Accuracy and percentage uncertainty

[koat]

hello

I have some questions which I was struggeling with
1. Is percentage error the same as percentage uncertainty?
Because percentage error is a measurement of accuracy and is percentage uncertainty also a measure of accuracy?

2. How do percentage uncertainty and percentage difference affect the accuracy of an experiment.

Please help I am totally lost and I can't get my head around it at all :(
thanks

 

[amy andrews]

Percentage error is how wrong you are, percentage uncertainty is how confident you are. Say you conduct a lab or experiment. In this experiment, you're calculating the value of the gravitational constant "g" using a pendulum. As part of the experiment you measure the length of the string that holds the weight on the pendulum. Maybe you find that the length is 10 cm. However, you're not absolutely sure of this value, so you add on an uncertainty- how far off could you be? You say that, well, you could be a millimeter off. So you say that your value for the length of the string is 10 cm plus or minus 1 mm. That's an uncertainty.

Say, in the same experiment, you calculate that the value of g= 10.0 m/s^2. The literature or accepted value of g is 9.8 m/s^2, so you calculate a percentage error to finish off your experiment: Subtract the experimental value from the literature value, and divide the absolute value of that by the literature value (then multiply by a 100 to get a percent). Your percentage error is 9.8-10/10 *100, or 2% error.

Think of how this would affect an experiment. You now have a wider margin of error and a wider range of values.

Hope this helps :)

 

[koat]

Thanks for your effort but I don't really understand that. :(

I still don't know if percentage uncertainty is a measure of accuracy?
And how do percentage uncertainty and percentage difference affect the accuracy of an experiment?

 

[amy andrews]

Percentage uncertainty is also a measure of accuracy, but in a different way than from percentage error. It's a measure of your accuracy while doing the experiment. Percentage error is a measure of the accuracy of your final result.

Overall, percentage uncertainty improves the accuracy of the experiment because you now have a wider range of results.

 

[koat]

Percentage uncertainty is also a measure of accuracy, but in a different way than from percentage error. It's a measure of your accuracy while doing the experiment. Percentage error is a measure of the accuracy of your final result.

Overall, percentage uncertainty improves the accuracy of the experiment because you now have a wider range of results.

Does it mean that when the percentage uncertainty gets bigger the accuracy gets bigger while I am doing the experiment?
And how do you know that I have a wider range of results?
Does the percentage difference have any effect on the accuracy?

 

[amy andrews]

Sorry I could not reply earlier.

Yes, the accuracy is higher the bigger the percentage uncertainty, but your vagueness also increases. When you have a percentage uncertainty added to a value, it increases the accuracy of the value. Say you have a value, 7[tex]\pm[/tex].2. (The .2 is the uncertainty.) You're saying, "This value could be 7, but it could also be (minimum) 7-.2=6.8, or it could be (maximum) 7+.2=7.2, or it could be anywhere in between those values." See what I mean? You have a higher chance of hitting the absolute correct value, but you lose the sharpness of just one value.

Now, if you use 7[tex]\pm[/tex].2 in an experiment, you'll have to calculate a maximum possible value of your result, and a minimum, in addition to just using 7 for your result. So now you have a range of values and a higher chance of hitting the correct result.

Hope that makes it clearer.