A confidence interval is calculated from a sample and provides a range of values that likely contains the unknown value of a population parameter. In this post, I demonstrate how confidence intervals and confidence levels work using graphs and concepts instead of formulas. In the process, you’ll see how confidence intervals are very similar to P values and significance levels. [Read more…] about How Hypothesis Tests Work: Confidence Intervals and Confidence Levels

# graphs

## How t-Tests Work: t-Values, t-Distributions, and Probabilities

T-tests are statistical hypothesis tests that you use to analyze one or two sample means. Depending on the t-test that you use, you can compare a sample mean to a hypothesized value, the means of two independent samples, or the difference between paired samples. In this post, I show you how t-tests use t-values and t-distributions to calculate probabilities and test hypotheses.

As usual, I’ll provide clear explanations of t-values and t-distributions using concepts and graphs rather than formulas! If you need a primer on the basics, read my hypothesis testing overview. [Read more…] about How t-Tests Work: t-Values, t-Distributions, and Probabilities

## How to Interpret the Constant (Y Intercept) in Regression Analysis

The constant term in regression analysis is the value at which the regression line crosses the y-axis. The constant is also known as the y-intercept. That sounds simple enough, right? Mathematically, the regression constant really is that simple. However, the difficulties begin when you try to interpret the *meaning* of the y-intercept in your regression output. [Read more…] about How to Interpret the Constant (Y Intercept) in Regression Analysis

## How F-tests work in Analysis of Variance (ANOVA)

Analysis of variance (ANOVA) uses F-tests to statistically assess the equality of means when you have three or more groups. In this post, I’ll answer several common questions about the F-test.

- How do F-tests work?
- Why do we analyze
*variances*to test*means*?

I’ll use concepts and graphs to answer these questions about F-tests in the context of a one-way ANOVA example. I’ll use the same approach that I use to explain how t-tests work. If you need a primer on the basics, read my hypothesis testing overview. [Read more…] about How F-tests work in Analysis of Variance (ANOVA)

## Check Your Residual Plots to Ensure Trustworthy Regression Results!

Use residual plots to check the assumptions of an OLS linear regression model. If you violate the assumptions, you risk producing results that you can’t trust. Residual plots display the residual values on the y-axis and fitted values, or another variable, on the x-axis. After you fit a regression model, it is crucial to check the residual plots. If your plots display unwanted patterns, you can’t trust the regression coefficients and other numeric results.

In this post, I explain the conceptual reasons why residual plots help ensure that your regression model is valid. I’ll also show you what to look for and how to fix the problems. [Read more…] about Check Your Residual Plots to Ensure Trustworthy Regression Results!

## When is Easter this Year?

When is Easter this year? I ask this question every year! This year, Easter occurs on April 16, 2017. Next year, Easter falls on April 1, 2018. I have a hard time remembering when it occurs in any given year. I think that March Easters are both early and unusual. Is that true?

Being a statistician, my first thought is to study the distribution of Easter dates. By analyzing the distribution, we can determine which dates are rare and which are common. How unusual are Easter dates in March? Are there patterns in the dates? [Read more…] about When is Easter this Year?

## Statistics, Exoplanets, and the Search for Earthlike Planets

I love astronomy! The discovery of thousands of exoplanets has made it only more exciting. You often hear about the really weird planets in the news. You know, things like low density puffballs, hot Jupiters, rogue planets, planets that orbit their star in hours, and even a Jupiter mass planet that is one huge diamond! As neat as these discoveries are, I also want to know how Earth fits in. [Read more…] about Statistics, Exoplanets, and the Search for Earthlike Planets