Page's L Test Table: Exact Critical Values

Page's L Table

Jump to a significance level below. Rows: number of blocks n · Columns: number of treatments k · Cells: critical L. Reject H₀ if L ≥ the cell.

Tip: click any value to highlight its row and column.

How to read this table

1. Rank the k treatments within each block, with treatments listed in the hypothesised order.
2. Add up the ranks Rⱼ for each treatment and compute L = Σ j·Rⱼ, where j is the treatment's position in the order.
3. Reject H₀ if L is greater than or equal to the table value.

Worked example

Five subjects each receive four increasing doses, and the rank sums in dose order give L = 137. Row n = 5, column k = 4 of the α = 0.05 table gives 137, so the ordered trend is significant.

Click the underlined links to highlight the value in the table.

Formula and how the values were computed

Values come from the exact null distribution of L, obtained by enumerating the k! orderings within one block and convolving over n independent blocks. Each entry is the smallest L with P(L ≥ l) ≤ α.

Frequently asked questions