# Statistics: How to differentiate Type A and B uncertainty?

#### Joon

Problem Statement
For the task, I was given a flow rate equation Q= kL(h^n), where k is a constant and L (width of rectangular weir) was set to 0.625 ft. A table with Q values and corresponding h' and h values was provided, please refer to the picture attached. h in the equation= h'-h in the table.

There are two variables in the equation, Q and h, and I need to determine the experimental value of n. I have learnt that for Type A uncertainty statistical calculations should be done and for Type B the least square method. After I calculate the Type A and B uncertainties, I will be able to calculate n.

I think Q is the Type B one whose uncertainty can be calculated using the least square method but I am not sure. By definition, Type A is based on the statistical analysis of measurements and Type B is based on other sources of information such as data book values.

Could someone help me clarify this?
Relevant Equations
Q = kL(h^n)
I tried to find examples on the internet but I am still confused.

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#### Mark44

Mentor
There are two variables in the equation, Q and h, and I need to determine the experimental value of n. I have learnt that for Type A uncertainty statistical calculations should be done and for Type B the least square method. After I calculate the Type A and B uncertainties, I will be able to calculate n.
<snip>
Could someone help me clarify this?
Relevant Equations: Q = kL(h^n)
I have taught Statistics a number of times, but I don't recall the books talking about Type A and Type B uncertainties in this way. Can you elaborate a bit more on what a Type A uncertainty is? Saying that "uncertainty statistical calculations should be done" doesn't shed any light on whatever technique this type of uncertainty entails.

In any case, I'd probably want to use a least squares technique. Taking the natural log of both sides of your equation yields $\ln Q = \ln k + \ln L + n\ln h$, with $\ln k$ and $\ln L$ being known values. This represents a linear relationship between $\ln Q$ and $\ln h$, where $n$ represents the slope of the line.

#### Joon

An example calculation was provided and I was told to use the same method for this task.

The example given was a crater created when a ball strikes sand from a vertical height h.
A table of results and additional information was provided- please refer to the attached file.
What was done for the example: from the equation D= cE^n, to find n, uncertainty calculations were made.

The calculations for U(E) and U(D) are shown in the files attached. As you can see from them, the calculation of U(E) is based on data book values and given data (scales etc) whereas the calculation of U(D) is based on statistical calculations.

A graph was then plotted with ln (U(E)) against ln (U(D)) to find the slope n.
In this example, D was Type A repeated measurements.

So, using the same method as the one used in this example, how should I start doing the calculations?
I was going to do something similar, from the equation Q= kL(h^n), I was thinking of seeing Q analogous to E in the example and h analogous to D in the example.

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"Statistics: How to differentiate Type A and B uncertainty?"

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