Interpreting a chi-square test

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In summary: 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.
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JulienB
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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.Thanks a lot in advance for your answers.Julien.
 

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  • #2
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
 

What is a chi-square test?

A chi-square test is a statistical test used to determine if there is a significant relationship between two categorical variables. It compares the observed frequencies of the variables with the expected frequencies to determine if the differences are due to chance or if there is a real relationship between the variables.

When should a chi-square test be used?

A chi-square test should be used when you have two categorical variables and want to determine if there is a significant relationship between them. It is commonly used in research studies and surveys to analyze data and make conclusions about the relationship between variables.

How do you interpret the results of a chi-square test?

The results of a chi-square test are typically presented as a p-value. This value represents the probability of obtaining the observed results if there is no real relationship between the variables. If the p-value is less than the chosen significance level (usually 0.05), then we can reject the null hypothesis and conclude that there is a significant relationship between the variables.

What is the difference between a chi-square test and a t-test?

A chi-square test is used to analyze categorical data, while a t-test is used to analyze continuous data. Additionally, a chi-square test is used to determine if there is a relationship between two variables, while a t-test is used to determine if there is a significant difference between two groups or conditions.

What are the limitations of a chi-square test?

One limitation of a chi-square test is that it can only be used for categorical data and is not appropriate for continuous data. Additionally, it assumes that the sample size is large enough and that the expected frequencies are greater than 5. If these assumptions are not met, the results of the test may be inaccurate.

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