# Standard error vs sd in brms' conditional_effects

Hey,
I was wondering about the output of the conditional_effects() function, especially about the interpretation of the standard error.
Until now I was assuming, that the standard error was the same as the standard deviation so that I could get the upper and lower bounds of a 95% (0.025 - 0.975) interval with mean ± 2se.
However, when I tried this for one of my models, I had a small error in there:

(0.01663656 + 2*0.002212549) - 0.02146316 should then give me 0 but results in -0.000401502 instead. I made sure to use `robust=FALSE` to get the mean and not the median so my guess is that my interpretation of the standard error is off.

Any help to figure this out would be appreciated.

• Operating System: Manjaro 20.0.3
• brms Version: 2.13.0

Hmm, well it’s very close to zero, so maybe a rounding error, which doesn’t make much of a difference? Let’s see what @paul.buerkner has to say about this.

On the basis of the OP, I don’t really know what was attempted so I cannot comment without further information.

@paul.buerkner Thanks for the reply. I want to present the conditional effect for one of my population-level effects with mean, median, sd and 95% interval and I thought `conditional_effects(fit, effects=c("effect)\$effect` would give me that information.
I was assuming, that the `se__` column of the resulting table was the same as the standard deviation, but when I tried to use the mean+2sd formula the result was not the same as the upper bound which confuses me.

This would be an example output:

``````> conditional_effects(mauroc1, effects = c("Algorithm"), robust = FALSE)\$Algorithm
Algorithm      AUROC           LOC      FixCount Project cond__ effect1__ estimate__        se__     lower__    upper__
1 Linespots 0.01646813 -1.021849e-17 -2.610217e-17      NA      1 Linespots 0.01663656 0.002212549 0.012685491 0.02146316
2  Bugspots 0.01646813 -1.021849e-17 -2.610217e-17      NA      1  Bugspots 0.01175480 0.001618417 0.008890391 0.01526760
``````

The approach mean +2se is a frequentist way to obtain CI bounds assuming normality of the estimate. We don’t need such approximation in Bayesian statistics when we have posterior draws from which we can simply compute CI bounds based on the quantiltes of the draws.

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Is my understanding correct then, that if the effect’s distribution were of perfect gaussian shape, the mean +2se approach would still work as expected?
Thank you for the quick answer!

yes, but 1.96se would be closer to the exact value than 2se.

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