Calculator Input
Example Data Table
This example shows five blocks with four ordered conditions. It produces a strong increasing trend.
| Block | Week 1 | Week 2 | Week 3 | Week 4 |
|---|---|---|---|---|
| Block 1 | 10 | 12 | 15 | 18 |
| Block 2 | 9 | 11 | 14 | 17 |
| Block 3 | 8 | 10 | 13 | 16 |
| Block 4 | 11 | 13 | 15 | 19 |
| Block 5 | 7 | 9 | 12 | 15 |
Formula Used
Step 1: Rank each row of repeated measurements from smallest to largest. If ties occur, assign average ranks.
Step 2: Compute each condition rank sum as Rj = Σ rij.
Step 3: Compute Page's statistic as L = Σ xjRj, where xj are the expected scores for the ordered alternative.
Step 4: Under the null hypothesis, the calculator also reports E[L] = n(c+1)Σxj/2.
Step 5: The variance is Var(L) = n·c(c+1)·Σ(xj−x̄)2/12. An exact or approximate one-sided p-value is then returned.
Here, n is the number of blocks and c is the number of conditions. The test is designed for ordered alternatives in repeated-measure or blocked data.
How to Use This Calculator
- Choose the number of blocks and the number of ordered conditions.
- Set your alpha level and select whether the expected trend increases or decreases across conditions.
- Optionally enter custom expected scores if your ordering needs unequal spacing.
- Type the raw repeated measurements into the matrix. Each row represents one block or subject.
- Submit the form to view Page's L statistic, p-values, ranked data, and the Plotly graph.
- Use the download buttons to export the result summary as CSV or PDF.
Frequently Asked Questions
1. What does the Page trend test measure?
It checks whether repeated measurements follow a prespecified ordered pattern across conditions. The method is useful when you expect a monotonic increase or decrease rather than any arbitrary difference.
2. When should I use this calculator?
Use it for blocked or repeated-measure designs where the same subjects, items, or matched sets are observed under several ordered conditions.
3. Can I enter raw scores instead of ranks?
Yes. The calculator automatically ranks values within each block before computing the test statistic, so you can enter the original repeated measurements directly.
4. How are ties handled?
Tied values inside a block receive average ranks. That keeps the ranking fair, but ties can prevent exact enumeration, so the calculator may switch to a normal approximation.
5. Why do I sometimes get an exact p-value and sometimes an approximate one?
Exact p-values are available only when the input supports direct permutation enumeration. Otherwise, the calculator reports the asymptotic normal approximation for the one-sided test.
6. What does a small p-value mean here?
A small p-value means the observed ordering is unlikely under the null hypothesis of no ordered trend. That supports the direction you selected.
7. What do custom expected scores change?
They let you define how strongly each condition contributes to the ordered alternative. This is useful when condition spacing is not equally weighted.
8. What input sizes are supported?
This page accepts 2 to 30 blocks and 3 to 8 conditions. Exact enumeration is limited to smaller untied integer-score setups.