We now show how to perform ANCOVA based on ANOVA instead of regression.
Example 1: Redo Example 1 of Basic Concepts of ANCOVA using an ANOVA approach to ANCOVA.
We start by calculating the slopes of the regression lines of the reading scores for each method versus the family income of the children in that sample based on the raw data in Figure 1 of Basic Concepts of ANCOVA. The results are displayed in Figure 1.
Figure 1 – Slopes of regression lines for Example 1
Some representative formulas in Figure 1 are presented in Figure 2.
Figure 2 – Representative formulas from Figure 1
The next step is to run a one-way ANOVA on the reading scores (input data range B5:E15)and another on the family incomes (input data range G5:J15) using either Excel’s Anova: Single Factor data analysis tool or the Real Statistics Single Factor Anova data analysis tool (see Figure 3).
Figure 3 – ANOVA on readings scores and family income
Using the results from Figure 1 and 3, we can now create (in Figure 4) the same two versions of ANCOVA that appear in Figure 3 and 4 of Regression Approach to ANCOVA.
Figure 4 – ANCOVA for Example 1
To see how this is done, we show in Figure 5 some representative formulas from Figure 4.
Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the ANCOVA data analysis tool.
To use the tool for the analysis of Example 1, click on cell L1 (where the output will start), enter Ctrl-m and double click on Analysis of Variance (as shown Figure 0 of Anova Confidence Interval). Select ANCOVA and press OK. Then fill in the dialog box that appears as shown in Figure 6.
Figure 6 – Dialog box for Analysis of Covariance
The output is shown in Figure 7.
Figure 7 – Analysis of Covariance data analysis tool