6.5.7. Page’s L Trend

This is an extension of Friedman Two-Way 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.