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### Estimating Sample Size for Correlation Tests in Biostatistics

For a correlation test in biostatistics (such as the Pearson or Spearman test), pick the scatter chart that looks like an important amount of correlation. Each chart shows the value of [more…]

### Sample Size Estimation for Unpaired Student t Tests in Biostatistics

In biostatistics, when comparing the means of two independent groups of subjects using an unpaired Student t test, the *effect size* is expressed as the ratio of Δ [more…]

### Sample Size Estimation for Paired Student t Tests in Biostatistics

In biostatistics, when comparing paired measurements (such as changes between two time points for the same subject) using a paired Student t test, the [more…]

### Estimating Sample Size When Comparing Two Proportions in Biostatistics

The proportion of subjects having some attribute (such as responding to treatment) can be compared between two groups of subjects by creating a cross-tab from the data, where the two rows represent the [more…]

### Biostatistics For Dummies Cheat Sheet

To estimate sample size in biostatistics, you must state the *effect size of importanc**e,* or the *effect size worth knowing about.* If the true effect size is less than the “important” size, you don’t care [more…]

### The Building Blocks of Mathematical Formulas for Biostatistics

No matter how they're written, mathematical formulas are just concise "recipes" that tell you how to calculate something or how something is defined. You just have to know how to read the recipe. To start [more…]

### Powers, Roots, and Logarithms for Use in Biostatistics

These three mathematical operations — working with powers, roots, and logarithms — are all related to the idea of repeated multiplication. These basic functions are used to help build more complex formulas [more…]

### Factorials and Absolute Values

Most mathematical operators are written *between* the two numbers they operate on, or *before* the number if it operates on only one number (like the minus sign used as a unary operator). But factorials and [more…]

### 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…]