Describing Dispersion or Measuring Spread
This is a summary of lecture four of the Teaching Company course Meaning from Data: Statistics Made Clear. The course is very basic but it has helped to improve and revise my understanding of statistics. All I can recall from introductory statistics at university was confusion and anxiety.
In order to get meaning from a bunch of numbers we need to look at the traits that the data have. Below is a diagram I created to assist in my description.
The mean and median are measures of central tendency. The mean is the ‘balancing point’ around which all data sit. Outliers have a effect on that balance. The median is the mid point of the data points and is not affected by outliers. Neither gives us an indication of how spread out the data are.
A histogram gives us an visual approximation of the spread of the data. A five-number summary gives an simple numerical summary of the data from which spread can be deduced but does not allow us to visualise the overall shape of the data the way a histogram can.
Standard deviation and variance give a single digit summary of how varied the data are relative to the mean.
The next diagram gives a mechanical representation of the way the data is processed in order to produce the standard deviation.
The mean as well as each of the data points are fed into the equation in order to produce a single standard deviation value. The limitations that are associated with expressing data using the mean are incorporated into the standard deviation value, that is, it also is susceptible to outliers.
Political Party Stereotypes and Stereotyping in General
“In the US, issue ownership analysis is part of broader theories about voter ignorance. We know from many surveys that the general public has very limited knowledge of political institutions and policies. They tend not to know very much about broader social trends either. This means that electors draw on various informational short-cuts to make political decisions. This includes stereotypical views of political parties, based on assumed previous policy success or failure, or on perceptions of how political party members feel about an issue, on the assumption that interest or sincerity will translate into successful policy.
According to the American literature, some issues are not owned by any party but are ‘performance’ issues. The economy is put into this category, as whether or not it is going well is sufficiently obvious to voters, from regular news reports and everyday experience, for them to form their own views directly on the issue without going via a prior party stereotype (in one paper, parties can have a ‘lease’ on the economy as an issue, but one which would end with their recession or another party’s boom).
Even where issues are ‘owned’, the standing of parties is not immune to very salient contrary information, such as debacles and scandals. Sometimes there are long-term changes (this seems to have happened in Canada). But in the more normal course of events, when there is little grabbing voters’ attention, they draw on party stereotypes to form views. Once established, these stereotypes tend to be reinforced; we all have our theories about the world, and pay more attention to information that confirms our views than to information that challenges our views.”
The above quote comes from an article by Andrew Norton on the subject of issue ownership by political parties in Australia (drawing upon US scholarship on the subject.) It got me thinking (a little) about how common stereotyping is in general. I have no doubt that racism and anti-Semitism are kinds of stereotyping where select members of each group (the ‘bad’ ones) are held out as representative of the entire group and used to reinforce negative stereotypes about the entire group. It is not just blacks and Jews that are stereotyped in this manner. Roman Catholic clergy are subject to stereotypes that are no more logically justified than the racist and anti-Semitic ones. Priests are routinely stereotyped as sexually repressed and ‘suspect’, and in more extreme cases they’re characterised as paedophiles. Bishops are stereotyped as dishonest ‘enablers’ of abuse. No doubt that given the large size of each group there will be some that ‘fit’ the stereotype perfectly. But if individuals deserve to be treated on their merits then stereotyping may not only be illogical but also immoral. The unfortunate thing is that stereotypes often effectively serve the interests of some individual or individuals. Anti-Catholic and anti-clerical stereotypes are often used to further a reform agenda (which may or may not be a justified end.) Plenty of other negative stereotyping occurs, for example, those on the political left are often described ‘bleeding hearts’ and those on the right are often viewed as lacking compassion. War time also sees stereotypes used to ‘demonise’ opponents.
Stereotyping in politics occurs not only at the party level but at the individual level. The previous Prime Minister was often stereotyped (as being ‘clever’ in the pejorative sense) and the present Prime Minister already has the ‘nerd’ stereotype thing happening (and I’m sure there are worse to come.) When a member of a party does something wrong, they are held out as being representative of their party as a whole rather than as an individual who has failed and who may or may not be representative of their party as a whole. The stereotyping that goes back and forth in standard political discourse sets a very bad example , but perhaps is unavoidable given the way the electorate responds to things.
Stereotyping is part of the pathology of some mental illnesses, such as social phobia where sufferers often stereotypes themselves as overly anxious (more than they ‘really’ are) and socially incompetent with others viewed as confident and intolerant of the sufferer’s flaws (leading to even more anxiety.)
We seem to have a logical double standard though because negative stereotyping is considered wrong (unless it’s against ‘bad’ people) but positive stereotyping is fine. Perhaps all the positive stereotyping that occurs sets the wrong example and people conclude that if positive stereotyping is logically sound then negative stereotyping is as well. I try not to stereotype if at all possible (in a positive or a negative sense) but I don’t think I’m 100% successful at it.
