his misleading graphs and one teacher, Adam Creen (@adamcreen) tweeting him with corrected “Mulhollands” that his Y9 class had completed.

This was obviously effective, as each time a piece of campaign literature has arrived since I have scoured it and there has only been one chart on any of them, and that was correctly drawn! A success! Bizarrely, as I have had many other folks looking out for them, this seems a success that has been widespread as I’ve not come across any hideously inaccurate graphs this year.

I did think that this election season would pass without any mention on this blog but today I came across two interesting graphs from a neighbouring ward. Both are accurate, but they tell very different stories, and reminded me a little of Simpson’s Paradox, without actually being directly related to it.

Exhibit A

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This graph is from the Lib Dems in Horsforth ward for the Leeds City Council elections, it’s not wholly accurate in terms of the bar charts,  but it’s near enough to not irk me too much. It shows that of the 5 previous local elections in the area the Lib Dems have won 3 and the Conservatives have won 2. They are using this to sell the idea that it’s only them or the Conservatives who can with the seat. However…….

Exhibit B

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This is from a Labour party leaflet in the very same ward and it shows that in the last Local Election the Labour party candidate came second to the Conservative candidate and that the Lib Dem ended in last place. The inference here is that Labour are more likely to beat the Conservatives as they came second last time.

Both leaflets are presenting true facts selected to further their narrative, and both are presenting them accurately, although one could argue they are both a little misleading.

I’ve looked at the stats from the last few years, it seems that on general election years the tories win by a fair way, but that in local election years it is tight between all three parties, but the lib dem vote has been steadily dropping. It could be an interesting ward to judge the national feeling on on Friday when the results come in, as it is really a 3 way marginal in non GE years.

The anomaly that is the general election year is interesting, more people do vote nationally when there is a GE, but the massive swing to the tories is fairly unusual, as they tend to be good at mobilising the vote. I do know that the Lib Dems in that constituency didn’t really campaign during the GE and the seat was a Tory Labour marginal, and that in a neighbouring Lib Dem Labour marginal the Conservatives didn’t campaign, so perhaps this had an effect.

If you have found any terrible election graphs, please send me them!

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Statistical Deception

April 21, 2014 6 comments

When teaching and talking about statistics I always emphasise the need to be careful what you believe and to always ask yourself “what agenda does the person presenting this data have?”

I’ve written before about how stats can legitimately be manipulated to serve different points of views, especially when there are false variables at work. But recently I’ve noticed at darker art in statistical manipulation, one that is, at its heart, lying.

We are less than six weeks away from local elections now, and it is becoming silly season for party political leaflets coming through our letterboxes. Now we all know that the political parties will present data in a way that makes them look better, they are trying to win your vote afterall, but we would expect them not to lie. For the data to be accurate and presented correctly. Unfortunately, however, this is not always the case:

Exhibit A

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This popped up a number of times in my twitter feed from a variety of sources. I believe it is from a Lib Dem leaflet in Manchester. As you can see, they have presented a bar chart with proportions labelled as percentages. The first screaming error is that the red bar and the orange bar are massively different heights, yet are both emblazoned by the label 39%. The second glaring error is that the percentages add up to more than 100%. The first implies that either the Lib Dems are deliberately trying to mislead voters into thinking they are in a stronger position in the ward than they are, or that they don’t realise that 39% is equal to 39%. I’m not sure which is worse?!

Here’s an excel interpretation of what the graphs should look like:

Manc

Exhibit B

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This graph came through my door in Leeds North West parliamentary constituency. The first thing that caught my eye was that although the gap between the number of votes between Lib Dems and Labour; and between Labour and Conservative is almost the same, the difference in the gaps between the bars was almost 5 times as big, which would imply almost five times as many less votes! An obvious fallacy. Either it’s a deliberate attempt to mislead, or they can’t draw a bar chart. If it’s the latter, do we want them in charge of our local authority budgets?! (or the entire economy for that matter!!)

Something else that struck me as deciving, although this time mathematically correct at least, was the choice of data. This was a leaflet issued in the run up to a local election, and the data set used was from the last local election. Why then, is the data that for the parliamentary constituency rather than the council ward? The ward makes up around a quarter of the constituency, and the vote share in the ward is radically different to that of the constituency. The sitting councilor is conservative and sits on a huge majority, and the Lib Dem candidate last time out cane third. To issue a leaflet in the run up to a local election which implies the conservatives can’t win in a ward where they have a large majority and back it up with local election data for a parliamentary constituency is deliberately deceptive and misleading.

Here’s an excel interpretation of what this one should look like:

LeedsNW

Exhibit C

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This one comes from “across the pond” and is another which was viral. This one seemed to appear constantly for a few days everywhere I looked. If you are still wondering what’s wrong with it, take a little look at those numbers down the left hand side…. See it? The y axis goes upwards to zero! Drew Barker (@twentythree) made this version which gives a much better picture as to what’s going on.

