Timeline for How to choose the null and alternative hypothesis?
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8 events
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| Dec 4, 2019 at 21:14 | comment | added | MSIS | @heropup: I undrstand and agree but, as you said, the case of a jury is a special one since the systems agrees to go by " Innocent until proven guilty". My understanding was that 'Null' stood for null-effect , that the claim being made about some effect is assumed false, e.g., the treatment has no effect. But I need to think through the first part of your first of two comments here. | |
| Dec 4, 2019 at 8:48 | comment | added | heropup | @MSIS (cont.) To illustrate the analogy, in a criminal court of law, a defendant is assumed innocent of a crime, and the prosecution must establish guilt through presenting evidence. The strength of this evidence must be such that no reasonable logic could exculpate the defendant. Otherwise, the burden of proof is not met. That is not to say the defendant is truly innocent: it simply means the evidence is lacking to establish guilt beyond a reasonable doubt. Similarly, failure to reject the null does not imply the null is true; rather, the data is simply lacking. | |
| Dec 4, 2019 at 8:44 | comment | added | heropup | @MSIS You've omitted a critical detail that is present in my original characterization: "the alternative hypothesis is the statement that, if true, is strongly supported by the evidence furnished by the data." You want to choose the alternative in such a way that if you conduct the test and reject the null in favor of the alternative, a high standard of evidence has been met to support this decision. But this does not mean the null is "usually" true or that the alternative "should be" true. It is like the legal principle of "innocent until proven guilty beyond a reasonable doubt." | |
| Dec 3, 2019 at 21:27 | comment | added | MSIS | But I don't understand how your layout agrees with the 3rd case. You said the alternative is the one that should be strongly supported from data provided in sample. How do we know that the means being different is what is to be strongly-supported by the data? Why isn't the assumption that means are equal the one to be strongly -supported by the data? | |
| Nov 22, 2015 at 5:22 | comment | added | heropup | @qazwsx What one believes about the likelihood of rejecting the null hypothesis has no bearing on the appropriate construction of the hypothesis test that correctly tests the inference of interest. That is to say, if one is interested in demonstrating with a high degree of confidence that there is a difference between two (or more) means, then the way to test this hypothesis is to use the structure specified in (3), no matter what the data says, because the hypothesis is necessarily pre-specified. | |
| Nov 21, 2015 at 20:23 | comment | added | qazwsx | The third example seems worse than the first two in that, in reality, with a finite size sample, no two distinct products will almost never sell at exactly same amount and $H_0$ as formulated above will almost always be rejected? | |
| Nov 10, 2014 at 21:25 | comment | added | RedViper16 | Thank you so much.. Also your response has been of great help :D | |
| Nov 9, 2014 at 17:38 | history | answered | heropup | CC BY-SA 3.0 |