# Chi-Square to P-Value - Basic Stats

In a review problem for a class, we were asked to perform a Chi-Square Test Statistic for a 2x2 Table without a continuity correction. In the answer key, my professor included the following:

I totally follow all of the math up until the p-value portion. Where did she get the 0.25 p-value? Any suggestions you have would be much appreciated! Thank you!

I am currently thinking about it such that: if the x2observed < 0.25 alpha's X2crit (which is 1.32) then it definitely will be less than 0.05 alpha's x2 crit of 3.84? However, where the p-values come into play is still unclear to me.

• Run pchisq(.607 , df = 1, lower.tail = FALSE) in $\mathsf R.$ Commented Sep 28, 2022 at 14:57
• This sort of thing shows up when someone is consulting a table of critical values and the table does not include any significance levels above $0.25$ (which, with $df=1$ here, would correspond to a critical value of $1.323$). In other words, your teacher might only know that $0.607$ is less than $1.323.$
– whuber
Commented Sep 28, 2022 at 15:47
• So can I think about it like: if the x2observed < 0.25 alpha's X2crit (which is 1.32) then it definitely will be less than 0.05 alpha's x2 crit of 3.84? But how did she get a p-value of 0.25? Is the 1.32 the p-value??
– Cat
Commented Sep 28, 2022 at 17:12

Here $$0.25$$ is not a p-value, but the significance level, $$\alpha$$, to which the p-value is compared. The significance level is decided upon before the experiment and any calculations The results are then considered significant only if $$p < \alpha$$.

The value of $$P(\chi_{df=1}^2\geq 0.607)$$ is either taken from a table (e.g., like this one) or computed using a typical statistical software.

Remark: In fact $$0.25$$ is a very high number for a significance level, so most likely it is just the approximate value of $$P(\chi_{df=1}^2\geq 0.607)$$.

• Seems legit. Maybe it's like $0.25 > 0.05.$ But this seems to be weird for any standard. Anyway, +1. Commented Sep 28, 2022 at 15:01
• @User1865345 p-value is too high, so no conclusions can be made (we can only reject the null hypothesis if $p<\alpha$, but if otherwise, we cannot claim that it is correct.) Commented Sep 28, 2022 at 15:10
• Exactly. Pretty evident by definition of $p$-value. What I am wondering is the rationale behind choosing $0.25.$ Commented Sep 28, 2022 at 15:12
• @User1865345 scipy.stats gives a value rather different from $0.25$, so I suppose it is the confidence level after all. Commented Sep 28, 2022 at 15:18
• So can I think about it like: if the x2observed < 0.25 alpha's X2crit (which is 1.32) then it definitely will be less than 0.05 alpha's x2 crit of 3.84? But how did she get a p-value of 0.25? Is the 1.32 the p-value??
– Cat
Commented Sep 28, 2022 at 17:11