Monday, October 12, 2015

How an Analysis is Framed can Determine the Conclusion Drawn -- Even from a Common Data Set

I quote from an article in The Economist:
Do dark-skinned footballers get given red cards more often than light-skinned ones?....Raphael Silberzahn of IESE, a Spanish business school, and Eric Uhlmann of INSEAD, an international one.... illustrate in this week’s Nature, it is not (an easy question to answer). 
The answer depends on whom you ask, the way the analysts frame the problem, and the methods they use.
Dr Silberzahn and Dr Uhlmann sought their answers from 29 research teams. They gave their volunteers the same wodge of data (covering 2,000 male footballers for a single season in the top divisions of the leagues of England, France, Germany and Spain) and waited to see what would come back. 
The consensus was that dark-skinned players were about 1.3 times more likely to be sent off than were their light-skinned confrères. But there was a lot of variation. Nine of the research teams found no significant relationship between a player’s skin colour and the likelihood of his receiving a red card. Of the 20 that did find a difference, two groups reported that dark-skinned players were less, rather than more, likely to receive red cards than their paler counterparts (only 89% as likely, to be precise). At the other extreme, another group claimed that dark-skinned players were nearly three times as likely to be sent off......
Their 29 volunteer teams used a variety of statistical models (“everything from Bayesian clustering to logistic regression and linear modelling”, since you ask) and made different decisions about which variables within the data set were deemed relevant. (Should a player’s playing position on the field be taken into account? Or the country he was playing in?) It was these decisions, the authors reckon, that explain why different teams came up with different results.
The article concludes that "when important questions are being considered—when science is informing government decisions, for instance—asking several different researchers to do the analysis, and then comparing their results, is probably a good idea."

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