I have read this great paper by David Colquhoun: An investigation of the false discovery rate and the misinterpretation of p-values (2014). In essence, he explains why false discovery rate (FDR) can be as high as $30\%$ even though we control for type I error with $\alpha=0.05$.

However I am still confused as to what happens if I apply FDR control in the case of multiple testing.

Say, I have performed a test for each of many variables, and calculated the q-values using Benjamini-Hochberg procedure. I got one variable that is significant with $q=0.049$. I am asking what is the FDR for this finding?

Can I safely assume that in the long run, if I do such analysis on a regular basis, the FDR is not $30\%$, but below $5\%$, because I used Benjamini-Hochberg? That feels wrong, I would say that the $q$-value corresponds to the $p$-value in Colquhoun's paper and his reasoning applies here as well, so that by using a $q$-threshold of $0.05$ I risk to "make fool of myself" (as Colquhoun puts it) in $30\%$ of the cases. However, I tried to explain it more formally and I failed.

I have read this great paper by David Colquhoun: An investigation of the false discovery rate and the misinterpretation of p-values (2014). In essence, he explains why false discovery rate (FDR) can be as high as $30\%$ even though we control for type I error with $\alpha=0.05$.

However I am still confused as to what happens if I apply FDR control in the case of multiple testing.

Say, I have performed a test for each of many variables, and calculated the $q$-values using Benjamini-Hochberg procedure. I got one variable that is significant with $q=0.049$. I am asking what is the FDR for this finding?

Can I safely assume that in the long run, if I do such analysis on a regular basis, the FDR is not $30\%$, but below $5\%$, because I used Benjamini-Hochberg? That feels wrong, I would say that the $q$-value corresponds to the $p$-value in Colquhoun's paper and his reasoning applies here as well, so that by using a $q$-threshold of $0.05$ I risk to "make fool of myself" (as Colquhoun puts it) in $30\%$ of the cases. However, I tried to explain it more formally and I failed.

I have read this great paper by David Colquhoun: An investigation of the false discovery rate and the misinterpretation of p-values (2014). In essence, he explains why false discovery rate (FDR) can be as high as 30% even though we control for type I error with $\alpha=0.05$.

However I am still confused as to what happens if I apply FDR control in the case of multiple testing.

Say, I have performed a test for each of many variables, and calculated the q-values using Benjamini-Hochberg procedure. I got one variable that is significant with $q=0.049$. I am asking what is the FDR for this finding?

Can I safely assume that in the long run, if I do such analysis on a regular basis, the FDR is not 30%, but below 5%, because I used B-H? That feels wrong, I would say that the q-value corresponds to the p-value in Colquhoun's paper and his reasoning applies here as well, so that by using a q-threshold of 0.05 I risk to "make fool of myself" (as Colquhoun puts it) in 30% of the cases. However, I tried to explain it more formally and I failed.

I have read this great paper by David Colquhoun: An investigation of the false discovery rate and the misinterpretation of p-values (2014). In essence, he explains why false discovery rate (FDR) can be as high as $30\%$ even though we control for type I error with $\alpha=0.05$.

However I am still confused as to what happens if I apply FDR control in the case of multiple testing.

Say, I have performed a test for each of many variables, and calculated the q-values using Benjamini-Hochberg procedure. I got one variable that is significant with $q=0.049$. I am asking what is the FDR for this finding?

Can I safely assume that in the long run, if I do such analysis on a regular basis, the FDR is not $30\%$, but below $5\%$, because I used Benjamini-Hochberg? That feels wrong, I would say that the $q$-value corresponds to the $p$-value in Colquhoun's paper and his reasoning applies here as well, so that by using a $q$-threshold of $0.05$ I risk to "make fool of myself" (as Colquhoun puts it) in $30\%$ of the cases. However, I tried to explain it more formally and I failed.