Update:
Check out this post on the neurology of stereotypes for a more detailed discussion of the subject.
Free Online Classes
I was directed to a compilation of free online classes from a gHacks.net post titled ‘Online Free Classes.’ So far, the ones on making and using rules and judges and the law look interesting. If I go through them, I’ll include a post or an aside on what they were like.
Supply of, and Demand for, ‘Skills’
During and in the run-up to the 2007 Federal Election, a point was made about a ‘skills shortage’ and its effect on the economy. I do not know enough about economics to give an authoritative response but I do have an amateur’s opinion on the subject. A recent article in the Herald-Sun (with variants in other publications) about the Federal Labor Government boosting training places by 20,000 prompted me to write this post.
I understand that the ideal situation is, from an economic perspective, one where all the demand for skills is fully satisfied by skilled workers. I also understand that it is quite difficult to precisely estimate future demand because of the large number of variables involved in such a prediction (and the uncertainty associated with each one). So should we aim to be cautious in an economic sense and aim to have an oversupply of skilled workers or should be cautious in a social sense and have unmet demand for skilled workers? I’ll explain why I call unmet demand for skilled workers ‘socially cautious.’
When someone trains for a particular career they do not do it so that they will end up a ‘product’ that is placed in a metaphorical warehouse should the market one day demand their services. They do it because they think that it will give them a better life. Often they become very emotionally involved in their career choice and it becomes a significant part of their life. They pour their hopes into it. In a situation where the supply of workers in their profession exceeds demand (the economically cautious position) some of these trainees will end up either unemployed, or will have to accept a different job to the one they set their hearts set on. They may even have to start training for another career. I call these things socially harmful because they cause distress and frustration among a subset of the population.
If we set a target that is below the estimated future demand (we’re socially cautious) we will often end up with too few qualified workers and thus a skills shortage, with whatever economic consequences that entails. If we set a target above the estimated future demand (we’re economically cautious) then we will often end up with too many qualified workers and thus a lot of disappointed and potentially bitter individuals. If our estimates are always of a fuzzy nature where at most we can predict a very broad ‘band’ of possible targets that will often be wrong, why are we so harsh on governments that ‘fail’ to prevent skills shortages that were due to the inherent imprecision of our estimates?
I remember in the early 1990′s when Paul Keating spoke of Australia becoming a ‘clever country’, excelling not just in mining and other resource related industries, but in science, technology and the arts. At the time I naively concluded that a career in science would be a good choice. One I graduated with an honours science degree I discovered that there was no work available. I don’t suggest that the then Prime Minister actively encouraged me to do that particular degree, but how much more frustrating would it be to someone whose government actively encouraged them to train in a particular field in order to meet a skills shortage only to find out that there is no job for them once they complete their training and that the government knew in advance that a significant oversupply would occur unless their overestimated targets proved correct?
I think this element has been ignored in the media discussion of the skills shortage. What happens when the government encourages many people to train for jobs that (probably) won’t be there? And even worse, what if the best predictions of future demand suggest that for a significant number of trainees the jobs won’t be there but because the government erred on the side of economic caution they nonetheless encouraged people to train for that particular career anyway? It seems that this process is balancing the economic harm that comes from unmet demand for skilled workers against the social harm that comes from training people up for jobs that for many will not be there. This balancing process is more complex and not readily broken down to ‘sound-bite’ format and that is why it is rarely discussed by anyone in the media or by politicians.
The Extent to which People Lie
I read an interesting interview with David Livingstone Smith about the extent to which people lie and why they do it. I found it via Loren Rosson’s blog, in a post that included comments on Jesus’ historical identity.
The Five Primary Colours of Morality
Steven Pinker has written an article that was published in the New York Times on the science and philosophy of morality. I have created a diagram below that I hope accurately summarises the key points of the article.
The steps involved in forming a moral reaction to a given scenario.
- Some scenario occurs and is observed or some scenario is imagined.
- The brain reacts to the scenario.
- The brain examines the scenario from five perspectives, with some more relevant to different scenarios than others.
- Each perspective is given weight and priority. They are then balanced against one another.
- The moralisation ‘switch’ is either turned on or remains off. If it is switched on, rationalisation follows. If it remains off, any non-moral thoughts will win out.
Ghacks Article
gHacks.net has an article on how to properly link to websites. I am going to use this approach from now on.
Confirmation Bias
The research described in this article, if sound, provides an example of how our cognitive biases can have demonstrable health consequences. In this case, the bias appears to be confirmation bias. Clinical depression and a range of anxiety disorders also often result from cognitive biases.
