Question

Just because two or more values are different does not mean that they are different in a statistically significant manner. Researchers rely on the p values that are generated for each of their statistical tests to determine significance. If the p value is larger than the alpha, then they are not different in a statistically significant manner, and therefore the values are not considered different. In this journal activity, consider these concepts in terms of the differences between null and alternative hypotheses, and discuss this question: What is the difference between failing to reject the null hypothesis and having evidence to support the alternative hypothesis?

Answer 1

If we fail to reject the null hypothesis, it does not means the null hypothesis is true. That because a hypothesis test does not determine which hypothesis is true, or even which is most likely: it only accesses whether available evidence exits to reject the null hypothesis.

Look at this one - " innocent until proven guilty" in a court room. As the person analyzing the data, you are judge. The hypothesis test is the trial, and the null hypothesis is a defendant. The alternative hypothesis is like the prosecution , which need to make its case beyond the reasonable doubt.

If the evidence presented doesn't prove the defendant is guilty beyond the reasonable doubt, you still have not proved the defendant is innocent, but based on the evidence, you can't reject that possibility.

So how would the verdict be announced? It enter the court record as 'not guilty'?

That phrase is perfect. 'Not guilty' doesn't means the defendant is innocent. Because that has not be proven. It just the prosecution could not have proved its statement, beyound the reasonable doubt standard. It failed to convinces the judge to abandon the assumption of innocence.

" failure to reject the null' its just the statistical equivalent of 'not guilty'. In the trail, the burdon of proof falls to the prosecution. When analyzing data, the entire burdon of proof falls, to the sample data you have collected. Just as 'not guilty' is not the same thing as innocent, neither its falling to teject, the same as accepting the null hypothesis.