How do you combine the error of a device with the standard deviation of the readings from it? I have recorded 3 readings of pressure at a set flow rate for about 8 different flow rates. I know the accuracy of my manometer, and can calculate stddev from the 3 points for each. How do you combine these to give the total error? For the sake of error bars and such.
 A: If I am interpreting your scenario correctly, you are using repeated measurements on one event to produce an average that is as close as possible to the true value you are trying to measure.  In other words you are measuring the pressure at time t 3 times.  And you have many of these triplet measurements that comprise your data set.
When you make a measurement with your manometer your accuracy spec says that you can not be more accurate than $\pm$4 Pa.  For example, if you measure 43 Pa, you know that the true value of the measurement is between 39 and 47 Pa.  If you repeat that measurement, you could record 42, 45, and 47 Pa, at time t.  Averaging the three measurements yields an Expected Value ( a mean ) at time t.  
Because the Expectation operator is linear the mean would have an accuracy of the same $\pm$4 Pa.  If X = (42,45,47) and E[X] is defined as the Expected Value of X and c is a constant defined as $\pm $4 Pa 
then:
E[X $\pm$ c] = E[X] $\pm$ c.
Your standard error is an indication of how varied your observations are and not an indication of how accurate they are. 
Consider this. If system A produced measurements 43, 44, and 42 then your accuracy would still be the same: $\pm$ 4 Pa. 
However, if system B produced measurements 42,45,47 system A would vary less than system B, but the accuracy remains constant $\pm$ 4 Pa,. I point this out to assert that the accuracy is a constant and can be treated as such to calculate the Variance of a system.
So in short, if you wanted to combine these errors your would take the Variance of E[X $\pm c$].  Since Variance is invariant with respect to changes in a location parameter. That is, if a constant is added to all values of the variable, the variance is unchanged. 
It is in this since that your accuracy is already incorporated in your standard deviation.
