Multicollinearity occurs when independent variables in a regression model are correlated. This correlation is a problem because independent variables should be *independent*. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results. [Read more…] about Multicollinearity in Regression Analysis: Problems, Detection, and Solutions

# interpreting results

## Benefits of Welch’s ANOVA Compared to the Classic One-Way ANOVA

Welch’s ANOVA is an alternative to the traditional analysis of variance (ANOVA) and it offers some serious benefits. One-way analysis of variance determines whether differences between the means of at least three groups are statistically significant. For decades, introductory statistics classes have taught the classic Fishers one-way ANOVA that uses the F-test. It’s a standard statistical analysis, and you might think it’s pretty much set in stone by now. Surprise, there’s a significant change occurring in the world of one-way analysis of variance! [Read more…] about Benefits of Welch’s ANOVA Compared to the Classic One-Way ANOVA

## Standard Error of the Regression vs. R-squared

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. The standard error of the regression is also known as residual standard error.

[Read more…] about Standard Error of the Regression vs. R-squared

## Chi-Square Test of Independence and an Example

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? This test is also known as the chi-square test of association.

[Read more…] about Chi-Square Test of Independence and an Example

## Multivariate ANOVA (MANOVA) Benefits and When to Use It

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: Benefits and an ANOVA Example

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

## Hypothesis Testing and the Mythbusters: Are Yawns Contagious?

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?

## Statistical Analysis of the Republican Establishment Split

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