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Introduction to statistical methods Introduction to statistical methods
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Basic concepts Basic concepts
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Populations, samples, and sampling Populations, samples, and sampling
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Probability and random sampling Probability and random sampling
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Complex sampling Complex sampling
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Describing variables Describing variables
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Categorical variables Categorical variables
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Quantitative variables Quantitative variables
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Frequency distributions Frequency distributions
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Measures of location Measures of location
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Measures of variability Measures of variability
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Probability distributions Probability distributions
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The normal distribution The normal distribution
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Sampling variability Sampling variability
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Sampling distributions Sampling distributions
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Confidence intervals Confidence intervals
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Confidence interval for a mean Confidence interval for a mean
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Confidence interval for a proportion Confidence interval for a proportion
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Basic principles and methods of comparative analysis Basic principles and methods of comparative analysis
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Group comparisons Group comparisons
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Comparing proportions or percentages Comparing proportions or percentages
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The Pearson chi-squared test The Pearson chi-squared test
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Limitations of the Pearson chi-squared test Limitations of the Pearson chi-squared test
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Comparing means Comparing means
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The two-sample t-test The two-sample t-test
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Analysis of variance Analysis of variance
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Assumptions of the two-sample t-test and ANOVA Assumptions of the two-sample t-test and ANOVA
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Repeated measurements of a quantitative variable Repeated measurements of a quantitative variable
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Correlation and regression Correlation and regression
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Scatter plots Scatter plots
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Coefficients of association Coefficients of association
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Pearson correlation coefficient Pearson correlation coefficient
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Significance of the correlation coefficient Significance of the correlation coefficient
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Types of association and correlation Types of association and correlation
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Regression Regression
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Assumptions of correlation and regression analyses Assumptions of correlation and regression analyses
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Survival data Survival data
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Additional comments on censoring Additional comments on censoring
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Multivariable analysis Multivariable analysis
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Normal theory regression Normal theory regression
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Logistic regression Logistic regression
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Poisson regression Poisson regression
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Cox proportional hazards regression Cox proportional hazards regression
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The proportional hazards assumption and time-dependent variables The proportional hazards assumption and time-dependent variables
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Variations and extensions to other probability models Variations and extensions to other probability models
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Summary Summary
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Acknowledgements Acknowledgements
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References References
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Cite
Abstract
This chapter provides an introduction to statistical methods with illustrative examples from public health and epidemiological research. The chapter begins by distinguishing between a study sample and a target population. It goes on to outline different methods of sampling, including probability and non-probability sampling methods. In the following section, the distributions of epidemiological variables are considered, leading on to discussion of probability distributions and statistical inference. Methods for comparing data from two or more groups are then outlined, including methods for continuous and categorical variables. Analysis of time-to-event data to evaluate survival times is then outlined. The final section of the chapter discusses the application of multivariable models to epidemiological data, including extensions of basic models to more complex data distributions. The chapter concludes by cautioning that increasing ease of access to sophisticated statistical methods may increase the risk of erroneous application. There is little substitute for consulting a qualified statistician, particularly with complex designs.
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