Typically, I tell students that the two primary categories of “basic” statistics is whether they (a) determine the relationship between things or (b) the differences between groups. Sometimes, however, you want to do both. To do this, dummy-coded regression can help out. This page is a brief lesson on how to perform a dummy-coded regression in Jamovi, which might be the easiest program ever to perform a dummy-coded regression. As always, if you have any questions, please email me at MHoward@SouthAlabama.edu!
The typical type of regression is a linear regression, which identifies a linear relationship between predictor(s) and an outcome. Believe it or not, a linear regression can also identify the differences between groups pretty well – as long as we know how to code our predictors correctly. This is where dummy coding can come into play, which can be used to answer the following questions and similar others:
- What is the relationship of people’s training groups on their job performance while accounting for their job satisfaction?
- What is the relationship of people’s county of residence on their life satisfaction while accounting for their income?
- What is the relationship of a widget’s manufacturing process on its assessed quality while accounting for the machine operator’s tenure?
Of course, there is more nuance to dummy-coded regression, but we will keep it simple. To answer these questions, we can use Jamovi to calculate a regression equation. If you don’t have a dataset, you can download the example dataset here. In the dataset, we are investigating the relationships of three training groups and conscientiousness with sales. So, training groups is the categorical variable for which we want to compare the groups on the outcome, whereas conscientiousness is the continuous variable for which we want to assess its relation with the outcome.
Also, this file is in .xls format, but Jamovi cannot open this format. To learn how to change this .xls file to a .csv file, which Jamovi can open, please click here. Also, the pictures below are a little small on the page. Click on the link above each picture to view a larger version of the picture in a new window.
The data should look something like this:
With most statistical programs, we would have to create our dummy codes before conducting our dummy-coded analysis. Fortunately, Jamovi does this for us when we conduct the analysis. How convenient!
So, we can proceed directly to conducting the analysis. To do this, we first click on the “Regression” button at the top of the screen.
And then click on “Linear Regression”.
You should see a screen that looks like the following:
Let’s start by identifying our outcome variable in Jamovi. To do so, click on your Sales variable, and then click on the right-facing arrow next to the “Dependent Variable” box.
Next, let’s include our continuous variable as a predictor, which is conscientiousness in this example. Continuous variables should be added to the “Covariates” box in Jamovi. So, click on your conscientiousness variable, and then click on the right-facing arrow next to the “Covariates” box.
Let’s now include our categorical variable as a predictor, which is groups in this example. Typically, we would have needed to create dummy codes for this categorical variable in other statistical programs; however, Jamovi can automatically create these dummy codes for us. To do so, click on your groups variable, and then click on the right-facing arrow next to the “Factors” box.
Now, your window should look like the one below:
Before looking at our results, I want to obtain two more statistics regarding our analyses. First, I want indicators of multicolinearity. To obtain these indicators, we click on the “Assumption Checks” tab.
You should have a new window pop open. In this new window, click on the box next to “Collinearity Statistics”.
With this setting clicked, we can now close our Assumption Checks window by clicking on the tab that reads, “Assumption Checks”.
Second, I want to obtain standardized coefficients from our analyses. To get these, we want to open the Model Coefficients tab by clicking on the label that reads, “Model Coefficients”.
From here, we want to click on the box next to “Standardized Estimate”.
From here, we want to close this open menu.
Now we have our final results – nice! Check my output below and see whether you got the same results. If you got the same results, great! If not, go back through the guide and see where your results differed.
Now, let’s interpret our results. First, we should look at the bottom table, which provides our multicolinearity statistics. Our VIF for both predictors was 1.0. There are a lot of different cutoffs for VIF. Some authors say that VIF should be no higher than 3, 4, 5, or even 10. Whichever cutoff that you choose, none of them are smaller than 1.0. So, multicolinearity is not an issue with our data.
In the first table, we can also see that our R^2 is extremely at .84. This means that our two predictors explain 84% of the variance in job performance. That’s a lot! We wish it was ever this high!
Next, we can look at the p-value column on the second table to see the significance of our predictors. The p-value associated with conscientiousness was .02. This means that conscientiousness is a statistically significant predictor of sales.
Interpreting our grouping variable is a little bit more difficult. When performing dummy-coded regression, the results associated with our grouping variables represent group comparisons. By default, Jamovi codes our grouping variable to compare Group 1 against all other groups. So, the first row associated with our grouping variable (“2 – 1”) represents the comparison of Group 2 and Group 1. The second row associated with our grouping variable (“3 – 1”) represents the comparison of Group 3 and Group 1.
When looking at these dummy-coded results, the p-value associated with the comparison of Group 2 and Group 1 is .057. This is not statistically significant, and therefore there is not a significant difference between Group 2 and Group 1 regarding the outcome of Sales. The p-value associated with the comparison of Group 3 and Group 1 is < .0001. This is statistically significant, and therefore there is a significant difference between Group 3 and Group 1 regarding the outcome of Sales.
In sum, these results indicate that both conscientiousness and our grouping variable had a significant impact on sales. In regards to the grouping variable, Group 3 and Group 1 had a statistically significant difference regarding the outcome of sales.
There is a lot more that we could assess with our dummy-coded regression, but we will leave it here. We have already covered a lot! Now you should be able to perform a dummy-coded regression in Jamovi. As always, if you have any questions or comments, please email me a MHoward@SouthAlabama.edu!