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• W126909969 abstract "The purpose of this paper is to demonstrate the use of the statistics of relative risk and odds ratios in mathematics education. These statistics are widely used in other fields (especially medical research) and offer a useful but currently under-utilised alternative for education. The demonstration uses data from a longitudinal study of students’ understanding of decimal notation. We investigate the statistical significance of results related to the persistence of misconceptions and the hierarchy between misconceptions. Relative risk and odds ratio techniques provide confidence intervals, which give a measure of effect size missing from simple hypothesis testing, and enable differences between phenomena to be assessed and reported with impact. This paper demonstrates some possibilities for analysing educational data, which draw upon methods that are widely used in reporting results of medical, environmental and epidemiological research. We believe that these measures provide very useful techniques for testing for statistical significance and reporting confidence intervals, which will enhance mathematics education research. Capraro (2004) draws attention to important recent policy changes within the American Psychological Association, evident in their publication manual, that stress the importance of researchers supplementing statistical significance testing with measures of effect size and confidence intervals, with many journals making them mandatory. For those worried about deep vein thrombosis (DVT) after long flights, BUPA’s website (Newcombe, 2003) cites Farrol Kahn as saying that “Several studies have shown [wearing flight socks] to be of benefit and it reduces the risk by up to 90 per cent.” However, we can be cheered that “The researchers discovered the risk of developing DVT after a long-haul flight seemed to be low - at about 1 per cent of all long-haul passengers.” Some of us can be further comforted by the observation of Runners’ World (Reynolds) that “Being athletic accounts for ten times more victims than any other risk factor.” These reports in the popular press, along with reports in research literature, are mostly describing the results in terms of relative rather than absolute risk. So, for example, instead of commenting that DVT developed in only about 0.10% (10% of 1%) of passengers wearing flight socks, the website reports that the risk is reduced by up to 90%. This puts what might be seen as a tiny reduction in risk (just 90% of 1%) into perspective and shows its importance. In this paper, we will show how these ideas of relative risk can be applied to educational data and discuss the benefits and issues arising. We illustrate the methods and challenges by some reanalyses of longitudinal data on students’ understanding of" @default.
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• W126909969 date "2005-01-01" @default.
• W126909969 modified "2023-09-27" @default.
• W126909969 title "ANALYSING LONGITUDINAL DATA ON STUDENTS' DECIMAL UNDERSTANDING USING RELATIVE RISK AND ODDS RATIOS" @default.
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