Question

. Big picture question: Now that you understand statistics. I want you to answer a couple of questions. Can a skilled statistician “make anything significant”? How would this be/not be accomplished? How could you design a study to guarantee significance? What is statistical power and how is it relevant to this big picture question? [6 Points]

Answer 1

Sol:

Significant results depends on the data values and how the data values affect statistical parameter ? So first we see what is meant by statistical significance?

Statistical Significance:

Statistical significance is a determination by an analyst that the results in the data are not explainable by chance alone. Statistical hypothesis testing is the method by which the analyst makes this determination. This test provides a p-value, which is the probability of observing results as extreme as those in the data, assuming the results are truly due to chance alone. A p-value of 5% or lower is often considered to be statistically significant.

Statistical significance is a determination about the null hypothesis, which hypothesizes that the results are due to chance alone. A data set provides statistical significance when the p-value is sufficiently small.

When the p-value is large, then the results in the data are explainable by chance alone, and the data are deemed consistent with (while not proving) the null hypothesis.

When the p-value is sufficiently small (e.g., 5% or less), then the results are not easily explained by chance alone, and the data are deemed inconsistent with the null hypothesis; in this case the null hypothesis of chance alone as an explanation of the data is rejected in favor of a more systematic explanation. For example, Statistical significance is often used for new pharmaceutical drug trials, to test vaccines, and in the study of pathology for effectiveness testing and to inform investors on how successful the company is at releasing new products.

Power is the probability of making a correct decision (to reject the null hypothesis) when the null hypothesis is false.

Power is the probability that a test of significance will pick up on an effect that is present.

Power is the probability that a test of significance will detect a deviation from the null hypothesis, should such a deviation exist.

Power is the probability of avoiding a Type II error.

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