Two-Way ANOVA

Two-Factor ANOVA with Repeated Measures on Both Factors

This page will perform a two-way factorial analysis of variance for designs in which there are 2-4 levels of each of two variables, A and B, with each subject measured under each of the AxB combinations.

	B1	B2	B3
A1	subj 1 X(A1B1) subj 2 X(A1B1) etc.	subj 1 X(A1B2) subj 2 X(A1B2) etc.	subj 1 X(A1B3) subj 2 X(A1B3) etc.
A2	subj 1 X(A2B1) subj 2 X(A2B1) etc.	subj 1 X(A2B2) subj 2 X(A2B2) etc.	subj 1 X(A2B3) subj 2 X(A2B3) etc.

The programming assumes that all active cells include the same number of measures. Thus, with 2 rows and 3 columns, there is a total of 2x3=6 measures for each subject, arranged as illustrated in the adjacent table.

subj = subject
X = measure

Procedure:

Initial Setup:_T
Enter the number of rows and columns in your analysis into the designated text fields, then click the 'Setup' button._T
Entering Data Directly into the Text Fields:_T
After clicking the cursor into the scrollable text area for A1B1 (row1/column1), 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
Within the spreadsheet application or other source of your data, select and copy the column of data for A1B1. Then return to your web browser, click the cursor into the text area for A1B1 and perform the 'Paste' operation from the 'Edit' menu. Perform the same procedure for the other samples in your analysis._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
For a two-way repeated-measures ANOVA, it is esential that the values within each cell be entered in the correct sequence and that the active cells all contain the same number of entries. The programming for the page assumes that each active cell contains the same number of entries as cell A1B1. If you are working on a Macintosh platform, you can check the accuracy of your data entry by clicking the button labeled 'Data Check.' (The data- check feature does not work with Windows.)_T
When all sample values have been entered, click the button labeled 'Calculate.'

Two-Factor ANOVA with Repeated Measures on Both Factors
Number of rows in analysis (A) = Number of columns in analysis (B) =
Data Entry
	B1	B2	B3	B4
A1
A2
A3
A4


Data Check

n's for Cells, Rows, Columns, and Total
	B1	B2	B3	B4	Totals
A1
A2
A3
A4
Totals

Number of subjects: Measures per subject:

Means for Cells, Rows, Columns, and Total
	B1	B2	B3	B4	Totals
A1
A2
A3
A4
Totals

ANOVA Summary
A = row variable B = column variable Subj = subjects
Source	SS	df	MS	F	P
Subjects
Within Subjects
A
Subj x A
B
Subj x B
A x B
Subj x A x B
TOTAL