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I can’t wait to see what my classes make of these!

nb I haven’t “selected” these graphs as an attack on the Lib Dems, it’s just they are the only party who have sent me a leaflet with incorrect maths. I’ll gladly expose any of the parties if they themselves do. I do collect these, so if you spot anything similar, do send me it!

Graphs, Graphs and Further Graphs

March 28, 2014 Leave a comment

Recently my Year 11 class have been doing a lot of work around graphs. Not plotting graphs, but the stuff that comes under the banner of “further graphs”, so recognising, sketching and transforming quadratics, cubics, logarithmic graphs, exponential graphs and everyone’s favourite trigonometric graphs.

I hadn’t taught it to a KS4 class before, so I had a good long think about it and created some new resources, and rejigged a couple from A Level classes! You can see all the resources on TES here.

I started off with a match up, I gave them a number of graphs and the equations they matched too, some they had met before, some they hadn’t, but I gave them calculators and whiteboards and 15 minutes to have a crack at it. The class responded really well to this and a number of them managed to correctly match up all the graphs to the equations without any help whatsoever. The rest of the lesson was spent sketching and solving quadratics, they had touched on this before, but were glad to revisit it.

The next lesson was spent on cubics, sketching and solving and becoming familiar with the shapes, and how to factorise ones with a constant term of zero.

The next lesson was spend on transforming graphs, this was a lesson adapted from my A level class and it worked well, the class fully getting to grips with graph transformations. To finish the unit I then did the lesson from the standards box on trig graphs. They also responded well. I’ve not use all the activities from the standards box, but I have always found the ones I have used have gone well!

Drawing Axes

November 7, 2013 2 comments

Today I’ve been thinking about drawing axes (as in the plural of axis, not as in two discworld dwarves preparing for a duel). The reason for this has been this:

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This is the question on yesterday’s edexcel exam paper on drawing linear graphs. On the face of it a rather straightforward question, but there is one slight difference to its predecessors. The axes were not already drawn.

I’ve written before (here), about drawing axes. I always used to give out paper with axes drawn on as that was how the exams were, but then I observed an A-Level physics lesson and was baffled by the amount of time it too them to draw a set of axes, so I have started getting classes to draw their own. It is a skill that they should be able to do.

While thinking about this exam question I can’t help wonder how many pupils around the country Lost marks because they didn’t read the question properly and drew the graph in one quadrant.

I am liking the way the exam boards are trying to ensure the papers are less predictable, and I loved the triangle question (8 or 9). I’m excited about the changing curriculum and I can’t wait to see what the exam boards will do with it.

Observing, and cross-curricular ideas

July 13, 2013 Leave a comment

This week has been a good one. It’s been the last real teaching week before summer, as next week is ICE week (Immersion Curriculum Enrichment week) which means we are off timetable doing a week of activities around a theme. The theme this time us the environment, and the activities look to be fun. One of my favourite bits about ICE week is the chance to do something different and hone my teaching skills in an unfamiliar situation, but more on that later.

Back to this week. We have had most of our new staff in this week, including one of the new NQTs who I am mentoring. I am looking forward to the role of mentor, and have now informally observed him twice. Already there has been a marked improvement and a response to advice, which is pleasing. I was a bit worried about observing in this capacity but the mock observations project I completed with my PE colleague earlier this year and the ITT student observations I have done definitely helped. I also gained a good insight into my own teaching by observing and there are always bits to pick up.

Also this week I completed a joint observation with my HoD on a colleague who was kind enough to volunteer. Again this was unofficial and the purpose was so she could check my ability to grade and give feedback. This was great, my confidence as an observer was boosted as she picked up on exactly the same positive points and areas for development that I did and we agreed on the grade. I also learned a lot about giving feedback and she gave me some great pointers in that respect.

There were also tons of things from the lesson that I picked up, my favourite being this: During a traffic light show me activity he put three wrong answers up. The majority of the kids chose the nearest one and some assumed they must be wrong. This was a superb discussion point and there was some real good contributions from the class. I was unsure if he had done this on purpose, so asked him afterwards. He said that he had in this instance and often does this because he did it once by accident and the results were great. I think this is a superb idea that I will use myself.

Also in Thursday I observed a new y9 science lesson. A couple of my form were in the class and have been in trouble a bit in science so I went to see how they were and offer assistance if required. The lesson was on penguins (always a winner) and cooling rates and included an experiment where the pupils were simulating the huddles emperor penguins stand in to keep warm. It was good fun and the difficulties some members of the class had with graphing made me think that as a maths department we need to embed this skill better in KS3. It also got my brain flying about cross curricular lessons with science on graphing and I hope to implement those next year.

This is one of three cross curricular projects I have in the pipeline, all of which excited me. The second is with an English colleague (@goldfishbowlMM) and involves looking at “The maths of Shakespeare”, and is very exciting. The third is once that a music colleague has suggested to me and involves trying to help improve the times tables of our pupils using the medium if hip-hop!

With these projects and mentoring an NQT, next year is looking incredibly exciting already!

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