I need to construct Bayes Factor for testing: $$ H_0: \quad 0 = \mu_t - \mu_c $$ $$ H_1: \quad 0 \neq \mu_t - \mu_c $$ and my prior knowledge is modeled by distribution of effect size: $ \delta = \frac{\mu_t - \mu_c}{\sigma} \backsim N(\lambda, \sigma_{\delta})$

I've based on this properties of Cohen's effect size: enter link description here So: $$ BF = \frac{\frac{\theta}{\sqrt{V/v}}}{\frac{\theta + \sigma}{\sqrt{V/v}}}$$ and I get: $$ BF = \frac{T_v(t|0,1)}{T_v(t|\lambda n_{\delta}^{1/2}, n_{\delta}\sigma_{\delta})} $$ because $\theta + \sigma \backsim N(\lambda n_{\delta}^{1/2}, n_{\delta}\sigma_{\delta})$ and $n_{\delta} = \frac{n_T n_C}{n_t + n_C}$

I'm right?



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