A 56-year-old man with exertional chest pain comes to the office because his exercise stress echocardiogram showed evidence of mild ischemia in the posterior wall. He was recently diagnosed with type 2 diabetes mellitus and hypertension. He is a current smoker but is willing to quit. His father died of a heart attack at age 51. Physical examination is unremarkable. Laboratory results are as follows:
Based on the information in the drug advertisement,
According to the drug advertisement, the investigators reported the median value and the median percentage change from baseline for triglyceride levels in the study patients. Which of the following best explains the reason for reporting median values as opposed to mean values?

Question

A 56-year-old man with exertional chest pain comes to the office because his exercise stress echocardiogram showed evidence of mild ischemia in the posterior wall.  He was recently diagnosed with type 2 diabetes mellitus and hypertension.  He is a current smoker but is willing to quit.  His father died of a heart attack at age 51.  Physical examination is unremarkable. Laboratory results are as follows:
 Based on the information in the drug advertisement,
According to the drug advertisement, the investigators reported the median value and the median percentage change from baseline for triglyceride levels in the study patients.  Which of the following best explains the reason for reporting median values as opposed to mean values?

Quizplus · Accepted Answer

Explanation: In the drug advertisement, the median value and median percentage changes were reported for triglyceride levels, but mean values and mean percentage changes were reported for the other variables examined. Three measures of central tendency are most often used to describe data sets: Mean equals the sum of observations divided by the number of observations. Median equals the observation in the center when all the observations are ordered from smallest to largest. When there is an even number of observations, the median is defined as the mean of the middle 2 data points. Mode equals the observation that occurs most frequently. 11ec2b69_c0e0_2c19_8f63_a32640536dc2_MD0005_00 Although the symmetrical bell-shaped curve is cited as the ideal distribution curve, most data sets generated during "real-world" statistical analysis have asymmetrical distributions. When a distribution curve is asymmetrical, it is either positively or negatively skewed. With a negative skew, larger numbers predominate in the data set and the long slope of the curve (the tail) extends in the negative direction (mean < median < mode). With a positive skew, smaller numbers predominate in the data set and the long slope of the curve (the tail) extends in the positive direction (mean > median > mode). As evidenced by the above image, in strongly skewed distributions, the median is a better measure of central tendency than the mean. How does one decide on which measure of central tendency to use? For continuous data that are normally distributed, the mean is the best choice for central tendency. For ordinal data or continuous data that are highly skewed, the median is the best choice for central tendency. Ordinal data can be ordered in a logical fashion (eg, freshman, sophomore, junior, and senior). For nominal data, using the mode or describing the frequency or proportion of subjects in each category is best. Nominal data cannot be ordered in a logical fashion (eg, male and female). (Choice A) A high number of missing values may have a significant impact on some or all measures of central tendency, including the median (especially if the missing values are in the middle of the data set). A skewed data set is a better reason for why the investigators used the median instead of the mean in their triglyceride analysis. (Choice B) The range equals the difference between the largest and smallest observation. It is a measure of dispersion and is used to describe the variability in a sample or population. It is usually used in conjunction with a measure of central tendency to provide an overall description of a set of data. Changes in range may not always equate to changes in central tendency. For example, a wide or narrow range may still be skewed or have a normal distribution. (Choice D) The sample size does not always correlate with the measures of central tendency. For example, a smaller sample size may be normally distributed, making the mean score the best measure of central tendency. Instead, sample size correlates with the power of a study and the likelihood of reaching statistical significance. Educational objective: In strongly skewed distributions, the median is a better measure of central tendency than the mean.

A 56-Year-Old Man with Exertional Chest Pain Comes to the Office