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I am conducting a meta-analysis of Cohen's d and some raw effect sizes are unstandardised regression coefficients. Of these unstandardised regression coefficients:

  1. Some are based on a binary independent variable and a continuous dependent variable
  2. Others are based on a continuous independent variable and a continuous dependent variable

To convert unstandardised regression coefficients to Cohen's d when the independent variable is binary and the dependent variable is continuous (1), I am using a standard formula used in the "esc_B" function from the "esc" package in R. This requires N1 and N2, the sample size in the treatment and control group.

However, I am not sure how to convert unstandardised regression coefficients to Cohen's d when both independent and dependent variables are continuous?

I can think of two potential options:

  1. Convert the unstandardised regression coefficient to a standardised coefficient (by multiplying the unstandardised coefficient by SD_independentVar / SD_dependentVar) and then convert to Cohen's d

  2. Use the conversion formula (from unstandardised coefficient to Cohen's d) for a binary independent variable, inputting N1 and N2 based on an assumption of the sample sizes if the continuous variable was to be dichotomised.

Any advice on this would be greatly appreciated.

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  • $\begingroup$ See this question stats.stackexchange.com/questions/348502/… and @dbwilson answer. $\endgroup$ Commented Dec 1, 2021 at 3:47
  • $\begingroup$ Thank you @JacquesWainer, I had seen that but the formula requires sample sizes for two groups on the independent variable (N1 and N2). As my independent variable is continuous, I am not sure if it will be valid? $\endgroup$
    – JRB
    Commented Dec 1, 2021 at 7:42

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Cohen's d compares the means of two groups, specifically standardized relative to the standard deviation of these groups.

With two continuous variables, standardized effect size statistics would include r or r-squared.

With two continuous variables, Cohen's d really doesn't make any sense.

There are formulas for conversions among standardized effect size statistics, such as between r and Cohen's d. But it's important to understand what these conversions are doing. In the case of r to d it assumes that there are two groups, and that the r was determined treating one variable as a binary continuous variable. If you use this conversion in other contexts --- at least in my opinion --- the result has no meaning or meaningful comparison to d statistics from other studies. But converting d to r to make it commensurate with other r-like statistics probably makes sense.

There are r-like statistics for two groups of continuous variables, two groups of ordinal variables, two continuous variables, two ordinal variables, two binary variables. And reasonable statistics where there are more than two groups of continuous, ordinal, or --- maybe --- nominal variables.

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