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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.

JRB
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  • See this question https://stats.stackexchange.com/questions/348502/cohens-d-from-a-linear-regression-model and @dbwilson answer. – Jacques Wainer Dec 01 '21 at 03:47
  • 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? – JRB Dec 01 '21 at 07:42

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