1-cdf value vs chi-squared statistic mislabeled on site?

In summary, the labeling of the graph in the Wikipedia page for Pearson's chi-squared test is confusing. While the values on the vertical axis appear to be the expected p-values, the graph is labeled as the chi-squared distribution, which is misleading. Clicking on the term leads to a site where the term refers to the probability density function, which is not what the graph is showing. However, it is clarified that the graph is a variation of the chi-squared distribution and the density function given on the second page is correct. The first page graph is merely showing the function of a statistic, not a random variable.
  • #1
nomadreid
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I am confused by the labeling of the (only) graph in
http://en.wikipedia.org/wiki/Pearson's_chi-squared_test
The values on the vertical axis appear to be the values of 1-(the chi-squared cumulative probability distribution values*)
as I would expect in finding the p-values.
However, this graph is labeled the "chi-squared distribution" -- which is ambiguous enough, but when one clicks on this term under the graph, one is directed to a site where the term means the chi-squared probability density function. But the graph cannot be the probability density function: the values are different*, and a probability density function has probability densities on the vertical axis, not probabilities.
So, is this mislabeled?

(*The pdf and cdf graphs were taken from http://en.wikipedia.org/wiki/Chi-squared_distribution#Probability_density_function, and individual values, for more precision, from http://www.danielsoper.com/statcalc3/calc.aspx?id=11)
 
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  • #2
The graph isn't actually labeled as the chi-squared distribution. It's merely saying it's a variation of the chi-squared distribution. The density function given on the second page is correct. Chi-squared is just a gamma distribution so it's obvious the first page doesn't show a standard chi-squared. The graph on the first page is just the function of a statistic, not a random variable.
 
  • #3
ahhhhh. That solves that mystery. Thanks, jwatts.
 

Related to 1-cdf value vs chi-squared statistic mislabeled on site?

1. What is a 1-cdf value and how does it relate to the chi-squared statistic?

A 1-cdf value is a probability value that is calculated from the chi-squared statistic. It represents the probability that the observed data could have occurred by chance alone, assuming that the null hypothesis is true. The chi-squared statistic is used to determine the significance of the relationship between two categorical variables.

2. How is the 1-cdf value vs chi-squared statistic mislabeled on the site?

The 1-cdf value and chi-squared statistic are often mislabeled on websites as being the same thing, when in fact they are two different values. The 1-cdf value is the probability value, while the chi-squared statistic is the test statistic that is calculated from the data.

3. Why is it important to distinguish between the 1-cdf value and chi-squared statistic?

It is important to distinguish between these two values because they serve different purposes. The 1-cdf value is used to determine the significance of the relationship between two variables, while the chi-squared statistic is used to test the null hypothesis. Confusing these two values can lead to incorrect interpretations of statistical tests.

4. How can one avoid mislabeling the 1-cdf value and chi-squared statistic?

To avoid mislabeling these values, it is important to understand the difference between them and how they are calculated. When presenting results, it is also helpful to clearly label the values and explain their meanings to ensure accurate interpretations.

5. Are there any other common misconceptions about the 1-cdf value and chi-squared statistic?

Yes, another common misconception is that a larger chi-squared statistic always indicates a stronger relationship between variables. In reality, the strength of the relationship is also influenced by the sample size and the degrees of freedom. It is important to consider all of these factors when interpreting the results of a chi-squared test.

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