With n=
count
 A
 B
 C

1_{1} 2_{2} 3_{3}
:
n_{n}
 A_{1} A_{2} A_{3}
:
A_{n}
 B_{1} B_{2} B_{3}
:
B_{n}
 C_{1} C_{2} C_{3}
:
C_{n}

Given k=3 correlated samples of n measures each, of the general form shown in the adjacent table, the Friedman test begins by rankordering the values across each of the rows, which is tantamount to ranking the measures within each of the n subjects or within each of the n randomized blocks, depending on the design. The resulting ranks are then summed down the columns. On the null hypothesis that there is no difference among the k sets of measures, the sum of each column of ranks should approximate
n(k+1)/2. As a measure of the aggregate degree to which the observed column rank sums differ from this nullhypothesis value, the Friedman test calculates a version of the chisquare statistic, which is symbolized here
as csq_{r}.
Procedure
Direct Entry: Enter the observed measures for samples A, B, and C into the designated cells under the heading "Raw Data," beginning in the top
most cell of each column. Pressing the "tab" key after each entry will take you down to the next cell in the column. After all values have been entered, click the «Calculate» button. The rankordering within rows will be performed automatically.
Option for Importing Raw Data from a Spreadsheet ...
Within
the spreadsheet application or other source of your data, select and copy the column of data for sample A. Then return to your web browser, click the cursor into the text area for sample A and perform the 'Paste' operation from the 'Edit' menu. Perform the same procedure for samples B
and C. When importing raw data into the Friedman test, it is essential that the numbers of data items for samples A, B, and C are precisely the same as the value of n that you have specified in setting up this page. For each sample, make sure that the final entry in the list is not followed by a carriage return. To perform this check, click the cursor immediately to the right of the final entry in the list, then press the downarrow key. If an extra line is present, the cursor will move downward. Extra lines can be removed by pressing the downarrow 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}
Import Raw Data_{T}
Data Entry:_{T}
*If n is sufficiently large, the sampling distribution of csq_{r} is a close approximation of the sampling distribution of chisquare with df=k—1. With k=3 and df=2, "sufficiently large" begins at about n=7. If the size of your sample is smaller than 7, you should treat the calculated Pvalue as an imperfect approximation.
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©Richard Lowry 2001
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