By coincidence I happen to be working on the effect of education on what I call liberal values (or tolerance) and early versions of this work focused on homophobia, see here and here also. I use the European Social Survey data (spanning the period 2002-2010) which uses a different instrument to the WVS. Specifically it asks people’s agreement or otherwise (on a 5 point scale) to the statement “Gays and lesbians should be free to live life as they wish”. My other outcome is a measure of sexism based on responses, on a similar 5 point scale, to the statement “Men should have more rights to jobs than women when jobs are scarce”. I was curious to know what the pattern of responses was across countries (though my research is a micro-study using only UK and Irish data). So I plotted (see below) the cross country means (across the population) of binary measures of sexism and homophobia. The binary measures score 1 if people agree or agree strongly with the statement about gays and disagree or disagree strongly with the statement about jobs (and =0 otherwise).

Countries to the right of the graph are less homophobic and countries to the top are less sexist. There is a fairly strong positive correlation with Denmark and the other Nordics leading in tolerance, though Finland deviates a bit from this trend. Southern and eastern Europe is at the other extreme (especially Russia, Ukraine and Turkey). Ireland is one of a clump of western European countries that are pretty liberal on both accounts. By this data, France is not the most homophobic country in western Europe being to the right in the picture of Germany, Spain, Switzerland, Austria and certainly Greece and Italy. It shows that these cross-country patterns can be quite sensitive to measurement. It seems that there is a common tolerance factor around Europe and, most importantly, that there is huge variation in those attitudes.

A good summary of some of this work by Frank, Gilovich & Regan is here. They consider a number of studies using experimental game theory to see whether economics students differ in their behaviour from other students. Using the classic Ultimatum Game and Free Rider Games one finds that, yes, economics students are more selfish or less pro-social. Another finding is that business students are more selfish (or more rational) in the Ultimatum Game than psychology students.

The title of the Frank et al. piece “Does studying economics inhibit cooperation” is misleading since, as far as I know, all that is established is a correlation. In other words, it may be the case that the people who select into economics or business studies were less co-operative or pro-social beforehand. This could be tested. It would also be very useful to extend this work to other groups of students (literature, science etc) as well as the non-student population. There is a separate literature looking at cross-cultural differences in experimental game theory.

I was reminded of this topic by a just released paper that shows that students who select into experiments only do it for the money but that those who do and those who don’t aren’t really different.

Appearances can be deceptive: instructor fluency increases perceptions of learning without increasing actual learning

S K Carpenter et al.   Psychonomic Bulletin and Review May 2013

The context to this is there is a new syllabus for mathematics, so-called Project Mathematics. There seems to be a certain amount of uncertainty and confusion around this new syllabus and these sessions are partly to address this gap. There all sorts of issues about this new syllabus, such as whether it amounts to dumbing down, but thats another day’s work.

The new syllabus has a lot of statistics so I was interested in that part of the material. I believe that statistical literacy is very important. After all, much of how we interpret the world is by reference to data & there is lots more data about these days. Moreover, interpretation is far from easy and there are lots of fallacies about. The media is full of stories that, unwittingly or otherwise, are misleading about data.

The material being asked for in the syllabus looks pretty good to me although a lot of it is very applied and not pure mathematics. If our school leavers knew all that I would be very happy. Although I would not want it to be at the expense of core topics like calculus.  I was struck by two statements in this set of notes for students which are widely held to be true but are in fact false. I confess that while I knew one was false, the other surprised me.

One statement was that the mode is always between the median and the mean i.e. either median>mode>mean or mean<mode<median. This statement actually occurs in the well known text of Kendall & Stuart (The Advanced Theory of Statistics, vol 1). This is easily falsified by a distribution that looks like an “M”. The mean & median coincide and the two modes lie to the left and right. Even for unimodal distributions however, these inequalities need not hold. These Leaving Certificate notes make some remark like “the mode always lies between the median and the mean, as you would expect, since it is the typical value”. This is nonsense and a smart student will be left wondering “What exactly is a typical value?” Mean, mode and median are all measures of central tendency and all have claims to being a “typical value” but really one needs to be more precise.

The second error, which I am guilty of too, is the statement that in a right (positively) skewed distribution the mean is greater than the median and in a left skewed one the reverse is true. Many statistics books hold this to be true & certainly in a lot of the empirical distributions that economists work with (earnings for example) it seems to be the case. Although it is  common to find this to be the case empirically and it holds for some theoretical distributions, it is not true in general (i.e. as a rule). Note that failures of this statement to be true occur not just in contrived examples but can occur with, for example, the Weibull distribution.

A good overview of the relations between mean, mode and median can be found here.

See here for more information on Preparing For Life.

The deadline for the post is May 19^th and applications must be made through the UCD website http://www.ucd.ie/hr/jobvacancies/ (search for post number 005866).

My initial reaction on hearing the news was “So what?” The results are not at all surprising. That said, it is useful to have good up-to-date information on this and the Department of Education have gone to great lengths integrating a variety of data sources to pull together these numbers.

The obvious limitation of these numbers is that they are simple bivariate comparisons: they tell us nothing about what causes what and they cannot directly inform policy (nor do they claim to). But knowing these differences at least alerts us to possible problems with our educational system. One interesting question would be whether the fee/non-fee difference remains after one controls for socio-economic status (SES):  is it that the well-off progress more rather than than whether the school is free per se? It would also be useful to look at whether educational attainment (for example Leaving Certificate results) differ by school type. In 2011 I highlighted a paper by two Israeli statisticians who looked at whether students in “private” schools did better using Irish PISA data. They find that selection (i.e. student “quality”) explains the difference and that “public” schools actually perform better on average.

Let us hope that researchers are able to access publicly available data which allows us to tackle the really important questions: what causes these differences in educational differences across populations. Otherwise, it’s all a bit pointless, isn’t it?

I had a few other blog-posts on the subject here and here if you are interested.