Two-Way ANOVA


Two-Way Analysis of Variance for Independent Samples
The logic and computational details of the two-way
ANOVA for independent samples are described in
Chapter 16 of Concepts and Applications.
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 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 row1/column1. Then return to your web browser, click the cursor into the text area for row1/column1 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
  • When all sample values have been entered, click the button labeled «Calculate.» The default analysis is a standard weighted-means analysis. If you wish to perform an unweighted-means analysis, click the «Unweighted» button before calculating.
QNumber of rows in analysis =
QNumber of columns in analysis =
Q

Click this button only if you wish to perform
an unweighted-means analysis. Advice: do
not perform an unweighted-means analysis
unless you have a clear reason for doing so.

Click this button to return to a standard
weighted-means analysis
Data Entry
Col 1 Col 2 Col 3 Col 4
Row 1
Row 2
Row 3
Row 4
Summary Data
Within each box:
Item 1 = N Item 2 = X Item 3 = Mean
Item 4 = X2 Item 5 = Variance
Item 6 = Std. Dev. Item 7 = Std. Err.
C1 C2 C3 C4 Total
R1
R2
R3
R4
Total
ANOVA Summary
Source
SS
df
MS
F
P
Rows





Columns





r x c





Error



Total


Critical Values for the Tukey HSD Test
HSD[.05]
HSD[.01]
HSD=the absolute [unsigned] difference between any two means (row means, column means, or cell means) required for significance at the designated level: HSD[.05] for the .05 level; HSD[.01] for the .01 level. The HSD test between row means can be meaningfully performed only if the row effect is significant; between column means, only if the column effect is significant; and between cell means, only if the interaction effect is significant.
Rows
Columns
Cells



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