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Extra info for Developing Thinking in Statistics (Published in association with The Open University)

Sample text

Where variation is wide (as with people’s heights), observed differences between two measures are more likely to be explained by natural variation. But if variation is small, given the same degree of observed difference, it is more likely that the two measures really do come from different populations. 2 and finding helpful ways of picturing variation will be a theme of Chapter 6. ’) raises a number of interesting measurement issues to do with making comparisons. First, the term ‘better driver’ is not well defined: it could mean ‘safer’ or ‘more proficient’ (that is, better technically).

If you are unsure about the validity of this conclusion, consider the following simple, made-up example based on a sample of three men and three women. 2, when the three men viewed pictures of men, they were poor at reading their expressions, leading to an average of 50% success (column 1). The men’s overall average score was therefore 70%. Assume that the women scored the same overall average scores of 70%, but their reading of the opposite sex was less good than the men (80% as compared with 90%).

2, the divisor was population size, but another possibility might have been the number of athletes from each country attending the games. Similarly, with the Dotheboys Comprehensive School example, the divisor could have been the total school population or the number of learners taking the examinations or the number of learners eligible to take the examinations. Basically, the choice of divisor must be made with care, bearing in mind the precise comparison you want to make. 3 Big Dipper Which do you think is riskier, riding on a white-knuckle fairground machine such as ‘Nemesis’ or ‘Oblivion’ at Alton Towers or cycling on a main road in the UK?

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