We show how to conduct Three Factor ANOVA using capabilities found in the Real Statistics Resource Pack.
Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the Three Factor ANOVA data analysis tool. Two types of input formats are supported. The first format, which we will call standard format by rows is like the input in Example 1 of ANOVA with more than Two Factors.
We will start by looking at this format. We will look at the other format, standard format by columns shortly.
Example 1: Repeat the analysis conducted in Example 1 of ANOVA with more than Two Factors using the Real Statistics’s Three Factor ANOVA data analysis tool.
To use the tool for the analysis of Example 1, click on cell Q1 (where the output will start), enter Ctrl-m and select the Three Factor ANOVA option from the menu that appears. The dialog box in Figure 1 will now appear.
Figure 1 – Dialog box for Three Factor Anova
Enter A4:O11 in the Input Range, click on Column headings included with data, select Std by Rows as the Input Format and select Anova as the Analysis Type and click on the OK button. The output is shown in Figure 2.
Figure 2 – Three Factor ANOVA data analysis
The left side of the figure contains a table of descriptive statistics. Cell T30 contains the total sample size, cell U30 contains the total mean and cell V30 contains SST. The right side of the figure contains the Anova table, which is similar to the analysis shown in Figure 3 of ANOVA with more than Two Factors..
Observation: As mentioned previously, two input formats are supported by the data analysis tool. In addition to the input format shown above, the data analysis tool also supports standard format by columns. This is similar to the stacked format used for Two Factor Anova.
Example 2: Perform an analysis of variance for the data in range A3:D38 of Figure 3.
Figure 3 – Three Factor ANOVA on data in stacked format
To do this, enter Ctrl-m and select the Three Factor ANOVA option from the menu that appears. When the dialog box in Figure 1 appears, enter A3:D38 in the Input Range, unclick Column headings included with data, select Std by Columns as the Input Format, select ANOVA as the Analysis Type and click on the OK button. The output is shown in Figure 3.
The output is similar to that obtained when the standard by rows input format is used and includes descriptive statistics tables and the ANOVA results. In addition, you have the option to convert the input data into the standard by rows format (in sorted order). To do this, also check Convert data in input range to Rows format in the dialog box shown in Figure 1. The result is displayed in Figure 4.
Figure 4 – Converting from by column to by row format
Real Statistics Functions: The Real Statistics Resource Pack contains the following supplemental array functions for converting between the two types of Three Factor Anova formats.
Anova3Rows(R1): takes the data in R1 which is in standard format by columns and outputs an array with the same data in standard format by rows.
Anova3Cols(R1): takes the data in R1 which is in standard format by rows and outputs an array with the same data in standard format by columns.
Observation: Referring to Figure 3 and 4, note that =Anova3Cols(A3:D38) generates the output in range T3:V14 and =Anova3Row(T3:V14) generates output similar to that in range A3:D38, but in sorted order.
Observation: In the all examples given the group samples have the same number of elements (balanced model). In Three Factor ANOVA using Regression we show how to use the Regression option of the Three Factor Anova data analysis tool to analyze unbalanced models.
Also when the Regression option is used for input data in standard format by rows the data is automatically converted to standard format by columns (see Three Factor ANOVA using Regression).