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

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*-valueSample

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*errorType II error, or

*β*error

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.

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 ...