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Chapter 4: Problem 105

Significant and Insignificant Results (a) If we are conducting a statistical test and determine that our sample shows significant results, there are two possible realities: We are right in our conclusion or we are wrong. In each case, describe the situation in terms of hypotheses and/or errors. (b) If we are conducting a statistical test and determine that our sample shows insignificant results, there are two possible realities: We are right in our conclusion or we are wrong. In each case, describe the situation in terms of hypotheses and/or errors. (c) Explain why we generally won't ever know which of the realities (in either case) is correct.

Short Answer

Expert verified
When results are significant, and we're correct, we've rightly rejected the null hypothesis. If we're wrong, we commit a Type I error. When results are not significant, and we're correct, we've rightly accepted the null hypothesis. If we're wrong, we commit a Type II error. Ultimately, we don't know for sure due to the nature of probabilities in statistics.

Step by step solution

01

Understand Significant Results

When we conclude that our sample gives us significant results, we reject the null hypothesis and accept the alternative hypothesis. If we're right, we have correctly rejected the null hypothesis. However, if we're wrong, we committed a Type I error, where we have incorrectly rejected the null hypothesis while it is true.
02

Understand Insignificant Results

When we conclude that our sample gives us insignificant results, we accept the null hypothesis. If we're right, we have correctly accepted the null hypothesis. But, if we're wrong, we committed a Type II error, where we failed to reject the null hypothesis while it is false, thus accepting the wrong hypothesis.
03

Explain Uncertainty of Conclusions

We will generally never know which of these realities is correct because in statistics, we work within probabilities. Although we can calculate the probability of rejecting the null hypothesis given that it is true (Type I error rate) or the probability of failing to reject the null hypothesis given that it is false (Type II error rate), we cannot be 100% sure about whether the null hypothesis is true or false. We base our conclusions on the evidence our data provides, but there is always room for error.

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Most popular questions from this chapter

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