In statistics, the standardized mean of a contrast variable (SMCV or SMC), is a parameter assessing effect size. The SMCV is defined as mean divided by the standard deviation of a contrast variable. The SMCV was first proposed for one-way ANOVA cases and was then extended to multi-factor ANOVA cases . Background Consistent interpretations for the strength of group comparison, as represented by a contrast, are important. When there are only two groups involved in a comparison, SMCV is the same as the strictly standardized mean difference (SSMD). SSMD belongs to a popular type of effect-size measure called "standardized mean differences" which includes Cohen's and Glass's In ANOVA, a similar parameter for measuring the strength of group comparison is standardized effect size (SES). One issue with SES is that its values are incomparable for contrasts with different coefficients. SMCV does not have such an issue. Concept Suppose the random values in t groups represented by random variables have means and variances , respectively. A contrast variable is defined by where the 's are a set of coefficients representing a comparison of interest and satisfy . The SMCV of contrast variable , denoted by , is defined as where is the covariance of and . When are independent, Classifying rule for the strength of group comparisons The population value (denoted by ) of SMCV can be used to classify the strength of a comparison represented by a contrast variable, as shown in the following table. This classifying rule has a probabilistic basis due to the link between SMCV and c+-probability. Statistical estimation and inference The estimation and inference of SMCV presented below is for one-factor experiments. Estimation and inference of SMCV for multi-factor experiments has also been discussed. The estimation of SMCV relies on how samples are obtained in a study. When the groups are correlated, it is usually difficult to estimate the covariance among groups. In such a case, a good strategy is to obtain matched or paired samples (or subjects) and to conduct contrast analysis based on the matched samples. A simple example of matched contrast analysis is the analysis of paired difference of drug effects after and before taking a drug in the same patients. By contrast, another strategy is to not match or pair the samples and to conduct contrast analysis based on the unmatched or unpaired samples. A simple example of unmatched contrast analysis is the