The standard error of the regression (S) and R-squared are two key goodness-of-fit measures for regression analysis. While R-squared is the most well-known amongst the goodness-of-fit statistics, I think it is a bit over-hyped. [Read more…] about Standard Error of the Regression vs. R-squared
The Chi-square test of independence determines whether there is a statistically significant relationship between categorical variables. It is a hypothesis test that answers the question—do the values of one categorical variable depend on the value of other categorical variables? [Read more…] about Chi-Square Test of Independence and an Example
Multivariate ANOVA (MANOVA) extends the capabilities of analysis of variance (ANOVA) by assessing multiple dependent variables simultaneously. ANOVA statistically tests the differences between three or more group means. For example, if you have three different teaching methods and you want to evaluate the average scores for these groups, you can use ANOVA. However, ANOVA does have a drawback. It can assess only one dependent variable at a time. This limitation can be an enormous problem in certain circumstances because it can prevent you from detecting effects that actually exist. [Read more…] about Multivariate ANOVA (MANOVA) Benefits and When to Use It
Repeated measures designs, also known as a within-subjects designs, can seem like oddball experiments. When you think of a typical experiment, you probably picture an experimental design that uses mutually exclusive, independent groups. These experiments have a control group and treatment groups that have clear divisions between them. Each subject is in only one of these groups. [Read more…] about Repeated Measures Designs: Benefits and an ANOVA Example
Happy Saint Patrick’s Day! This holiday got me thinking about four-leaf clovers and probability theory. Now, I know that four-leaf clovers are not Shamrocks. And, it is shamrocks that are actually associated with St. Patrick’s Day. A shamrock is a young patch of three-leaf white clover that grows in winter. Nonetheless, the holiday started me thinking about four-leaf clovers and probabilities. [Read more…] about How Probability Theory Can Help You Find More Four-Leaf Clovers
When it comes to hypothesis testing, statistics help you avoid opinions about when an effect is large and how many samples you need to collect. Feelings about these things can be way off—even among those who regularly perform experiments and collect data! These hunches can lead you to incorrect conclusions. Always perform the correct hypothesis tests so you understand the strength of your evidence.
Back in 2014, House Speaker John Boehner resigned, and then Kevin McCarthy refused the position of Speaker of the House before the vote. The Republican’s search for a new speaker ultimately led to Paul Ryan. Simultaneously, the Republican Freedom Caucus was making the news with a potential shutdown of the government that was controversial even amongst some Republicans. [Read more…] about Statistical Analysis of the Republican Establishment Split
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
Who would’ve thought that an old TV game show could inspire a statistical problem that has tripped up mathematicians and statisticians with Ph.Ds? The Monty Hall problem has confused people for decades. In the game show, Let’s Make a Deal, Monty Hall asks you to guess which closed door a prize is behind. The answer is so puzzling that people often refuse to accept it! The problem occurs because our statistical assumptions are incorrect.