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Statistics By Jim

Making statistics intuitive

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analysis example

Guide to Stepwise Regression and Best Subsets Regression

By Jim Frost 13 Comments


Automatic variable selection procedures are algorithms that pick the variables to include in your regression model. Stepwise regression and Best Subsets regression are two of the more common variable selection methods. In this post, I compare how these methods work and which one provides better results. [Read more…] about Guide to Stepwise Regression and Best Subsets Regression

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

Goodness-of-Fit Tests for Discrete Distributions

By Jim Frost 23 Comments

Discrete probability distributions are based on discrete variables, which have a finite or countable number of values. In this post, I show you how to perform goodness-of-fit tests to determine how well your data fit various discrete probability distributions. [Read more…] about Goodness-of-Fit Tests for Discrete Distributions

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

Examples of Hypothesis Tests: Busting Myths about the Battle of the Sexes

By Jim Frost 12 Comments

In my house, we love the Mythbusters TV show on the Discovery Channel. The Mythbusters conduct scientific investigations in their quest to test myths and urban legends. In the process, the show provides some fun examples of when and how you should use statistical hypothesis tests to analyze data. [Read more…] about Examples of Hypothesis Tests: Busting Myths about the Battle of the Sexes

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

Making Predictions with Regression Analysis

By Jim Frost 35 Comments

If you were able to make predictions about something important to you, you’d probably love that, right? It’s even better if you know that your predictions are sound. In this post, I show how to use regression analysis to make predictions and determine whether they are both unbiased and precise. [Read more…] about Making Predictions with Regression Analysis

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

Curve Fitting using Linear and Nonlinear Regression

By Jim Frost 42 Comments


In regression analysis, curve fitting is the process of specifying the model that provides the best fit to the specific curves in your dataset. Curved relationships between variables are not as straightforward to fit and interpret as linear relationships. [Read more…] about Curve Fitting using Linear and Nonlinear Regression

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

How to Interpret P-values and Coefficients in Regression Analysis

By Jim Frost 250 Comments


P values and coefficients in regression analysis work together to tell you which relationships in your model are statistically significant and the nature of those relationships. The linear regression coefficients describe the mathematical relationship between each independent variable and the dependent variable. The p values for the coefficients indicate whether these relationships are statistically significant. [Read more…] about How to Interpret P-values and Coefficients in Regression Analysis

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

How to Interpret Adjusted R-Squared and Predicted R-Squared in Regression Analysis

By Jim Frost 134 Comments

R-squared tends to reward you for including too many independent variables in a regression model, and it doesn’t provide any incentive to stop adding more. Adjusted R-squared and predicted R-squared use different approaches to help you fight that impulse to add too many. The protection that adjusted R-squared and predicted R-squared provide is critical because too many terms in a model can produce results that you can’t trust. These statistics help you include the correct number of independent variables in your regression model. [Read more…] about How to Interpret Adjusted R-Squared and Predicted R-Squared in Regression Analysis

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

Multicollinearity in Regression Analysis: Problems, Detection, and Solutions

By Jim Frost 192 Comments


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

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

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

By Jim Frost 63 Comments

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

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

Standard Error of the Regression vs. R-squared

By Jim Frost 130 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. The standard error of the regression is also known as residual standard error.
[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 85 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? This test is also known as the chi-square test of association.
[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 152 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 24 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, experimental design, interpreting results

Hypothesis Testing and the Mythbusters: Are Yawns Contagious?

By Jim Frost 3 Comments

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 2 Comments

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

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    Top Posts

    • How to Interpret P-values and Coefficients in Regression Analysis
    • How To Interpret R-squared in Regression Analysis
    • Z-table
    • How to do t-Tests in Excel
    • Multicollinearity in Regression Analysis: Problems, Detection, and Solutions
    • How to Find the P value: Process and Calculations
    • F-table
    • How to Interpret the F-test of Overall Significance in Regression Analysis
    • Mean, Median, and Mode: Measures of Central Tendency
    • One-Tailed and Two-Tailed Hypothesis Tests Explained

    Recent Posts

    • Sampling Frame: Definition & Examples
    • Probability Mass Function: Definition, Uses & Example
    • Using Scientific Notation
    • Selection Bias: Definition & Examples
    • ANCOVA: Uses, Assumptions & Example
    • Fibonacci Sequence: Formula & Uses

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