Graph analysis - how closely histogram fits poisson curve

In summary, the speaker is conducting research on random radioactive decay and is using a histogram and the Poisson distribution to analyze the data. They are looking to determine how well the data fits the theoretical model and are considering using a goodness of fit test such as the chi-square or Kolmogorov-Smirnov test. They also plan to compare the results of the test on their 50 interval and 100 interval graphs to see if the 100 interval graph provides a better fit.
  • #1
Platypus26
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Homework Statement



This isn't really a question, its a report thing.

Its about random radioactive decay. I have a histogram showing the number of counts recorded in 3 second intervals and I've drawn the Poisson Curve on the same graph.

I have a graph for 50 intervals and one for 100 intervals and I need to analyse how well the data agrees with Poisson Distribution...and see if the 100 interval graph is any better than the 50 intervals.


Homework Equations



n/a

The Attempt at a Solution



I was thinking I should add up the differences between each bar on the histogram and the curve...subtracting the ones under the curve and adding the ones above. I'm sure this has a name in statistics and I need to know what it is - that's basically my question.

What is the name of this graph analysis/statistics thing that I'm using? Or should I be doing something else?
 
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  • #2




Thank you for sharing your research with us. It seems like you are using the method of comparing observed data to a theoretical distribution, which is commonly known as goodness of fit testing. This method is often used in statistics to determine how well a given theoretical model fits observed data. In your case, you are comparing the observed data from your histogram to the Poisson distribution, which is a theoretical model commonly used to describe random radioactive decay.

To determine how well the data agrees with the Poisson distribution, you can use a statistical test such as the chi-square test or the Kolmogorov-Smirnov test. These tests will provide a numerical value that represents the level of agreement between your observed data and the theoretical model. The smaller the value, the better the fit between the two.

In terms of comparing the 50 interval and 100 interval graphs, you can perform the same goodness of fit test on both sets of data and compare the results. This will allow you to determine if the 100 interval graph provides a better fit to the Poisson distribution compared to the 50 interval graph.

I hope this helps and good luck with your analysis!
 

1. What is graph analysis?

Graph analysis is a method used by scientists to examine and interpret data collected in a graph or chart form. It involves visualizing and studying the relationship between variables and patterns within the data.

2. How do you determine the fit between a histogram and poisson curve?

To determine the fit between a histogram and poisson curve, you can use a statistical test such as the chi-square test. This test compares the observed data in the histogram to the expected data from the poisson curve and calculates a p-value. A low p-value indicates a poor fit between the two, while a high p-value indicates a good fit.

3. What does a good fit between a histogram and poisson curve indicate?

A good fit between a histogram and poisson curve indicates that the data follows a poisson distribution, which is a probability distribution commonly used to model the occurrence of rare events. This means that the data is clustered around a central value and decreases in frequency as it moves away from the center.

4. Can a histogram ever perfectly fit a poisson curve?

Technically, yes, a histogram can perfectly fit a poisson curve if the data perfectly follows a poisson distribution. However, in most cases, there will be some degree of deviation due to the random nature of data and limitations of sampling.

5. How is graph analysis used in real-world applications?

Graph analysis is used in a variety of fields, including biology, economics, and social sciences, to analyze and interpret data. For example, in biology, it can be used to study the distribution of species in an ecosystem, while in economics, it can be used to analyze stock market trends. It is a valuable tool for understanding complex data and making informed decisions based on the results.

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