rowvars

Rowvars refers to the computation of the variance across the columns for each row in a two-dimensional numeric array or matrix. The result is a vector whose length equals the number of rows, with each element representing how much that row varies across columns. This operation is used in statistical analysis to assess the stability or variability of each row, for example when rows represent variables such as genes and columns represent samples or conditions.

To compute row variances, let X be an n-by-p matrix and let x_i be the i-th row. The row variance Var_i is commonly defined as the sample variance: Var_i = sum_j (x_ij - mean(x_i))^2 / (k_i - 1), where k_i is the number of non-missing values in row i. Handling missing values is common; most implementations provide an option to ignore missing entries (na.rm or equivalent). If a row has fewer than two non-missing values, its variance is undefined or returned as NA.

Rowvars can be obtained directly in many programming environments via specialized functions or by applying row-wise calculations that combine means and sums of squares in a vectorized form for efficiency. In practice, row variances are used for data normalization, quality control, outlier detection, and feature selection, particularly in high-dimensional datasets where row-wise variability can carry meaningful information.

Limitations include sensitivity to outliers and dependence on the data scale. The interpretation of row variances depends on context: large variances indicate substantial dispersion across columns, while small variances suggest consistency across conditions.

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