1) One specifies "" and "" hypotheses. The null hypothesis is that the groups do not differ. Other ways of stating the null hypothesis are as follows:
Of course, we may be wrong. A p-value of 0.0023 could arise when eitherH0 orHA holds. However it isunlikely when H0 is trueand more likely when HAis true.
An is computed for each hypothesis you are testing.
The is the one you would believe if the null hypothesis is concluded to be untrue. The evidence in the trial is your data and the statistics that go along with it. All hypothesis tests ultimately use a -value to weigh the strength of the evidence (what the data are telling you about the population). The -value is a number between 0 and 1 and interpreted in the following way:
What a p-Value Tells You about Statistical Data - dummies
This criticism only applies to two-tailed tests, where the null hypothesis is "Things are exactly the same" and the alternative is "Things are different." Presumably these critics think it would be okay to do a one-tailed test with a null hypothesis like "Foot length of male chickens is the same as, or less than, that of females," because the null hypothesis that male chickens have smaller feet than females could be true. So if you're worried about this issue, you could think of a two-tailed test, where the null hypothesis is that things are the same, as shorthand for doing two one-tailed tests. A significant rejection of the null hypothesis in a two-tailed test would then be the equivalent of rejecting one of the two one-tailed null hypotheses.
What a p-Value Tells You about Statistical Data
A fairly common criticism of the hypothesis-testing approach to statistics is that the null hypothesis will always be false, if you have a big enough sample size. In the chicken-feet example, critics would argue that if you had an infinite sample size, it is impossible that male chickens would have exactly the same average foot size as female chickens. Therefore, since you know before doing the experiment that the null hypothesis is false, there's no point in testing it.
Three Things the P-Value Can't Tell You about Your Hypothesis Test
Computer statistics programs can give somewhat inaccurate P values when they are very small. Once your P values get very small, you can just say "PP value.
P Value and Confidence Interval | P Value | Null Hypothesis
A related criticism is that a significant rejection of a null hypothesis might not be biologically meaningful, if the difference is too small to matter. For example, in the chicken-sex experiment, having a treatment that produced 49.9% male chicks might be significantly different from 50%, but it wouldn't be enough to make farmers want to buy your treatment. These critics say you should estimate the effect size and put a on it, not estimate a P value. So the goal of your chicken-sex experiment should not be to say "Chocolate gives a proportion of males that is significantly less than 50% (P=0.015)" but to say "Chocolate produced 36.1% males with a 95% confidence interval of 25.9 to 47.4%." For the chicken-feet experiment, you would say something like "The difference between males and females in mean foot size is 2.45 mm, with a confidence interval on the difference of ±1.98 mm."