Which of the following statements is not true about samples that can be treated as matched pairs data?
I. Data collected on these samples is analyzed by calculating the differences between paired observations and using that data in one sample tests.
II. Each value in the first group of numbers has a relationship to a value in the second group.
III. It's best to analyze related samples by conducting hypothesis tests on the mean from the first and the second groups, in that order.
II only
II and III only
I, II, and III
I and III only
III only
2 only
To determine which of the statements is not true about samples that can be treated as matched pairs data, let's analyze each statement:
I. Data collected on these samples is analyzed by calculating the differences between paired observations and using that data in one sample tests.
This statement is true. In matched pairs data, the paired observations are analyzed by calculating the differences between them, and these differences are used for further analysis, such as hypothesis testing.
II. Each value in the first group of numbers has a relationship to a value in the second group.
This statement is also true. In matched pairs data, each value in the first group is paired with a corresponding value in the second group. These pairs have a clear relationship, such as a before-and-after measurement.
III. It's best to analyze related samples by conducting hypothesis tests on the mean from the first and the second groups, in that order.
This statement is not true. When analyzing related samples with matched pairs data, it's actually more appropriate to conduct hypothesis tests on the mean difference between paired observations. By testing the mean difference, we can directly assess the effect of the treatment or intervention.
Therefore, the statement that is not true about samples that can be treated as matched pairs data is III only.