Chapter 10. Statistical Methods for Multiple Variables

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  The choice of statistical methods depends on the research question, the scales on which the variables are measured, and the number of variables to be analyzed.
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  Many of the advanced statistical procedures can be interpreted as an extension or modification of multiple regression analysis.
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  Many of the statistical methods used for questions with one independent variable have direct analogies with methods for multiple independent variables.
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  The term “multivariate” is used when more than one independent variable is analyzed.
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  Multiple regression is a simple and ideal method to control for confounding variables.
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  Multiple regression coefficients indicate whether the relationship between the independent and dependent variables is positive or negative.
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  Dummy, or indicator, coding is used when nominal variables are used in multiple regression.
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  Regression coefficients indicate the amount the change in the dependent variable for each one-unit change in the X variable, holding other independent variables constant.
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  Multiple regression measures a linear relationship only.
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  The Multiple R statistic is the best indicator of how well the model fits the data—how much variance is accounted for.
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  Several methods can be used to select variables in a multivariate regression.
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  Polynomial regression can be used when the relationship is curvilinear.
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  Cross-validation tell us how applicable the model will be if we used it in another sample of subjects.
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  A good rule of thumb is to have ten times as many subjects as variables.
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  Analysis of covariance controls for confounding variables; it can be used as part of analysis of variance or in multiple regression.
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  Logistic regression predicts a nominal outcome; it is the most widely used regression method in medicine.
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  The regression coefficients in logistic regression can be transformed to give odds ratios.
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  The Cox model is the multivariate analogue of the Kaplan–Meier curve; it predicts time-dependent outcomes when there are censored observations.
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  The Cox model is also called the proportional hazard model; it is one of the most important statistical methods in medicine.
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  Meta-analysis provides a way to combine the results from several studies in a quantitative way and is especially useful when studies have come to opposite conclusions or are based on small samples.
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  An effect size is a measure of the magnitude of differences between two groups; it is a useful concept in estimating sample sizes.
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  The Cochrane Collection is a set of very well designed meta-analyses and is available at libraries and online.
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  Several methods are available when the goal is to classify subjects into groups.
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  Multivariate analysis of variance, or MANOVA, is analogous to using ANOVA when there are several dependent variables.

Presenting Problem 1

In Chapter 8 we examined the study by Jackson and colleagues (2002) who evaluated the relationship between BMI and percent body fat. Please refer to that chapter for more details on the study. We found a significant relationship between these two measures and calculated a correlation coefficient of r = 0.73. These investigators knew, however, that variables other than BMI may ...