Chi Squared and Gaussian Population Question

In summary, the conversation discussed a frequency distribution of 200 variables from a Gaussian population with mean=26.00 and standard deviation=5.00, plotted as a histogram with bins of 2 units. The conversation also covered calculating the Gaussian function representing the parent distribution, using the mean and standard deviation, and finding the expectation value of (chi-squared) to test the agreement between the data and the theoretical curve. The (chi-squared) probability of the fit was also discussed, using a table to find the probability of drawing a random sample from the parent population that would yield a value of (chi-squared) as large as or larger than the calculated value.
  • #1
a1sh1teru
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The following data represent a frequency distribution of 200 variables drawn from a parent Gaussian population with mean=26.00 and standard deviation=5.00. the bins are 2 units wide and the lower edge of the first bin is at x=14.
4;8;11;20;26;31;29;22;26;13;5;2;3

a. plot a histogram of these data
b. from the mean and standard deviation, calculate the Gaussian function that represents the parent distribution, normalized to the area of the histogram. Your first point should be calculated at x=15, the midpoint of the first bin.
c. calculated (chi-squared) to test the agreement between the data and the theoretical curve.
d. what is the expectation value of (chi-squared)?
e. refer to (chi-squared) distribution table to find the (chi-squared) probability of the fit, that is, the probability of drawing a random sample from the parent population that will yield a value of (chi-squared) as large as or larger than your calculated value.


I have plotted the histogram of the data and I believe I have figured out part B... however I am having great difficulty with part C. I was given the answer already (14.2) but I can't seem to figure out how to get it from the data provided.

I'm REALLY lost with this problem, any and all help with it would be greatly appreciated.
Thank you so much.
 
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  • #2
To determine the chi-square statistic, you take the difference of your data and the theoretical curve at each bin, square it and then sum those up.

In slightly more detail:
First calculate what your theoretical Gaussian value should be at each histogram bin center.
Then take the value of each real-data histogram bin, and find the difference.
Square each difference.
Sum those squares.
Then compare that value (your measured chi-square statistic) with the expected Chi-square value in your table. Hint the table's Chi-square is based on the number of degrees of freedom you have.

There is actually a bit of theory behind all of this, but ignoring all of that for now, that is what you want to do.
 

1. What is Chi Squared and how is it used in statistics?

Chi Squared is a statistical test used to determine if there is a significant difference between observed data and expected data. It is often used to analyze categorical data and can help determine if there is a relationship between two variables.

2. How do you calculate Chi Squared?

Chi Squared is calculated by taking the difference between the observed data and expected data, squaring that difference, and then dividing it by the expected data. This process is repeated for all categories and the results are then summed together to get the Chi Squared value.

3. What is the difference between a Chi Squared test and a t-test?

A Chi Squared test is used to compare categorical data, while a t-test is used to compare numerical data. Additionally, a Chi Squared test does not assume a normal distribution of data, while a t-test does.

4. What is a Gaussian population?

A Gaussian population, also known as a normal population, is a type of probability distribution that is symmetrical and bell-shaped. This means that the majority of the data falls in the middle and tails off on either side.

5. How is Chi Squared used to test for a Gaussian population?

Chi Squared can be used to test if a dataset follows a Gaussian distribution by comparing the observed data to the expected data. If the Chi Squared value is low, it indicates that the data is similar to a Gaussian population. However, if the Chi Squared value is high, it suggests that the data does not follow a Gaussian distribution.

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