Question

What is significance good for? Which of the following questions does a test of significance answer? Briefly explain your replies. (a)Is the sample or experiment properly designed? (b)Is the observed effect due to chance? (c)Is the observed effect important?

(a)Is the sample or experiment properly designed?

(b)Is the observed effect due to chance?

(c)Is the observed effect important?

Answer 1

In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis.More precisely, a study's defined significance level, denoted α, is the probability of the study rejecting the null hypothesis, given that the null hypothesis were true;and the p-value of a result, p, is the probability of obtaining a result at least as extreme, given that the null hypothesis were true. The result is statistically significant, by the standards of the study, when p < α. The significance level for a study is chosen before data collection, and typically set to 5%or much lower, depending on the field of study.

In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone. But if the p-value of an observed effect is less than the significance level, an investigator may conclude that the effect reflects the characteristics of the whole population, thereby rejecting the null hypothesis.

This technique for testing the statistical significance of results was developed in the early 20th century. The term significance does not imply importance here, and the term statistical significance is not the same as research, theoretical, or practical significance. For example, the term clinical significance refers to the practical importance of a treatment effect.

In part (a),

                  I am interpreting this question as, “Can a p-value result tell you if the experiment is properly designed?” The response is no, I can do that by looking at my sample size, how the data is going to be gathered, size of significance level, etc...

In part (b),

                   I am interpreting this question as, “Can I use the p-value to determine if the model, using the null hypothesis, is plausible?” The answer is yes, that is the whole point of the test. We assume the null is correct, and if our result differs (effect) from the expectation we will determine if that difference is small enough to say our null value is plausible(due to chance). If the difference is large enough we may say that the null is not correct, thus explaining why we are seeing such a large difference.

In part (c),

                    I am interpreting this question as, “Can I use the p-value to determine if the result is an important one?” And we spent time discussing this in-class, the answer is no.