# Interpreting a chi-square test

1. Jun 25, 2016

### JulienB

1. The problem statement, all variables and given/known data

Hi everybody! In the context of a physics experiment about radioactivity, I am asked to perform two distributions (poisson and normal) and run a chi-square test for both of them in order to define which one is the most adapted to the histogram (see attached picture).

2. Relevant equations

$\chi^2 = \sum \frac{(k_j(x) -n \cdot P_j)^2}{n \cdot P_j}$

3. The attempt at a solution

So I've used the equation above and got for the Poisson distribution $\chi^2 = 13.992$. How do I interpret this result? I've got 11 degrees of freedom (13 bins - 1 - 1 parameter) so I looked in that table: http://passel.unl.edu/Image/Namuth-CovertDeana956176274/chi-sqaure distribution table.PNG
and I see that $\alpha \approx .25$. What does that mean? Is that good/bad? With this calculator: http://stattrek.com/online-calculator/chi-square.aspx
I've got for p-value .77, which seems to be $1- \alpha$. I'm just not sure just what to think about those numbers.

Julien.

#### Attached Files:

• ###### chisquare.jpg
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2. Jun 26, 2016

### CWatters

It's been 40 years since I did statistics so I'm a bit rusty. But nobody has replied yet so...

a) What is hypothesis? Presumably that the data has a Poisson distribution (or Normal distribution)?
b) Read up on the chi-squared test and "goodness of fit".
c) Find out what it means for the hypothesis if the p-value is > or < than α
d) If I remember correctly α gives you the level of confidence so if α was 0.05 you would be 95% confident in the hypothesis