MDSC 643.01 Fall 2003 Quiz 4 Answer Key

  1. True or False? A statistical computer package (Stata) will only print out a p-value or a confidence interval if the conditions for its validity are met. Explain with one sentence.

False – A computer package calculates with specific formulae without any evaluation of the validity regarding the appropriateness of the calculation

  1. What is the difference between a t-statistic and a z-statistic?

The z-statistic contains the (population) standard deviation of the estimate, while the t-statistic uses the (sample) standard error of the estimate.

  1. Why might a researcher consider the use a logarithmic transformation before using a t-analysis?

A specific data transformation may be well established in the literature in the field of study. Typically, logarithms are used to attempt to reduce skewness in the population distributions under study. Skewness can create problems with the mean (the mean may be ‘pulled’ toward the longer tail and no longer reflect a meaningful measure of the centre) and the variance (the variances can be inappropriately measured and unequal).

  1. Consider a researcher studying the comparison of a fish oil diet and a regular oil diet with regard to reduction in blood pressure (Quiz 3). Suppose there were 100 volunteers; 50 randomized to each diet group. Further suppose that a boxplot of all 100 reductions looks skewed and contains outliers but separate boxplots for the 2 diet groups both look reasonably symmetrical and no outliers are identified. A t-analysis is being considered. Which graph is appropriate for the assessment of assumptions and/or outliers: The boxplot of all 100 reductions or the separate boxplots each based on 50 reductions? Explain with one sentence.

A t-analysis is used to study the potential difference between the means of 2 populations. To evaluate the two groups with regard to the assumptions for a t-analysis (p56- independence, approximate normality, approximately equal variances), you need to look at the distributions of the two groups as on p 58, 59. Viewing one boxplot of the combined data will not aid in this evaluation. (the asymmetry and outliers in a single boxplot may be artifacts of combining 2 different distributions)