Timeline for Why does the critical value varies inversely with the level of significance in hypothesis testing?

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Nov 9, 2015 at 0:26	vote	accept	Ébe Isaac
Nov 8, 2015 at 19:54	comment	added	Chris C		@RichardHardy Sorry, I must have minced my words. By acceptance region, I meant the region where you reject your null. I should have been more accurate with my terminology. While keeping the same df, if you decrease $\alpha$ / increase $\chi^2_{crit}$ then you are decreasing the area under the probability curve where you would reject $H_0$. I thought it would illustrate what I was saying but unfortunately not.
Nov 8, 2015 at 19:45	comment	added	Richard Hardy		@ChrisC, I am not sure if I understand your last sentence. I would say, the acceptance versus the rejection regions are separated by the critical value, and the critical value depends on d.f. Meanwhile, the regions do not depend on the actual realization of the test statistic, $\chi^2$.
Nov 8, 2015 at 19:41	comment	added	Richard Hardy		We are becoming stricter when we require harder evidence against $\text{H}_0$, which is to say, we expand the region of insufficient evidence (non-rejection of $\text{H}_0$).
Nov 8, 2015 at 16:10	answer	added	Glen_b		timeline score: 3
Nov 8, 2015 at 15:00	comment	added	Chris C		The $P$ value is the proportion of the distribution which is greater than the critical value, not less than it. For an increasing $\chi^2$ value, you have a smaller acceptance region, assuming the same df.
Nov 8, 2015 at 14:35	history	asked	Ébe Isaac	CC BY-SA 3.0