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

AI Thread Summary
The discussion centers on the labeling of a graph in the Wikipedia article on Pearson's chi-squared test, which appears to show values related to the cumulative distribution function (CDF) rather than the probability density function (PDF). Users express confusion over the graph's vertical axis, which seems to represent probabilities instead of probability densities, leading to questions about its accuracy. Clarifications indicate that the graph is a variation of the chi-squared distribution and not the standard chi-squared distribution itself. The density function referenced is deemed correct, and it is concluded that the graph represents a function of a statistic rather than a random variable. This resolves the initial confusion regarding the graph's labeling.
nomadreid
Gold Member
Messages
1,748
Reaction score
243
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)
 
Physics news on Phys.org
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.
 
ahhhhh. That solves that mystery. Thanks, jwatts.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
Back
Top