Question 6.70

6.70 Interpreting -value.

The reporting of -values is standard practice in statistics. Unfortunately, misinterpretations of -values by producers and readers of statistical reports are common. The previous two exercises dealt with a few incorrect applications of the -value. This exercise explores the -value a bit further.

  1. Suppose that the -value is 0.03. Explain what is wrong with stating, “The probability that the null hypothesis is true is 0.03.”
  2. Suppose that the -value is 0.03. Explain what is wrong with stating, “The probability that the alternative hypothesis is true is 0.97.”
  3. Generally, the -value can be viewed as a measure of discrepancy of the null hypothesis to the data. In terms of a probability language, a -value is a conditional probability. Define the event as “observing a test statistic as extreme or more extreme than actually observed.” Consider two conditional probabilities: versus . Refer to page 197 for the introduction to conditional probability. Explain which of these two conditional probabilities represents a -value.