Power for a factor-by-continuous interaction

Three habitat types where you suspect the slope of rainfall on biomass is not the same in every habitat: rainfall acts on biomass, but you expect that effect to be stronger or weaker depending on which habitat the sample comes from. That is a moderation, and in MCPower it is the model biomass ~ habitat * rainfall — the * expands to the two habitat contrasts, the rainfall slope, and the habitat:rainfall interaction that carries the moderation. The interaction is the focal test; with a 3-level habitat it is two dummy-by-rainfall terms (each non-reference habitat's slope vs the reference habitat's slope).

Variations

More than three habitat types. Bump habitat=(factor,4) (or higher) — the interaction grows to one dummy-by-rainfall term per non-reference level, all tested together when you target habitat:rainfall.
Swap the continuous moderator for a second factor. Replace rainfall with a categorical predictor and declare it as a factor; habitat * group becomes a factorial design (a two-way ANOVA written as regression).
Unequal group sizes. If the habitats are not balanced, set the factor level proportions so the design reflects the sampling you actually expect, rather than equal thirds.
Different moderation strength. The interaction effect (habitat:rainfall) is the quantity you are usually least sure about — re-run with it at the small (0.10) and large (0.40) continuous benchmarks to bracket how much power hinges on that guess.
Find the N instead of the power. Swap find_power(sample_size=...) for find_sample_size(target_test="habitat:rainfall", from_size=..., to_size=...) to get the smallest N that powers the moderation.
Same design, other fields:
- Clinical: recovery_days ~ dose_level * baseline_severity — does baseline severity moderate the dose-level effect on recovery time across three dose groups?
- Social: wage ~ sector * experience_years — does the experience-years wage slope differ across three employment sectors?

Not this setup?

If you'd rather have…

Three-level dummy-coded categorical predictor — same three-level dummy-coded habitat factor but as a main effect only, no interaction with a continuous predictor.
Continuous moderation with a covariate — a moderation (interaction) that also adjusts for an additional covariate alongside the interacting predictors.
Two interacting categorical predictors (factorial as regression) — keep the categorical habitat predictor but moderate it by another categorical factor instead of a continuous one (factorial as regression).

Copy-paste setup

from mcpower import MCPower

# Three-habitat study with a continuous moderator.
# Research question: does the effect of rainfall on biomass differ across the
# three habitat types -- i.e. does habitat moderate the rainfall slope?
# '*' expands habitat * rainfall to habitat + rainfall + habitat:rainfall.
model = MCPower("biomass = habitat * rainfall")

# habitat is a categorical predictor with 3 levels -> 2 dummy contrasts;
# rainfall is continuous (left at its default standardised distribution).
model.set_variable_type("habitat=(factor,3)")

# A 3-level factor expands to per-level dummies, so its effects and the
# interaction are named per level: habitat[2], habitat[3], and
# habitat[2]:rainfall, habitat[3]:rainfall (the bare names habitat / habitat:rainfall
# do not exist after expansion).
# Standardised effects:
#   habitat[2]=habitat[3]=0.5 -> factor benchmark (0.20/0.50/0.80), each
#                                 non-reference level shifts the outcome by
#                                 a medium amount.
#   rainfall=0.25              -> continuous benchmark (0.10/0.25/0.40), a
#                                 medium slope.
#   habitat[*]:rainfall=0.4   -> the moderation: how much each habitat's
#                                 rainfall slope departs from the reference slope.
model.set_effects(
    "habitat[2]=0.5, habitat[3]=0.5, rainfall=0.25, "
    "habitat[2]:rainfall=0.4, habitat[3]:rainfall=0.4"
)

# Power at N=200 for the interaction dummies -- the moderation is the focal test.
model.find_power(sample_size=200, target_test="habitat[2]:rainfall, habitat[3]:rainfall")

suppressMessages(library(mcpower))

# Three-habitat study with a continuous moderator.
# Research question: does the effect of rainfall on biomass differ across the
# three habitat types -- i.e. does habitat moderate the rainfall slope?
# '*' expands habitat * rainfall to habitat + rainfall + habitat:rainfall.
model <- MCPower$new("biomass ~ habitat * rainfall")

# habitat is a categorical predictor with 3 levels -> 2 dummy contrasts;
# rainfall is continuous (left at its default standardised distribution).
model$set_variable_type("habitat=(factor,3)")

# A 3-level factor expands to per-level dummies, so its effects and the
# interaction are named per level: habitat[2], habitat[3], and
# habitat[2]:rainfall, habitat[3]:rainfall (the bare names habitat / habitat:rainfall
# do not exist after expansion).
# Standardised effects:
#   habitat[2]=habitat[3]=0.5 -> factor benchmark (0.20/0.50/0.80), each
#                                 non-reference level shifts the outcome by
#                                 a medium amount.
#   rainfall=0.25              -> continuous benchmark (0.10/0.25/0.40), a
#                                 medium slope.
#   habitat[*]:rainfall=0.4   -> the moderation: how much each habitat's
#                                 rainfall slope departs from the reference slope.
model$set_effects(paste0(
  "habitat[2]=0.5, habitat[3]=0.5, rainfall=0.25, ",
  "habitat[2]:rainfall=0.4, habitat[3]:rainfall=0.4"
))

# Power at N=200 for the interaction dummies -- the moderation is the focal test.
invisible(model$find_power(
  sample_size = 200,
  target_test = "habitat[2]:rainfall, habitat[3]:rainfall"
))