Assertion: alternative hypothesis | /r/HasProperty | true
Facets:
value: in this situation
type: OTHER
Source sentences:
text: If the sample data are consistent with the null hypothesis, then do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then reject the null hypothesis and conclude that the alternative hypothesis is true.
text: The test's probability of correctly rejecting the null hypothesis when the alternative hypothesis is true.
text: If H 0 is rejected, the statistical conclusion is that the alternative hypothesis H a is true.
text: So, does this mean that we can reject the null hypothesis and conclude that our alternative hypothesis was in fact true?
text: The alternative hypothesis is the statement you want to be able to conclude is true based on evidence provided by the sample data.
text: If the sample data are consistent with the null hypothesis, then do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then reject the null hypothesis and conclude that the alternative hypothesis is true.
text: By contrast, if the alternative hypothesis is true, the distribution is dependent on sample size and the true value of the parameter being studied.
text: The significance level you choose should also depend on how likely you think it is that your alternative hypothesis will be true, a prediction that you make before you do the experiment.
text: If you are doing an experiment where the cost of a false positive is a lot greater or smaller than the cost of a false negative, or an experiment where you think it is unlikely that the alternative hypothesis will be true, you should consider using a different significance level.
text: The alternative need not be the logical negation of the null hypothesis; it predicts the results from the experiment if the alternative hypothesis is true.
text: On the other hand, it could be that the alternative hypothesis is true, but we did not use a large enough sample to obtain a significant result (or we were just unlucky).
text: In this situation (the alternative hypothesis is true but we do not reject the null hypothesis), we say that we have made a Type II error.
text: On the other hand, the alternative hypothesis could indeed be true.
text: Given these results, what is the probability that the alternative hypothesis is true?
text: We can therefore work out the probability of the alternative hypothesis being true given the observed p-value, using conditional probability:
text: So we are quite stuck: in the null hypothesis significance testing model, it is impossible to give a numerical answer to our key question: "Given our results, what is the probability that the alternative hypothesis is true?
text: Do we believe that the alternative hypothesis is true?
text: In this case, we are more likely to believe that the alternative hypothesis is true, because it makes a lot of sense that this feature will reduce the number of fatalities.
text: But the Fisher approach only tells us whether the results of our experiment are unlikely to have happened by chance if there is no real effect, it does not tell us whether the alternative hypothesis is (much) more likely to be true than the null hypothesis.
text: This approach also allows us to talk about the power of the test (as explored in Powerful Hypothesis Testing ), which means the probability of the null hypothesis being rejected if the alternative hypothesis is true.
text: Note that although 0.001 is a very low p-value, it cannot be used to prove that the null hypothesis is false, or that the alternative hypothesis is true - it can only be stated that it gives 'strong evidence against the null hypothesis'.
text: Is there or is there not enough evidence that the alternative hypothesis is true?