Abstract
Some experimental designs involve clustering within only one treatment group. Such designs may involve group tutoring, therapy administered by multiple therapists, or interventions administered by clinics for the treatment group, whereas the control group receives no treatment.
Model
Denote the j th observation in the i th cluster in the treatment by Y ij T ( i =1, . , m; j =1, . , n ), so that there are m clusters of size n in the treatment group. Denote the i th observation in the control group by Y i C ( i =1, . , N C ). Notice that there are no clusters in the control group.
Effect sizes
The most commonly used effect sizes in experimental educational and psychological research are standardized mean differences, defined as the difference between the treatment and control group means divided by (i.e., standardized by) a standard deviation.
Estimating the effect sizes
It is our experience that the information reported in studies will often involve S T (e.g., when the clustering within the treatment group was ignored in the statistical analysis). The actual data might be a standard deviation or a t or F statistic from an analysis that ignored clustering.
Adjusting the significance test for clustering in only one group
Research studies that involve clustering in one treatment group often ignore that clustering in their statistical analyses (Pals et al., 2008 ). This is important because it leads to computed levels of statistical significance that are smaller (and can be much smaller) than the actual level of statistical significance (see, e.g., Hedges, 2007a ).
Unequal cluster sizes
Previous sections of this article have involved the assumption that each cluster has the same number n of individuals. Although this will often be true (at least approximately), it need not always be true.
Conclusions
Experiments sometimes involve cluster sampling in one or both treatment groups. When there is clustering in only one group, such experiments are often improperly analyzed by ignoring the potential impact of clustering on significance tests or effect size calculation.