Strictly standardized mean difference

In statistics, the strictly standardized mean difference (SSMD) is a measure of effect size. SSMD is the mean divided by the standard deviation of a difference between two random values each from one of two groups. SSMD was initially proposed for quality controland hit selectionin high-throughput screening (HTS) and has become a statistical parameter measuring effect sizes for the comparison of any two groups with random values. In statistics, the strictly standardized mean difference (SSMD) is a measure of effect size. SSMD is the mean divided by the standard deviation of a difference between two random values each from one of two groups. SSMD was initially proposed for quality controland hit selectionin high-throughput screening (HTS) and has become a statistical parameter measuring effect sizes for the comparison of any two groups with random values. In high-throughput screening (HTS), quality control (QC) is critical. An important QC characteristic in a HTS assay is how much the positive controls, test compounds, and negative controls differ from one another. This QC characteristic can be evaluated using the comparison of two well types in HTS assays. Signal-to-noise ratio (S/N), signal-to-background ratio (S/B), and the Z-factor have been adopted to evaluate the quality of HTS assays through the comparison of two investigated types of wells. However, the S/B does not take into account any information on variability; and the S/N can capture the variability only in one group and hence cannot assess the quality of assay when the two groups have different variabilities.Zhang JH et al. proposed the Z-factor. The advantage of the Z-factor over the S/N and S/B is that it takes into account the variabilities in both compared groups. As a result, the Z-factor has been broadly used as a QC metric in HTS assays. The absolute sign in the Z-factor makes it inconvenient to derive its statistical inference mathematically. To derive a better interpretable parameter for measuring the differentiation between two groups, Zhang XHDproposed SSMD to evaluate the differentiation between a positive control and a negative control in HTS assays. SSMD has a probabilistic basis due to its strong link with d+-probability (i.e., the probability that the difference between two groups is positive). To some extent, the d+-probability is equivalent to the well-established probabilistic index P(X > Y) which has been studied and applied in many areas. Supported on its probabilistic basis, SSMD has been used for both quality control and hit selection in high-throughput screening. As a statistical parameter, SSMD (denoted as β {displaystyle eta } ) is defined as the ratio of mean to standard deviation of the difference of two random values respectively from two groups. Assume that one group with random values has mean μ 1 {displaystyle mu _{1}} and variance σ 1 2 {displaystyle sigma _{1}^{2}} and another group has mean μ 2 {displaystyle mu _{2}} and variance σ 2 2 {displaystyle sigma _{2}^{2}} . The covariance between the two groups is σ 12 . {displaystyle sigma _{12}.} Then, the SSMD for the comparison of these two groups is defined as