Two-Way Analysis of Variance Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER continued 12-2 Two-Way ANOVA 633 R Requires all data to be stacked in a single vector with the corresponding row category names in a separate vector and the corresponding column category names in a separate vector R command: aov1y=x1+x2+x1*x22 Additional Two-Way ANOVA details: summary(aov1y=x1+x2+x1*x22 ) where y contains the data values and x1, x2 contain the corresponding row and column category names. TIP: x1*x2 tests for an interaction effect. A complete list of R statistical commands is available at TriolaStats.com Excel XLSTAT Add-In Data can be in the format of columns or a table. The procedure below is for the default “column” format which requires all data to be stacked in a single column with the corresponding category names for each data value in two separate and adjacent columns. The row names should be in one of those columns and the column names should be in the other column. 1. Click on the XLSTAT tab in the Ribbon and then click Modeling data. 2. Select ANOVA from the dropdown menu. 3. Enter the range of cells containing sample values in the Y>Dependent variables box. 4. Select Qualitative box and enter the range of cells containing the row and column names in the X>Explanatory variables box, such as B1:C30. 5. If a variable label is included in the data range, check the Variable labels box. 6. Click the Options tab and confirm the Interactions, Level box is checked and set to 2. 7. Click the Outputs tab and check the box labeled Type I , II , III SS. 8. Click OK. Click All in the Factors and interactions window and click OK for the results. Look for key results under the heading of “Type I Sum of Squares analysis.” P-values are labeled Pr 7 F. Excel Data Analysis Add-In More than one entry per cell For two-way tables with more than one entry per cell, entries from the same cell must be listed down a column, not across a row. Enter the labels corresponding to the data set in column A and row 1, as shown in this example: A B C D 1 Low Medium High 2 Male 85 78 93 3 Male 90 107 97 f f f f f 1. Click on the Data tab in the Ribbon and then select Data Analysis in the top menu. 2. Select Anova: Two-Factor With Replication under Analysis Tools and click OK. 3. Enter the desired data range for Input Range. 4. In Rows per sample enter the number of values in each cell. 5. Click OK.
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