Section 13.6 Summary
Subsection 13.6.1 Glossary
- Response
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The variable who’s distribution one seeks to investigate.
- Explanatory Variable
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A variable that may affect the distribution of the response.
Subsection 13.6.2 Discuss in the Forum
Statistics has an important role in the analysis of data. However, some claim that the more important role of statistics is in the design stage when one decides how to collect the data. Good design may improve the chances that the eventual inference of the data will lead to a meaningful and trustworthy conclusion.
Some say that the quantity of data that is collected is most important. Other say that the quality of the data is more important than the quantity. What is your opinion?
When formulating your answer it may be useful to come up with an example from your past experience where the quantity of data was not sufficient. Else, you can describe a case where the quality of the data was less than satisfactory. How did these deficiencies affected the validity of the conclusions of the analysis of the data?
For illustration consider the surveys. Conducting the survey by the telephone may be a fast way to reach a large number of responses. However, the quality of the response may be less that the response obtained by face-to-face interviews.
Subsection 13.6.3 Formulas
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Test statistic for equality of expectations: \(t = (\bar x_a - \bar x_b)/ \sqrt{s_a^2/n_a + s_b^2/n_b}\text{.}\)
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Confidence interval: \((\bar x_a - \bar x_b) \pm \mbox{\texttt{qnorm(0.975)}}\sqrt{s_a^2/n_a + s_b^2/n_b}\text{.}\)
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Test statistic for equality of variances: \(f = s_a^2/s_b^2\text{.}\)
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Confidence interval:\begin{equation*} \big[(s_a^2/s_b^2)/\mbox{\texttt{qf(0.975,dfa,dfb)}} , (s_a^2/s_b^2)/\mbox{\texttt{qf(0.025,dfa,dfb)}}\big]\;. \end{equation*}
