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Standard Error of the Regression vs. R-squared

By Jim Frost 116 Comments


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

Filed Under: Regression Tagged With: analysis example, interpreting results

Chi-Square Test of Independence and an Example

By Jim Frost 52 Comments

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

Filed Under: Hypothesis Testing Tagged With: analysis example, interpreting results

Multivariate ANOVA (MANOVA) Benefits and When to Use It

By Jim Frost 105 Comments

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

Filed Under: ANOVA Tagged With: analysis example, choosing analysis, conceptual, interpreting results

Repeated Measures Designs: Benefits and an ANOVA Example

By Jim Frost 14 Comments

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

Filed Under: ANOVA Tagged With: analysis example, conceptual, interpreting results

How Probability Theory Can Help You Find More Four-Leaf Clovers

By Jim Frost 1 Comment

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

Filed Under: Fun Tagged With: probability

Hypothesis Testing and the Mythbusters: Are Yawns Contagious?

By Jim Frost 1 Comment

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.

[Read more…] about Hypothesis Testing and the Mythbusters: Are Yawns Contagious?

Filed Under: Hypothesis Testing Tagged With: analysis example, interpreting results

Statistical Analysis of the Republican Establishment Split

By Jim Frost Leave a Comment

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

Filed Under: Regression Tagged With: analysis example, interpreting results

Statistics, Exoplanets, and the Search for Earthlike Planets

By Jim Frost 2 Comments

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

Filed Under: Fun Tagged With: distributions, graphs

The Monty Hall Problem: A Statistical Illusion

By Jim Frost 168 Comments

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.

[Read more…] about The Monty Hall Problem: A Statistical Illusion

Filed Under: Fun Tagged With: assumptions

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