Converting Errors for Logarithmic Graphs for Scientists

In summary, the conversation is about how to add error bars to a graph in a lab report. The equation ln(I_REF/I) is mentioned and the question is how to convert errors in I and T into errors in Log(I) and Log(T) for graphing purposes. The suggestion is to handle the logarithm as usual, but note that the behavior of errors is different from the general behavior of the value, so two separate graphs may be needed.
  • #1
Fluorescent
9
0
I think this is probably the right place to put it, didn't really fit anywhere else.

I've got the joyless task of writing a lab report at university and need to put a graph in it, ideally with error bars. I don't have a problem with error bars normally, but I'm coming unstuck about what to do in this case.

I have the equation: [itex]ln\frac{I_{REF}}{I} = \frac{-hv}{k}[\frac{1}{T_{REF}} - \frac{1}{T}][/itex]. This is in the form y=mx.

If I were to have values for the errors in I and T, how would I convert these into the errors of Log(I) and Log(T) and thus graph them?
 
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  • #2
I don't see your logarithm on the right, but you can handle them as usual just take the logarithm beforehand, except the behaviour of errors is different from the general behaviour of the value. In that case two separate graphs might be useful.
 

FAQ: Converting Errors for Logarithmic Graphs for Scientists

What are error bars on log graphs?

Error bars on log graphs are a visual representation of the variability or uncertainty in a data point on a logarithmic scale. They are typically represented as lines or bars extending from the data point and indicate the range of possible values within which the true value is likely to fall.

Why are error bars important on log graphs?

Error bars are important on log graphs because they provide valuable information about the precision and accuracy of the data. They allow us to see the overall trend of the data while also accounting for the variability in each data point.

How are error bars calculated on log graphs?

The calculation of error bars on log graphs depends on the type of data being represented. For data with symmetric errors, the error bars are typically calculated by taking the standard deviation or standard error of the data and converting it to a logarithmic scale. For data with asymmetric errors, the upper and lower error bars are calculated separately.

What do different types of error bars on log graphs represent?

There are several types of error bars that can be used on log graphs, including standard error, standard deviation, confidence intervals, and range bars. Each type represents a different measure of variability in the data. Standard error and confidence intervals are used to show the precision of the data, while standard deviation and range bars show the spread or dispersion of the data.

How do you interpret error bars on log graphs?

The interpretation of error bars on log graphs depends on the type of data and the type of error bars used. In general, if the error bars for a data point are small, it indicates that the data is precise and the true value is likely to be close to the data point. If the error bars are large, it indicates that the data point is more uncertain and the true value could be farther away from the data point. It is important to also consider the overall trend of the data when interpreting error bars on log graphs.

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