Timeline for Why we do not accept the null hypothesis [duplicate]
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| Apr 7, 2023 at 17:02 | history | duplicates list edited | kjetil b halvorsen♦ | duplicates list edited from Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis? to Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?, If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | |
| Apr 7, 2023 at 17:00 | history | closed | kjetil b halvorsen♦ | Duplicate of Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis? | |
| Nov 12, 2021 at 22:01 | comment | added | kjetil b halvorsen♦ | Some possible dups: stats.stackexchange.com/questions/85903/…, stats.stackexchange.com/questions/275677/…, stats.stackexchange.com/questions/163957/…, stats.stackexchange.com/questions/60670/… | |
| Nov 12, 2021 at 19:56 | comment | added | Alexis | In my opinion, the statement "absence of evidence is not evidence of absence". Cool. I am gonna see if I can go publish a bunch of research demonstrating that treatment $A$ has no effect on condition $Y$ based on that reasoning... and I won't even need any funding to do so! After I I do not have any data on $A$ or $Y$ (i.e. I have an absence of evidence)… therefore I can conclude that I have evidence of absence of an effect of $A$ on $Y$! | |
| Nov 12, 2021 at 19:54 | comment | added | Alexis | @MiloMinderbinder Ah! You are correct. I wrote late at night, and misread "does not reduce" as something like "has no effect on". | |
| Nov 12, 2021 at 18:25 | comment | added | Dikran Marsupial | Personally I don't think NHSTs are a basis for accepting anything, you either "reject H0" or you "fail to reject H0". Rejecting H0 doesn't make H1 true, it is just that H1 has survived a test of its plausibility. "we have not proved the null hypothesis to be true." seems straying towards the p-value fallacy (the p-value is not the probability that H0 is true). | |
| Nov 12, 2021 at 18:08 | comment | added | figs_and_nuts | Thank you @DikranMarsupial . The insight that we know the null to be false a-priori is something I liked. In all one-tailed tests though, is it not the case that we do not know the null to be false a-priori? Also, do you have any idea what the author has in mind while stating those reasons for why we don't accept the null hypothesis? | |
| Nov 12, 2021 at 14:51 | comment | added | Dikran Marsupial | "absence of evidence is not evidence of absence" is often overused. Whether absence of evidence is evidence of absence depends on how how unlikely that absence is under each hypothesis. Bayes rule is good for demonstrating that, however the margin of this comment is too small to contain the proof. | |
| Nov 12, 2021 at 14:47 | comment | added | Dikran Marsupial | If you want to know how effective something is, I would have thought a confidence interval on the effect size would be better (or better still, a credible interval)? | |
| Nov 12, 2021 at 14:44 | comment | added | Dikran Marsupial | One reason we do not accept the null hypothesis is that often we know that it is false a-priori, e.g. the unbiasness of a coin will not be precisely zero (or at least it is essentially infinitely unlikely to be exactly zero). I don't think statistics can be used to prove anything. | |
| Nov 12, 2021 at 11:14 | comment | added | figs_and_nuts | In my opinion, the statement "absence of evidence is not evidence of absence" is wordplay without any scientific merit. How strong is an absence of evidence evidence of absence is what reliability engineering is, isn't it? The power of the test etc. If you think that your missing $100 is not in your pocket, you search for it and, you don't find it then you do have evidence that it actually isnt there. How rigorously you searched is the power of your search | |
| Nov 12, 2021 at 10:48 | comment | added | LuckyPal | I agree that the bold reasons are simply misstated and distracting from the actual problem. Your reasoning seems correct. To explain why accepting the null hypothesis after failing to reject is not possible, I prefer the nice saying "absence of evidence is not evidence of absence", which summarizes the philophical issue quite well. | |
| Nov 12, 2021 at 9:15 | comment | added | figs_and_nuts | I think the null proposed is what you are stating that it should be "Substance abuse treatment for prisoners does not reduce their rearrest rate after leaving prison". What am I missing here? And does it have a bearing upon why we do not accept the null hypothesis? | |
| Nov 12, 2021 at 9:12 | history | edited | figs_and_nuts | CC BY-SA 4.0 |
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| Nov 12, 2021 at 8:54 | comment | added | Alexis | If you are proposing something like $\text{H}_{0}\text{: }\theta_{1} = \theta_{2}$ for your null, and something like $\text{H}_{\text{A}}\text{: }\theta_1 < \theta_2$ for your alternative, then where does a reality where $\theta_1 > \theta_2$ fit within your set up? Should the null not be $\text{H}_{0}\text{: }\theta_{1} \ge \theta_{2}$? | |
| Nov 12, 2021 at 8:47 | history | asked | figs_and_nuts | CC BY-SA 4.0 |