By Stephen Gorard
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Extra resources for Using everyday numbers effectively in research
Example text
Put more simply, we should remain very sceptical of the apparent difference between the two sets of numbers because that difference is very small in comparison to the differences between the numbers within each set. This approach, of creating ‘effect’ sizes, is growing in popularity as a way of helping to assess the substantive importance of differences between scores, as opposed to assessing the less useful ‘significance’ of differences (Gorard 2006a). Where the individual numbers in each dataset are known, then this use of effect sizes is to be preferred to the simpler proportionate approach described above.
Well – consider the following example. We calculate the mean score in a school test for a group of boys, and find the answer 60 per cent. We also calculate the mean for a group of girls, and find the answer 70 per cent. Let us imagine that both means are around 90 per cent accurate. An error component of one part in ten may seem reasonable when considering either figure in isolation. e. 60 plus or minus six). e. 70 plus or minus seven). If we subtract the girls’ mean from the boys’, the answer is ten.
If the figure for 1995/96 was 40 and the figure for 2002/03 was 63 then our three-year cycle is well and truly broken. Probably the most fruitful way to seek an explanation is to look for different kinds of data. Policy documents and financial statements from each year, for example, could help explain variation in the demand for teachers. If schools in Wales were given a substantial increase in funding in 2001, then this could explain the increased demand for teachers in January 2002. Using everyday numbers in research leads, almost inevitably, to such combined methods approaches (Gorard with Taylor 2004).