Adjusted Risk Ratios

How do you estimate the specific risk a smoking has on the probability of being hospitalized.  If smokers on average have lower income and less educational achievement, is smoking truly causing the increase in hospitalization or could the covariates fully or partially explain the increased hospitalization rates? A paper by Kleinman and Norton suggests using…

The History of Least Squares

Let us say you have 10 observations of 2 different variables.  How do you determine which of the observations to use?  Should you throw out the outliers?  Should you only include the most similar values?  Does more observations increase or decrease the amount of measurement error? These problems can be answered by the discipline of Statistics.…

ANOVA

Let us say that you are a hospital administrator.  You are very clever and have come up with a system to score the quality of the work done by the physicians at your hospital.  To simplify things, lets assume that you only have 3 physicians who work at your hospital.  The physician’s scores are as…

Heckman’s “Econometric Causality”

Nobel laureate James Heckman has a nice summary of how applied econometricians and policy researchers should define causality. Some of the more interesting points I have excerpted below. On the source of randomness in a sample “One reason why many statistical models are incomplete is that they do not specify the sources of randomness generating…

Finite Mixture Models

Let us assume that there are two types of people: smart people an dumb people. Smart people’s test scores are normally distributed about 80% and dumb people’s tests scores are normally distributed about 40% on their test. If we observe the test score of one person, how do we know if they are smart or…

Serial Corelation and the Durbin Watson Statistic

What is the effect a country’s GDP on health? What about the country’s literacy rate on infant mortality rates? Often researchers try to answer these questions using time-series data. With time series data, we have observations of a few units (e.g.: countries or individuals) over many years. Let the subscript i represent the the individual…