Timeline for Logic of hypothesis testing
Current License: CC BY-SA 4.0
12 events
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| S Mar 1, 2023 at 11:32 | history | suggested | psmears | CC BY-SA 4.0 |
Fix a few typos
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| Mar 1, 2023 at 10:36 | review | Suggested edits | |||
| S Mar 1, 2023 at 11:32 | |||||
| Feb 28, 2023 at 19:29 | comment | added | user6527 | "What they are doing is an hypothesis test." it is probably a subjectivist Bayesian hypothesis test though, rather than a frequentist one. | |
| Feb 28, 2023 at 18:38 | comment | added | Sanyo Mn | Thank you, your comments really helped. However, I would like to add that there seems to be a lot of details and subtle points in hypothesis testing, that is why I'm looking for a formal treatment, otherwise, when specified with ordinary language, some points remain unclear. | |
| Feb 28, 2023 at 18:30 | comment | added | Ian Sudbery | "I see but in hypothesis testing isn't our aim to test hypotheses like "the coin is fair"" - hypothesis tests test whatever hypothesis we say they are testing. But that null hypothesis must be a full description of the world in order that we can accurately calculate the likelihood of the data under them. They almost always contain a whole load of unspoken assumptions. This is also why it is poor practice to accept the alternative hypothesis when we reject the null - we can never be entirely sure which bit of the null was false. | |
| Feb 28, 2023 at 18:27 | comment | added | Ian Sudbery |
At this point we would be in the world of interval estimation, which is indeed a framework that those that don't like hypothesis testing often favour. If you did want to stay within the hypothesis testing framework we would have to change the null hypothosis and say "this data is unlikely if P(heads) was more had x% away from 50%". In that case p(heads)=50% is not the null hypothesis, the null hypothesis is 50%-X < p(heads) > 50% +X and that the data would be unlikely if this were not true.
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| Feb 28, 2023 at 18:23 | comment | added | Ian Sudbery | But lets say that it is me making the call, and I am observing the coin directly. There are two different ways we can talk about getting 510 heads and 490 tails. First let us note that while 510/490 is compatible with 50% heads, 50% tails, it is also compatible with 51% heads, 49% tails, or 52% heads, 48% tails etc. In fact its compatible with an infinite number of values for P(Heads) in between. One can state that all credible values of values for P(Heads) are close to 0 (for some definition of close). This is valid, but is not a hypothesis test. | |
| Feb 28, 2023 at 18:22 | comment | added | Sanyo Mn | I see but in hypothesis testing isn't our aim to test hypotheses like "the coin is fair" | |
| Feb 28, 2023 at 18:17 | comment | added | Ian Sudbery | @SanyoMn The point here is not how many times the coin comes up heads or tail, but that what I tell the students bares no relation to what the coin actaully comes up as. The null hypothesis being tested here is not that the coin is fair. Its that the coin is fair and I am telling the truth about how many heads and tails there are. | |
| Feb 28, 2023 at 18:13 | comment | added | Sanyo Mn | What about this case? Toss the coin 1000 times, if the result is 510 heads and 490 tails, doesn't it support the hypothesis that the coin is fair (that is, 50% chance of heads and 50% chance of tail). | |
| S Feb 28, 2023 at 16:08 | review | First answers | |||
| Feb 28, 2023 at 17:05 | |||||
| S Feb 28, 2023 at 16:08 | history | answered | Ian Sudbery | CC BY-SA 4.0 |