Analytic Hierarchy Process (AHP)

The Analytic Hierarchy Process (AHP), developed by Thomas L. Saaty, is a structured decision-making method that derives priorities (weights) for a set of alternatives or criteria from pairwise comparisons rather than from direct ratings. AHP is widely used in environmental management, public policy, healthcare, supplier selection and any setting where stakeholders must trade off multiple, often qualitative, criteria.

In tickStat, AHP is a dedicated question type that automatically generates the full pairwise comparison matrix from a list of items and captures the respondent's judgement on a continuous importance slider.

When to use it

Use AHP when you need to elicit relative priorities among a small-to-medium set of options (typically 3–9) and direct rating questions are not informative enough — for example because respondents tend to rate everything as "important". Pairwise comparisons force respondents to reveal trade-offs, which makes AHP particularly suited to:

  • Stakeholder weighting of policy criteria.
  • Site selection with multiple environmental and social criteria.
  • Prioritisation of conservation actions, public investments or ecosystem services.
  • Multi-criteria decision analysis (MCDA) studies in general.

How it works in tickStat

The researcher selects an origin question whose answer options become the items to be compared. tickStat then automatically generates all n(n − 1)/2 pairwise comparisons.

For each pair, the respondent sees the two items side by side and uses a slider to indicate which item is more important and by how much. The slider corresponds to a continuous version of the classical Saaty 1–9 scale, in which the centre means equal importance and the extremes mean extreme importance of one item over the other.

Configuration options include:

  • Items origin question — the question that supplies the list of criteria or alternatives to compare.
  • Header text — custom instructions shown above the comparison grid.
  • Visual styling — colour scheme for the left and right items.

Captured data and analysis

For every pairwise comparison, tickStat records the two items and the importance value the respondent selected. From this data you can:

  • Build the pairwise comparison matrix for each respondent.
  • Compute priority weights via the principal eigenvector of the matrix (Saaty's standard method) or via the geometric-mean approximation.
  • Compute the Consistency Ratio (CR) to assess whether a respondent's judgements are internally coherent (CR ≤ 0.10 is the conventional threshold).
  • Aggregate weights across respondents for group decision-making — using geometric means of individual judgements (AIJ) or aggregation of individual priorities (AIP).

The raw comparison data is exported in the SPSS-format complete report so you can run the eigenvector and consistency calculations in R, Python, MATLAB or any AHP-specific tool.

Practical tips

  • Keep the number of items between 3 and 9. With more than 9 items, respondents struggle to keep all comparisons internally consistent and the matrix becomes long to fill in.
  • Consider grouping items hierarchically and running AHP at each level (the original Saaty methodology) rather than comparing 15 items in a single matrix.
  • Always report the share of respondents whose judgements meet the CR ≤ 0.10 threshold; high-CR respondents indicate that instructions were unclear or that items were not well differentiated.