Difference between systematic and random errors

[sgstudent]

I learned that random errors cannot be controlled and cannot be eliminated but only be reduced (averaging allows a result that is below the accepted answer to be accounted for by another result that is higher than the accepted result) and so it would cause bad precision. While systematic errors can be controlled and eliminated so the results would be quite precise but still inaccurate.

But when my teacher went through parallax error, she said I'd we continuously change the angle of our eyes from above and below the meniscus, it would be a random error. However, why would this be random? Because even though the results are not precise we are able to eliminate this error by just fixing our head into one position. So I'm not sure why that would be classified under random error. Can someone enlighten me over this?

Thanks so much for the help

 

[mikeph]

First paragraph I believe the last 4 words are mixed up. The precision is a measure of the standard deviation of multiple results from the mean. The accuracy is a measure of the distance from the mean to the true value.

Parallax error... even if you do fix your head over one position, you can't for certain say that your head is in the EXACT same position each time, even if you build some weird head rest thing, there will be some error remaining. If the head rest is aligned properly, then this error is modeled as a random error. (modelling something as a random error doesn't mean it has to be random in nature).

 

[sgstudent]

First paragraph I believe the last 4 words are mixed up. The precision is a measure of the standard deviation of multiple results from the mean. The accuracy is a measure of the distance from the mean to the true value.

Parallax error... even if you do fix your head over one position, you can't for certain say that your head is in the EXACT same position each time, even if you build some weird head rest thing, there will be some error remaining. If the head rest is aligned properly, then this error is modeled as a random error. (modelling something as a random error doesn't mean it has to be random in nature).

I thought precision was the reproducibility of the results while accuracy is whether the result is close to the correct or accepted result? Like the bulls eye example if all hits the bulls eye but are scattered it would be not precise but accurate. While if its completely out of the bulls eye but they are all close together they are precise by inaccurate?

Oh so if my head is fixed at one position it's a random error? But shouldn't it be systematic because the precision is about the same?

What about moving my head up and down for different readings? Because in this case I can generally control my head to be at a certain angle throughout the different readings yet during the reading I'm moving my head up and down causing the reading to not be precise.

I guess the general question would be if I were to get inconsistent and unprecise readings but I'm able to control them actually would it still be random?

Thanks so much for the quick reply :)

 

[sophiecentaur]

If you were reading, using a tall vertical scale (several metres), there would be a systematic parallax error, built in by the geometry of your height and the part of the scale you were reading. If this was taking place on top of a bus, there would be an additional random error. A 'mirror scale' such as they used on good analogue meters, helps to eliminate the systematic parallax error.

 

[mikeph]

I thought precision was the reproducibility of the results while accuracy is whether the result is close to the correct or accepted result? Like the bulls eye example if all hits the bulls eye but are scattered it would be not precise but accurate. While if its completely out of the bulls eye but they are all close together they are precise by inaccurate?

That is exactly what I mean. But it's not in agreement with your earlier sentence:

"While systematic errors can be controlled and eliminated so the results would be quite precise but still inaccurate."

Systematic errors ---> poor accuracy
Random errors ---> poor precision

If you were to eliminate systematic errors then, by definition, your mean result would converge to the true result as you take more and more measurements- precision is not required for this convergence, but accuracy is.

 

[sgstudent]

If you were reading, using a tall vertical scale (several metres), there would be a systematic parallax error, built in by the geometry of your height and the part of the scale you were reading. If this was taking place on top of a bus, there would be an additional random error. A 'mirror scale' such as they used on good analogue meters, helps to eliminate the systematic parallax error.

But what if I were to look up at it for one reading then down for the next. Because definitely we would get unprecise and inaccurate readings. but we we are able to correct this mistake so I'm wondering if its still random.

thanks :)