## CHAPTER OBJECTIVES

• Define and differentiate point estimation and interval estimation

• Describe important statistical distributions

• Explain the role of the central limit theorem in statistical analysis

• Explain the basic mechanics of hypothesis testing

• Explain how confidence intervals can be used to test hypotheses

• Differentiate among various types of hypothesis tests

• Explain the difference between the frequentist and Bayesian approaches to statistical inference

• Describe the basic principles of Bayesian statistical analysis

• Define and differentiate statistical significance and clinical significance

## KEY TERMINOLOGY

• Alternate hypothesis

• Bayes’ theorem

• Bayesian statistics

• Central limit theorem

• Clinical significance

• Confidence intervals

• Degrees of freedom

• Directional tests

• Empirical distribution

• Hypotheses

• Hypothesis testing

• Nondirectional tests

• Normal distribution

• Null hypothesis

• Parameters

• Point estimate

• Population

• Posterior distribution

• Power

• Prior distribution

• p-value

• Sample

• Statistic

• Statistical distribution

• Statistical estimation

• Statistical inference

• Statistical significance

• Test of difference

• Test of equivalence

• Test of noninferiority

• Test of superiority

• Type I error, or α error

• Type II error, or β error

## INTRODUCTION

Descriptive statistics provide a useful tool for presenting basic information, such as the central tendency (mean, median, or mode) and spread (standard deviation or interquartile range), of a given sample. While these are useful, the focus is often on taking the findings from a sample used for research and applying them to a target population of interest. For example, in a sample of 200 individuals, half of whom received a new medication to reduce LDL cholesterol and the other half received a placebo, the new medication reduced LDL cholesterol by 30 mg/dL. Initially, this finding may seem exciting, but subsequent steps would determine whether the observed reduction was indeed statistically significant (i.e., hypothesis testing) and provide an idea of how large the actual reduction might be in the target population of individuals with high LDL cholesterol (i.e., statistical estimation). Inferential statistics provide the tools to answer these questions.

This chapter begins with a brief discussion of statistical distributions and statistical theory supporting statistical inference. Information about basic principles of point and interval estimation is then presented followed by a discussion of hypothesis testing. A brief discussion of the Bayesian approach to statistical inference is then provided. This chapter finishes with a discussion of the importance of statistical and clinical significance in biomedical research.

## STATISTICAL DISTRIBUTIONS AND THE CENTRAL LIMIT THEOREM

A variable’s distribution is made up of all the possible values and their relative frequency of occurrence. When the values are taken from actual data and the relative frequencies of occurrence are calculated (e.g., the observed lengths of stay for patients in a hospital), this observed distribution is referred to as an empirical distribution. A statistical distribution is a type of distribution that is defined by some theoretical probability distribution.1 These statistical distributions are important since they describe the way in which random variables are expected to behave.2 They also form the ...

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