Power for an adjusted two-group regression

You are comparing monthly income between union members and non-members, but you want the comparison to hold years of experience fixed. The question: does monthly_income differ by union_member once you adjust for experience_years? This is the ANCOVA / parallel-slopes regression, and as an MCPower formula it is monthly_income ~ union_member + experience_years — a binary predictor (union_member) and a continuous predictor (experience_years) entered as separate main effects, with the two groups sharing a single experience slope. The power you care about is usually the union_member effect: the group gap that survives adjustment for experience_years.

Variations

• Swap the covariate's role. If experience_years is the predictor of interest and union_member is the nuisance control, nothing in the setup changes — just read power off experience_years instead of union_member by setting target_test="experience_years".
• Make the group difference larger or smaller. The union_member=0.50 benchmark is a medium binary effect; drop it to 0.20 for a small group gap or raise it to 0.80 for a large one and re-run to see how the required sample size moves.
• Add a second continuous control. Append another covariate, e.g. monthly_income ~ union_member + experience_years + tenure, and give it its own effect — the union_member power then reflects adjustment for both controls.
• Let the covariate be a factor instead. Swap the continuous experience_years for a 3-level factor such as sector; the slope term becomes a set of dummy contrasts rather than one coefficient.
• Search for N instead of fixing it. Replace find_power with find_sample_size(target_test="union_member", from_size=50, to_size=400, by=10) to find the smallest N that reaches 80% power on the union gap.
• Same design, other fields:
  • Clinical: blood_pressure ~ treatment + baseline_bp — treatment effect on blood pressure adjusting for the patient's baseline measurement.
  • Ecology: plant_biomass ~ habitat + rainfall — habitat effect on biomass adjusting for local rainfall.

Not this setup?

• Group difference where the slope itself differs by group — when the two groups should not share one experience slope.
• A different mix of binary and continuous predictors.
• Sample-size search for a continuous-predictor model.

If you'd rather have…

• Let gender and experience_years interact (gender moderates the experience slope) — instead of parallel slopes, fit wage ~ gender * experience_years so the experience effect is allowed to differ between the two groups.
• Compare the two groups alone (independent t-test) — drop the continuous covariate entirely and just test the group difference.
• Adjust for several continuous controls — when one covariate is not enough and you need to net out a whole block of continuous variables.
• A single continuous predictor, no grouping — when there is no group variable at all and you only have one continuous predictor.

Copy-paste setup

from mcpower import MCPower

# Continuous outcome monthly_income on a binary group (union_member) plus a
# continuous covariate (experience_years) — parallel slopes, no interaction.
# This is the ANCOVA/adjusted two-group comparison: the union_member effect is
# the group gap holding experience_years fixed.
model = MCPower("monthly_income = union_member + experience_years")

# union_member is the binary grouping variable; experience_years stays
# continuous (the default).
model.set_variable_type("union_member=binary")

# Fabricated-plausible effects on the benchmark scale: a medium binary group
# gap (0.50) and a medium continuous experience_years slope (0.25).
model.set_effects("union_member=0.50, experience_years=0.25")

model.find_power(sample_size=120, target_test="all", verbose=False)

suppressMessages(library(mcpower))

# Continuous outcome monthly_income on a binary group (union_member) plus a
# continuous covariate (experience_years) -- parallel slopes, no interaction.
# This is the ANCOVA/adjusted two-group comparison: the union_member effect is
# the group gap holding experience_years fixed.
model <- MCPower$new("monthly_income ~ union_member + experience_years")

# union_member is the binary grouping variable; experience_years stays
# continuous (the default).
model$set_variable_type("union_member=binary")

# Fabricated-plausible effects on the benchmark scale: a medium binary group
# gap (0.50) and a medium continuous experience_years slope (0.25).
model$set_effects("union_member=0.50, experience_years=0.25")

invisible(model$find_power(sample_size = 120, target_test = "all", verbose = FALSE))