Errors and their consequences

1. Errors and their consequences

From the null distribution that you just created,

2. Opportunity cost conclusion

it seems that reminding students to save does have a causal impact on the likelihood that they will buy a DVD. That's because the observed difference is not consistent with the null differences. But what is the consequence of concluding that a reminder causes students to be less likely to buy DVDs? What if our conclusion is wrong? Before completing the hypothesis test, it is important to understand how and why things can go wrong with statistical inference.

3. Errors in hypothesis testing

Notice that there are two possible decisions to make in hypothesis testing.

4. Errors in hypothesis testing

Either the observed data are inconsistent with the null hypothesis, in which case the null hypothesis is rejected.

5. Errors in hypothesis testing

Or the observed data are consistent with the null hypothesis,

6. Errors in hypothesis testing

in which case the null hypothesis is not rejected and no conclusion is made about a larger population.

7. Errors in hypothesis testing

There are also two possible "truth" states:

8. Errors in hypothesis testing

either the null hypothesis is true

9. Errors in hypothesis testing

or the alternative hypothesis is true.

10. Errors in hypothesis testing

Keep in mind, however, that we can't ever know the true state of the population. Because the research statement is almost always the same as the alternative hypothesis,

11. Errors in hypothesis testing

the goal of the scientific study is to be in the bottom box where the alternative hypothesis is true and the data provide convincing evidence to reject the null hypothesis.

12. Errors in hypothesis testing

However, any of the other three boxes are also possible. We cannot know which row has resulted, but we do know which conclusion has been made, thereby specifying the column.

13. Errors in hypothesis testing

Which is to say, if the null hypothesis is rejected, then either the science is correct or a type I error has been made.

14. Errors in hypothesis testing

If the null hypothesis is not rejected, it has either been done so correctly or a type II error has been made. Recall that the decision being made controls the type I error rate, that is the false positive rate, at, for example, (point) 05, for both mathematical and historical reasons.

15. Errors in US judicial system

The logic of hypothesis testing shares many key elements with the US judicial system. The jury does not know whether the defendant committed the crime, but they must decide whether or not to convict the individual. The jury is presented with evidence, akin to data, and asked whether the evidence is consistent with innocence. If the evidence is outside of what would be expected, the defendant is charged with a crime.

16. Let's practice!

OK, now it's your turn to practice what you've learned.

Create Your Free Account

By continuing, you accept our Terms of Use, our Privacy Policy and that your data is stored in the USA.