expectancy, we would expect that once we include these variables in the regression, the coefficient on LN will be reduced. The results are
(1.2)
The coefficient on LN has not gone to zero; in fact, it hasn't changed much. The coefficients on all but one of the other variables that we know affect life expectancy are insignificant. What are we to make of this?
Try it!
Run the above multiple regression. You should get the same coefficients and standard errors. Be sure you understand why the variables LN and LHB are “significant” while the others are not.
In reality, life expectancy is affected by a large set of variables in a complex way, and the natural logarithm of newspapers is a good proxy for these other variables. If we have some beliefs about which variables are more likely to be the true causes of an increase in life expectancy, we might be able to build a model that we think represents the cause and effect relationships. If we really want to find the causal effect of newspapers, we might also try more sophisticated methods that involve trying to find and compare countries that are similar in all respects except the number of newspapers per 1000 people. This sort of analysis leads into “the garden of forking paths,” a phrase used by the statistician Andrew Gelman (who specializes in causal inference) to describe the many decisions a researcher may take that can lead the researcher to unknowingly reaching spurious statistical conclusions.
For example, if an analyst analyzing the above data actually added variables and dropped variables until LN was insignificant and some other health‐related variables all were significant, she would have taken a trip through the garden of forking paths and would come up with a useless model. The model would be useless because she tested many hypotheses on the same set of data and her “results” almost assuredly are contaminated by false positives (i.e. type I errors): she thinks the coefficients are significant when they're really not.
To better illustrate this idea, let us have 10 covariates (independent variables) to use in building a model to describe a particular dependent variable, and we will be allowed to include anywhere from 1 to all 10 of the variables. For each variable there is a decision (fork) to include or exclude the variable. Then there are
The purpose of this example is to drive home the point that, in general, observational data simply are not up to the task of answering causal questions. In this book, we focus on an alternative approach to answering business questions, which is to conduct experiments.
We do not suggest that observational studies have no valid uses. To the contrary, there are many situations when experiments are not possible, and in such cases, there is no alternative to the use of observational data:
Sometimes it is impossible to run an experiment. For example, it would be unethical to randomly assign people to smoke versus not smoke, so our understanding of the causal relationship between smoking and cancer was built on observational data. (However, it took a long time to convince everyone, since observational data is easy to question.)
If you want to build a new store, it is foolish to construct several stores in random locations to test hypotheses about where to locate stores.
Establishing causality is not always necessary, and documenting correlations is sometimes sufficient for the purpose at hand. In fact, the whole field of “predictive analytics” focuses on prediction problems, where causality is not important. For example, if we are predicting defaults on mortgages, very often we only need to know the probability that a person will default, not the causal factors that determine the probability of default; correlation is sufficient, and causation is not necessary.
The outcome of interest is sufficiently rare that running an experiment with a large enough number of trials is expensive. Perhaps you can only afford a sample size of 100, but the response rate is 2%; you're never going to get a good estimate of the response rate with such a comparatively small sample.
Each trial is so expensive that even a small experiment is too expensive.
The population is too small to support an experiment. There is no point in remodeling a sample of stores to decide whether to remodel the entire population if the population is only 10 stores.
Hypothesis generation is an excellent use of observational data. The researcher explores the observational data looking for interesting ideas that might merit a follow‐up experiment.
Observational data can be used to shed light on causal questions, but the statistical machinery necessary to do so is very sophisticated and still not as good as actually running an experiment. These types of sophisticated analyses are usually performed when an experiment is impossible, not in lieu of an experiment. A standard reference for this type of analysis is Rosenbaum (2010). Using observational data to answer causal questions is hard; so we try to use experimental data, which is comparatively easy.
Notwithstanding the above, it is very common for people to use observational data to (mistakenly) make causal assertions outside of the narrow range in which it can be done. It is very common, therefore, for “causal” results from observational data to be later contradicted by experiments. Many instances can be found in the article by Young and Karr (2011) and the references therein. With respect to establishing causality, unless you are a very skilled statistician, analyzing observational data can only provide what researchers call hypothesis‐generating evidence. In other words, analyzing observational data can give you good ideas for experiments to conduct, but it can't tell you anything about causality.
It is important for the analyst to know whether she has an “umbrella problem” or a “rain dance problem.” If all she wants to know is whether or not she should carry an umbrella, then she has a pure prediction problem and causal questions are of secondary importance; she only needs to know whether the probability of rain is high or low. On the other hand, if there has been a long drought and she wants to end it, prediction is of little value: causal questions are of primary importance. If she wants to induce rainfall, she needs to know what variables cause rain and then try to manipulate those variables. We recall the experience of one analyst, trained in the field of predictive analytics, who had been given some observational data on donations from specific individuals and asked for insight as to whether or not attending fundraisers increased donations. She dropped the variable “number of fundraisers the person attended” because it had no predictive value. She just couldn't understand that her boss had given her a rain dance problem, not an umbrella problem.
Exercises
1 1.1.1 Find an example of an observational study. Answer the following questions: (i) What makes this an observational rather than an experimental study? (be specific) (ii) What is the purpose of the study? (iii) What is the primary variable of interest?
