# probability

### The Difference Between the Bernoulli and Binomial Distributions

February 8th, 2023 by

You might already be familiar with the binomial distribution. It describes the scenario where the result of an observation is binary—it can be one of two outcomes. You might label the outcomes as “success” and “failure” (or not!). (more…)

### Logistic Regression Analysis: Understanding Odds and Probability

November 22nd, 2021 by

Updated 11/22/2021

Probability and odds measure the same thing: the likelihood or propensity or possibility of a specific outcome.

People use the terms odds and probability interchangeably in casual usage, but that is unfortunate. It just creates confusion because they are not equivalent.

### How Odds and Probability Differ

They measure the same thing on different scales. Imagine how confusing it would be if people used degrees Celsius and degrees Fahrenheit interchangeably. “It’s going to be 35 degrees today” could really make you dress the wrong way.

In measuring the likelihood of any outcome, we need to know (more…)

### Effect Size Statistics: How to Calculate the Odds Ratio from a Chi-Square Cross-tabulation Table

August 12th, 2020 by

Lest you believe that odds ratios are merely the domain of logistic regression, I’m here to tell you it’s not true.

One of the simplest ways to calculate an odds ratio is from a cross tabulation table.

We usually analyze these tables with a categorical statistical test. There are a few options, depending on the sample size and the design, but common ones are Chi-Square test of independence or homogeneity, or a Fisher’s exact test.

### Confusing Statistical Term #8: Odds

December 10th, 2019 by

Odds is confusing in a different way than some of the other terms in this series.

First, it’s a bit of an abstract concept, which I’ll explain below.

But beyond that, it’s confusing because it is used in everyday English as a synonym for probability, but it’s actually a distinct technical term.

I found this incorrect definition recently in a (non-statistics) book: (more…)

### How to Understand a Risk Ratio of Less than 1

December 26th, 2018 by

When a model has a binary outcome, one common effect size is a risk ratio. As a reminder, a risk ratio is simply a ratio of two probabilities. (The risk ratio is also called relative risk.)

Risk ratios are a bit trickier to interpret when they are less than one.

A predictor variable with a risk ratio of less than one is often labeled a “protective factor” (at least in Epidemiology). This can be confusing because in our typical understanding of those terms, it makes no sense that a risk be protective.

### Member Training: Adjustments for Multiple Testing: When and How to Handle Multiplicity

May 3rd, 2018 by
A research study rarely involves just one single statistical test. And multiple testing can result in more statistically significant findings just by chance.

After all, with the typical Type I error rate of 5% used in most tests, we are allowing ourselves to “get lucky” 1 in 20 times for each test.  When you figure out the probability of Type I error across all the tests, that probability skyrockets.
(more…)