# Interpreting a chi-square test

• JulienB
Poisson distributionIn summary, the conversation discusses a physics experiment involving radioactivity and the use of Poisson and Normal distributions. The focus is on performing a chi-square test for both distributions in order to determine which one is best suited for the given data. The conversation also touches on the interpretation of the resulting chi-square values and p-values, as well as the concept of alpha and its relation to confidence in the hypothesis.

## Homework Statement

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).

## Homework Equations

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

## 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.

#### Attachments

• chisquare.jpg
31 KB · Views: 375
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