1. Definition of Linear Regression Model Multiple linear regression is a linear model accessing the relationship between a dependent variable (DV, or Y) and multiple intendent variables (IV, or X). For instance, you might want to test how consumer purchase intention can be impacted by price as well as by household income. In this case, … Read more
This tutorial shows how to write null and alternative hypothesis for two-way ANOVA. It is an extension of my other tutorial on this same topic. 1. Introduction A two-way ANOVA is used to test whether the means from the two or more categorieal variables are significantly different from one another. For instance, below, there are two categorical variables, … Read more
This tutorial shows how to calculate Sum of Squares Total (SST) in R. The following is the data being used. The hypothetical data being used has two categorical IVs (cities and stores) and one DV (sales). Note that, while it has two IVs, the calculation of SST actually does not need to use these two … Read more
Type 1 ANOVA is also called sequential sum of squares, because it considers the order effect of entering factors into the model. If you change the order of the factors in the model, the results will be different. The following uses an example in R to explain this. Step 1: Prepare the data The following is … Read more
1. Type I ANOVA 1.1 Definition of Type I ANOVA SS(A) for factor A SS(B | A) for factor B SS(AB | A, B) for interaction AB SS(A) is SS attributable to A, even including those that could also have been attributed to other factors like B or A*B. Thus, SS(A) is equal to the … Read more
1. Introduction What are the meanings of different types of ANOVA? In other words, what are Type 1 (Type I), Type 2 (Type II), and Type 3 (Type III) ANOVA? The following uses the model of factors A and B, and its interaction A*B as an example to explain the difference of Type 1 (Type … Read more
Two sample t-test is also called independent sample t-test or unpaired sample t-test. This tutorial explains what two sample t-test is, its formula, and examples of two sample t-test. Definition and Example Two sample t-test is used to test whether means from two different groups of people or objects are significantly different. The name of … Read more
One-Way ANOVA is to compare the means of different groups, to see whether the mean difference is statistically significant. For instance, you would like to compare the average household size of three cities. You can collect 3 samples from these three cities and conduct a one-way ANOVA to check the difference. Formulas of One-way ANOVA … Read more
What is Correlation? Correlation is a statistical measure of the relationship between two variables, X and Y. For instance, you can measure to what extent temperature (X) is related to the production of ice cream (Y). You probably would expect that higher temperatures correspond with higher production of ice cream. On the plot shown below, … Read more
How to Write Null and Alternative Hypotheses