  Randomized controlled trials (RCTs) are used to evaluate treatment effects.
When individuals are grouped together, clustered RCTs are conducted.
Stratification is recommended to reduce imbalance of baseline covariates
between treatment and control. In practice, this can lead to comparisons
between clusters of very different sizes. As a result, direct adjustment
estimators that average differences of means within the strata may be
inconsistent. We study differences of inverse probability weighted means of a
treatment and a control group -- H\'ajek effect estimators -- under two common
forms of stratification: small strata that increase in number; or larger strata
with growing numbers of clusters in each. Under either scenario, mild
conditions give consistency and asymptotic Normality. We propose a variance
estimator applicable to designs with any number of strata and strata of any
size. We describe a special use of the variance estimator that improves small
sample performance of Wald-type confidence intervals. The H\'ajek effect
estimator lends itself to covariance adjustment, and our variance estimator
remains applicable. Simulations and real-world applications in children's
nutrition and education confirm favorable operating characteristics,
demonstrating advantages of the H\'ajek effect estimator beyond its simplicity
and ease of use.
