2x2x2 Analysis of Variance for Independent Samples

This page will perform an analysis of variance for the situation where there are three independent variables, A, B, and C, each with two levels. As illustrated in the following table, this situation yields 2x2x2=8 unique treatment combinations— a1b1c1, a1b1c2, and so forth— one for each of 8 independent samples of subjects.

 A1 A2 C1 C2 C1 C2 B1 measuresfor sample a1b1c1 measuresfor sample a1b1c2 B1 measuresfor sample a2b1c1 measuresfor sample a2b1c2 B2 measuresfor sample a1b2c1 measuresfor sample a1b2c2 B2 measuresfor sample a2b2c1 measuresfor sample a2b2c2

Please note that this simple version of a three-way ANOVA is not recommended for data sets with an unbalanced design. A balanced design is one in which all eight cells in the analysis have equal values of n. The design is unbalanced in the degree that the eight cell values of n are heterogeneous.

Procedure:
• Entering Data Directly into the Text Fields:T
After clicking the cursor into the scrollable text area for a1b1c1, enter the values for that sample in sequence, pressing the carriage return key after each entry except the last. (On a Macintosh platform, the carriage return key is labeled 'Return'; on a Windows platform it is labeled 'Enter.') Perform the same procedure for the other samples in your analysis.T
• Importing Data via Copy & Paste:T
• Data Check:T
For each sample, make sure that the final entry is not followed by a carriage return. (A carriage return after the final entry in a sample will be interpreted as an extra data entry whose value is zero. Importing data via the copy and paste procedure will almost always produce an extra carriage return at the end of a column.) After all values for a sample have been entered, click the cursor immediately to the right of the final entry in the list, then press the down-arrow key. If an extra line is present, the cursor will move downward. Extra lines can be removed by pressing the down arrow key until the cursor no longer moves, and then pressing the 'Backspace' key (on a Mac platform, 'delete') until the cursor stands immediately to the right of the final entry.T
• When all sample values have been entered, click the button labeled «Calculate».

 Data Entry A1 A2 C1 C2 C1 C2 B1 B1 B2 B2

Values of N
 ABC A1 A2 C1 C2 C1 C2 B1 B1 B2 B2

A1
A2
B1
B2
C1
C2
Total

Mean Values
 ABC A1 A2 C1 C2 C1 C2 B1 B1 B2 B2
 AB A1 A2 B1 B2
 AC A1 A2 C1 C2
 BC B1 B2 C1 C2

 ANOVA Summary Source SS df MS F P A B C AB AC BC ABC Error Total

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