Statistical Evidence and Inference

Understanding the methods used by economists requires some basic terminology regarding the distribution of random variables. The mean of a distribution is simply the arithmetic average of all of the observations. The median is the observation that falls in the middle; half of the observations have values below the median and half are above. Both the mean and the median are measures of the center of the distribution, but the median is less sensitive to extreme observations. The variance is the average squared deviation from the mean for all of the observations, and is a measure of the spread of the distribution around the mean. The standard deviation is the square root of the variance. The standard tool of economic data analysis is regression, which is a form of curve …tting. The most common method of regression used is Ordinary Least Squares (OLS). OLS can be used to …t any linear model of the form y = a+bx+e, where a is a constant and b is the coe¢ cient that describes how y changes with changes in x. Because the relationship between x and y is not expected to hold exactly for every individual, there is an error term, e. For example, the relationship between age and hours worked (Figure 24) can be described as hours = a+ b age+ e, and OLS used to obtain estimates of the parameters a and b.