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### Simple and Complicated Expressions Used in Biostatistics

Simple expressions (also called formulas) have one or two numbers and only one mathematical operator (for example, 5 + 3). But most of the formulas you'll encounter in biostatistics are more complicated [more…]

### Using One-Dimensional Arrays to Describe Collections of Numbers

It's often convenient, when dealing with collections of numbers, to use a single variable name to refer to the entire set of numbers. A bunch of values referred to by a single variable name is generally [more…]

### Higher-Dimensional Arrays for Collections of Numbers

Two-dimensional arrays can be thought of as describing tables of values, with rows and columns (like a block of cells in a spreadsheet), and even higher-dimensional arrays can be thought of as describing [more…]

### Random Thoughts about Randomness and Statistics

The word *random* is something folks use all the timeYou probably have some intuitive concept of randomness, but find may hard it to put into precise language. [more…]

### Picking Samples from Populations

The idea of sampling from a population is one of the most fundamental concepts in statistics — indeed, in all of science. For example, you can't test how a chemotherapy drug will work in [more…]

### Probability Distributions in Biostatistics

Samples differ from populations because of random fluctuations. Statisticians understand *quantitatively* how random fluctuations behave by developing mathematical equations, called [more…]

### Statistical Estimation Theory

*Statistical estimation theory* focuses on the accuracy and precision of things that you estimate, measure, count, or calculate. It gives you ways to indicate how precise your measurements are and to calculate [more…]

### Statistical Decision Theory

Statistical decision theory is perhaps the largest branch of statistics. It encompasses all the famous (and many not-so-famous) significance tests — Student t tests, chi-square tests, analysis of variance [more…]

### The Language of Hypothesis Testing

The theory of statistical hypothesis testing was developed in the early 20^{th} century and has been the mainstay of practical statistics ever since. It was designed to apply the scientific method to situations [more…]

### The Meaning of the "p Value" from a Test

The end result of a statistical significance test is a *p value,* which represents the probability that random fluctuations alone could have generated results that differed from the null hypothesis [more…]

### Type I and Type II Errors in Hypothesis Testing

The outcome of a statistical test is a decision to either accept or reject H_{0} (the Null Hypothesis) in favor of H_{Alt} (the Alternate Hypothesis). Because H [more…]

### The Power of a Statistical Hypothesis Test

The power of a statistical test is the chance that it will come out statistically significant when it should — that is, when the alternative hypothesis is really true. Power is a probability and is very [more…]

### Go Outside the Norm with Nonparametric Statistics

All statistical tests are derived on the basis of some assumptions about your data, and most of the classical significance tests (such as Student t tests, analysis of variance, and regression tests) assume [more…]

### Commercial Software for Biostatistical Analysis

Commercial statistical programs usually provide a wide range of capabilities, personal user support (such as a phone help-line), and some reason to believe [more…]

### Free Biostatistics Software

Over the years, many dedicated and talented people have developed statistical software packages and made them freely available worldwide. Although some of these programs may not have the scope of coverage [more…]

### Calculators and Mobile Devices for Biostatistics

Over the years, as computing has moved from mainframes to minicomputers to personal computers to hand-held devices (calculators, tablets, and smartphones), statistical software has undergone a similar [more…]

### Identifying Aims, Objectives, Hypotheses, and Variables for a Clinical Study

The *aims* or *goals* of a study are short general statements (often just one statement) of the overall purpose of the trial. For example, the aim of a study may be [more…]

### Deciding Who Will Be in a Clinical Study

Because you can't examine the entire population of people with the condition you're studying, you must select a representative sample from that population. You do this by explicitly defining the conditions [more…]

### Using Randomization in a Clinical Study

*Randomized controlled trials* (RCTs) are the gold standard for clinical research. In an RCT, the subjects are randomly allocated into treatment groups (in a parallel trial) or into treatment-sequence groups [more…]

### Basic Mathematical Operations for Use in Statistics

The four basic mathematical operations are addition, subtraction, multiplication, and division (ah, yes — the basics you learned in elementary school). Different symbols indicate these operations. [more…]

### Test for Significance with Hypothesis Testing

All the famous statistical significance tests (Student t, chi-square, ANOVA, and so on) work on the same general principle — they evaluate the size of apparent effect you see in your data against the size [more…]

### How to Define Analytical Populations for a Clinical Study

*Analytical populations* are precisely defined subsets of the enrolled subjects that are used for different kinds of statistical analysis. Most clinical trials include the following types of analytical populations [more…]

### How to Deal with Missing Data from a Clinical Trial

Most clinical trials have incomplete data for one or more variables, which can be a real headache when analyzing your data. The statistical aspects of missing data are quite complicated, so you should [more…]

### How to Handle Multiplicity in Clinical Trial Data

Every time you perform a statistical significance test, you run a chance of being fooled by random fluctuations into thinking that some real effect is present in your data when, in fact, none exists. [more…]

### How to Incorporate Interim Analyses of Clinical Trial Data

An *interim analysis* is one that's carried out before the conclusion of a clinical trial, using only the data that has been obtained so far. Interim analyses can be blinded or unblinded and can be done [more…]