A simulated repeated-measures experiment in which the two conditions have,
by construction, the same mean reaction time while differing radically in
every other respect. Condition A has a short non-decision time (50 ms) and
a wide, heavily right-skewed distribution; condition B has a long
non-decision time (450 ms) and a narrow, nearly symmetric one. Twenty
participants each contribute 25 trials per condition.
Format
A data frame with 1,000 rows and 3 variables:
- Participant
Participant identifier (factor,
S01-S20).- Condition
Experimental condition,
"A"or"B".- RT
Reaction time, in seconds.
Details
The dataset exists to demonstrate the limits of the summary-statistics
approach: a linear model - including a correctly specified linear mixed
model with a random intercept per participant - finds no effect of
Condition, because a difference in shift, in spread and in tail weight is
invisible to a comparison of means. It is used in the RT models vignette
and in the cogmod paper.
Participants differ in their overall speed through an additive offset (SD = 30 ms) applied identically to both conditions, so that each participant's true condition effect is exactly zero and a random intercept is the correctly specified model for the between-participant variation. The latent offsets are not included in the data.
Examples
data(badlm)
# The two conditions have the same mean...
tapply(badlm$RT, badlm$Condition, mean)
#> A B
#> 0.6940667 0.6928665
# ...but nothing else in common
tapply(badlm$RT, badlm$Condition, sd)
#> A B
#> 0.33150456 0.04731473
# \donttest{
# A mixed model finds nothing
if (requireNamespace("lme4", quietly = TRUE)) {
summary(lme4::lmer(RT ~ Condition + (1 | Participant), data = badlm))
}
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: RT ~ Condition + (1 | Participant)
#> Data: badlm
#>
#> REML criterion at convergence: -32.3
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -2.3271 -0.3793 -0.0506 0.2039 6.1828
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> Participant (Intercept) 0.0005126 0.02264
#> Residual 0.0555791 0.23575
#> Number of obs: 1000, groups: Participant, 20
#>
#> Fixed effects:
#> Estimate Std. Error t value
#> (Intercept) 0.69407 0.01170 59.34
#> ConditionB -0.00120 0.01491 -0.08
#>
#> Correlation of Fixed Effects:
#> (Intr)
#> ConditionB -0.637
# }