How to Interpret Chi-Square Test Results in a Radioactivity Experiment?

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SUMMARY

The discussion focuses on interpreting the results of a Chi-Square test applied to a radioactivity experiment, specifically comparing Poisson and Normal distributions. The calculated Chi-Square value is 13.992 with 11 degrees of freedom, leading to an alpha level of approximately 0.25 and a p-value of 0.77. This indicates that the data does not significantly deviate from the Poisson distribution, suggesting that the Poisson model is a good fit for the histogram data. The conversation emphasizes understanding the implications of p-values in relation to alpha levels in hypothesis testing.

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  • Understanding of Chi-Square tests and their applications in statistics
  • Familiarity with Poisson and Normal distributions
  • Knowledge of hypothesis testing concepts, including p-values and alpha levels
  • Basic statistical software or online calculators for Chi-Square analysis
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  • Study the implications of p-values in hypothesis testing
  • Learn about the assumptions and applications of the Chi-Square test
  • Explore the differences between Poisson and Normal distributions in statistical modeling
  • Investigate the concept of "goodness of fit" in statistical analysis
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Students in physics or statistics, researchers conducting experiments involving statistical analysis, and anyone looking to deepen their understanding of Chi-Square tests and distribution fitting.

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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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
 

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