Error bars and slope error ??

curiousgeorge99

1. The problem statement, all variables and given/known data
I have to construct a graph with three lines. The middle line is 'best fit', one line is 'max slope' the other 'min slope', and error bars need to be drawn. The error for the Y axis is too small to draw so there is only an error bar for X axis. With this how do you create the min and max lines? I thought you had to draw the lines based on the Y error bars (i.e. tail of lowest bar to tip of highest type thing).

Also, I need to calculate slope error using these lines but not being able to draw the lines I'm having trouble.

Any ideas?

2. Relevant equations



3. The attempt at a solution

Mentz114

There is a statistical technique, called regression analysis that calculates the best ( least squares) fit to a straight line.

If you can't do that, calculate the average x and y and make sure all three lines go through that point. Calculate the slope of the three lines and that gives the error on the slope ( gradient). Using y = mx+c, you can now calculate the error bars on the points. I forgot the details, since I learnt about statistical line fitting.

nrqed

Draw your error bars on your graph (it does not matter that they are only along X rather than Y). Now use a transparent ruler. Place the ruler on your graph... can you make the ruler to touch all the error bars? (if not, some points must have been incorrectly measured or the errors underestimated).

If you are able to touch all the error bars then to get the max slope, simply do the following: tilt yoru ruler to make it as steep as possible without losing any of the error bars. Then draw the straight line (which will touch all the error bars and will touch at least one of the error bars on its leftmost point and one of the error bars on its rightmost point).
Repeat by drawing the line that touches all the error bars with the smallest slope.

Then, one may use the final slope to be

(max slope + min slope)/2 with an uncertainty (max slope - min slope)/'2

But tehre are other definitions of "best fit line" based on regression analysis, as Mentz mentioned.


Hope this helps

kdevil13

nrqed what you said about finding the max min slope is right. Thats how the teacher in my school teach us. But what if there is no error bars for both x and y axis. The uncertainty is too small to be seen with visible eyes. How do I graph max min slope then?

David Kann

Hi KDevil,

If you're uncertainty is so small you must have a lot of significant figures in your data. If that's the case, you can still pull an uncertainty out of your max-min slope as long as there is some difference between the max and the min slopes. I have created an Excel template to help students easily build graphs with max-min slopes. You should be able to find an uncertainty between the slopes as long as there is a difference withing 16 significant figures (I sure hope there is).

Give it a try. $2 will save you half an hour worth of frustration: http://davidkann.blogspot.com/2010/0...h-minimum.html

Salish99

or use this one for free:
http://drop.io/stats20100/

David Kann

Hi Salish99,

Thank you for putting your work out there for free. I'm too greedy to do that ;)

I think your template and mine can peacefully co-exist as they seem to suit different purposes. I optimized my template for IB Physics students to use in their IA's (reports).

They also do slightly different things. Your template can handle unique errors for each datum, while mine can handle errors in both the x and y variable simultaneously. We also have different methods for calculating the max and min slope.

Cheers! Good luck in your endeavours :)

Salish99

Oh, sorry, didn't mean to barge in.
Yours is way more elaborate, for sure!