6.5.7. Page’s L Trend
This is an extension of Friedman TwoWay ANOVA by ranks. Page’s L Trend is useful when trends between several variables are examined. It is defined as:
where tc is the column rank totals and c is the column number.
Data entry is in matrix format (see 6.0.5. Tests with Matrix Data). Columns selected for this test must have equal number of rows and rows containing at least one missing value are omitted.
The output includes the rank sum and mean rank for each variable. For the probability level, tables for Page’s L must be consulted.
Example
Table 85 on p. 227 from Cohen, L. & M. Holliday (1983). Cognitive gain scores in predicted order under four learning conditions are given. The null hypothesis “cognitive gains in the sample are not related to the predicted order of experimental treatments” is tested.
Open NONPARM2, select Statistics 1 → Nonparametric Tests (Multisample) → Page’s L Trend and select Condition 1, Condition 2, Condition 3 and Condition 4 (C13 to C16) as [Variable]s to obtain the following results:
Page’s L Trend

Cases 
Rank Sum 
Mean Rank 
Condition 1 
6 
8.5000 
1.4167 
Condition 2 
6 
12.0000 
2.0000 
Condition 3 
6 
17.0000 
2.8333 
Condition 4 
6 
22.5000 
3.7500 
Total 
24 
60.0000 
2.5000 
Number of Columns = 
4 
Number of Rows = 
6 
Page’s L Trend = 
173.5000 
For the probability value consult critical values table for Page’s L test
From tables, the critical value for 6 subjects and 4 conditions at 0.1% level is 172. Therefore, this result is significant at 0.001 (or 0.1%) level and thus reject the null hypothesis.