Statistics How To

Design of Experiments > Accuracy and Precision In any experiment, it is impossible to achieve perfect measurements (even the best atomic clock isn’t flawless: it loses a second every 300 billion years)[1]. The degree to which your measurement deviates from the true value is called accuracy. Another concept closely related to accuracy is precision, which … Read more

Probability Distributions > Chi-bar-squared distribution What is a chi-bar-squared distribution? A chi bar squared distribution is two or more chi-square distributions, mixed over their degrees of freedom. You’ll often find chi-bar-squared distributions when testing a hypothesis with an inequality [1]. More specifically, when testing a hypothesis where the alternate hypothesis has linear inequality constraints on means … Read more

Probability Distributions > Bradford distribution The Bradford distribution is a special type of right-skewed curve, first uncovered in 1949 by S.C. Bradford when he used it to explain how diverse information on a certain topic can be found across various sources and references – instead of being haphazardly scattered, the data follows an archetypal pattern. … Read more

Hypothesis Testing > Likelihood-Ratio Tests Contents: What is a Likelihood-Ratio Test? Likelihood Ratio in Medicine Likelihood Ratio Statistic What is a Likelihood-Ratio Test? The Likelihood-Ratio test (sometimes called the likelihood-ratio chi-squared test) is a hypothesis test that helps you choose the “best” model between two nested models. “Nested models” means that one is a special … Read more

Statistics Definitions > Alternate Hypothesis What is the Alternate Hypothesis? In order to understand what an alternate hypothesis (also called an alternative hypothesis) is, you first need to understand what the null hypothesis means. The word hypothesis means a working statement. In statistics, we’re interested in proving whether a working statement (the null hypothesis) is … Read more

Design of Experiments > Hazard Ratio Contents: About hazard rates, ratios and functions What is a Hazard Ratio? Log of the hazard. About hazard rates, ratios and functions A hazard rate, also known as the failure rate, force of mortality, or the instantaneous event rate, is a measure of the likelihood that an event, such … Read more

Probability Distribution: List of Statistical Distributions > Ferreri distributions Ferreri distributions (distribuzione di Ferreri) are a system of probability distributions described by Ferreri [1]. These univariate distributions have desirable properties such as support on the entire real real line. They are also continuous and unimodal (single-peaked) with exponential tails that are similar to the normal distribution … Read more

Correlation Coefficients > Kendall’s Tau (Kendall Rank Correlation Coefficient) Contents: What is Kendall’s Tau? When to use Kendall’s Tau Types of Kendall’s Tau Example Problem Perfect Agreement Calculating Statistical Significance What is Kendall’s Tau? Kendall’s Tau is a non-parametric measure of relationships between columns of ranked data. The Tau correlation coefficient returns a value of … Read more

Statistics Definitions > Residual Sum of Squares, Total and Explained   Contents: Sum of Squares. Total Sum of Sq. Explained Sum of Sq. Residual Sum of Sq. Sum of Squares Within Error Mean Sum of Squares. Extra Sum of Squares Uses. Watch the video for an overview of the normal distribution, or read on below. … Read more

Statistics Definitions > Normalizing Constant What is a Normalization Constant? A normalizing constant ensures that a probability density function (pdf) has a probability of 1. The constant can take on various guises: it could be a scalar value, an equation, or even a function. As such, there isn’t a “one size fits all” constant; every … Read more