Synthesis of a Standardized Regression Line

Standardized regression line

In recent years, the 標準化後的回歸直線 of structural equation modeling (SEM) has become increasingly popular among applied researchers. This has led to the rise of several user-friendly and powerful software programs that allow researchers to model complex relationships between quantitative dependent variables and one focal explanatory variable, controlling for other potentially influencing predictors. However, a critical component of this type of research — the synthesis of regression-based effect sizes — can be challenging.

A common method of effect size synthesis involves comparing standardized regression coefficients, or beta weights, across multiple studies. A standardized regression coefficient is the estimated number of standard deviation changes in the dependent variable that will be generated for a standard deviation unit change in the explanatory variable.

Interpreting Standardized Regression Coefficients

These estimates can be obtained in several different ways, depending on the research methods and reporting style used by each of the individual original studies included in a meta-analysis. For example, when the outcome variable is skewed and the original data are log-transformed, the estimated regression slope b and associated standard error SE(b) may be calculated using different methods in each of the evaluated articles.

Another common method is to normalize the regression slope by dividing it by the ratio of the mean and standard deviation of the variable. This produces the standardized regression coefficient b, which is defined as the slope of the line connecting the y-intercept to the regression line (as seen in the figure below). The standardized regression slope can then be compared between studies by calculating the t-test of the null hypothesis that the standardized beta weight is equal to 0.