Split-Plot Designs

Split-Plot Designs accommodate situations where some factors are hard-to-change (expensive or time-consuming to reset) while others are easy-to-change. This design efficiently handles the practical constraints of experimentation by grouping runs and applying appropriate randomization restrictions.

Design Structure & Methodology

Split-Plot ANOVA Model & Error Structure

Statistical Model:

Split-plot designs use two error terms: a whole-plot error for hard-to-change factors and a subplot error for easy-to-change factors and their interaction with whole-plot factors.

Split-plot linear model

yijk

= response for whole plot i, subplot j, replicate k

= whole-plot (hard-to-change) factor effect

δik

= whole-plot error

= subplot (easy-to-change) factor effect

εijk

= subplot error

F-test for the whole-plot factor

MSWP

= whole-plot factor mean square

MSWPE

= whole-plot error mean square

Subplot factors and the whole-plot x subplot interaction are instead tested against the (smaller) subplot error mean square, giving them higher power.

Key Assumptions

• • Whole-plot errors and subplot errors are independent and normally distributed
• • Homogeneity of variance within each error stratum
• • Randomization is correctly restricted to whole plots, then subplots

Reading the Split-Plot Design Layout

Analysis & Interpretation

Implementation Steps & Execution

When to Use Split-Plot Designs

Example Data Layout for Split-Plot Design Example (Manufacturing Process)

Example split-plot design studying temperature (hard-to-change) and pressure/speed (easy-to-change) factors. Temperature requires 4 hours to stabilize, while pressure and speed can be changed quickly. Minimum 2 whole plots with full factorial subplot design. Consider replication of whole plots for better precision on hard-to-change factors.

This is how your spreadsheet or CSV file should be structured before you upload it. Match the column names, keep one row per observation, and leave the analysis to the platform.