# conditional expectation

### An Explanation of Conditional Expectations… Part Two

In my first (found here) of a three part series on statistical analysis, I discussed how data can inform decisions within countless industries. My research in human capital, and specifically education, provides for various usages of data in decision making. Specifically, available data can be used for predictions of when, where, and which students may have trouble, determinants of parental satisfaction, admission decisions (at both secondary and collegiate levels), and student achievement both academically, on standardized tests, and in future wages.

This post is intended to shed light on the science of data analysis, specifically conditional expectations. The mathematical approach to conditional expectation is based on heavy statistical concepts, some of which are not appropriate for this venue. That being said, my intention is to provide an accessible explanation of the techniques used in statistical analysis. For a mathematical approach, I recommend the seminal text Econometric Analysis, by William Greene, 2002; or Econometric Analysis of Cross Section and Panel Data, by Jeffrey Wooldridge.

Econometrics, and essentially any data analysis, is based on determining a prediction. In statistical terms, this is called an expectation. A *conditional expectation* is a prediction based on available information.

For instance, consider guessing the height of a random human being. The average human height is 5 foot 6 inches, so, this would be a logical starting point for our prediction. But if we know more information about this random person, we can improve our expectation. Specifically, if we knew the person was male, we would want to change our expectation conditional on that fact. The average height of an adult man is 5 foot 9.5 inches, so that would be our new prediction given some information.

If we also knew that the person weighed 240 pounds, we may want to increase our expected height. Note here that there is no causal assumption, just a change in our expectation, given some piece of information. This is correlation: the taller a person is the more, on average, we expect that person to weigh. We may predict 6 foot 1 inch for our random male weighing 240 pounds. Data analysis can help us with our predictions, given some imperfect information.

Next, consider that we also knew this random person’s SAT score was 1200. We probably would not consider changing our expectation of height. If we had data on a sample of people with the variables height, sex, weight, and SAT score, some variables may be good predictors of height and be statistically significant while others, SAT score in this example, would not be statistically significant and would not persuade us to change our expectation.

Multiple Regression Analysis essentially considers a sample of data and determines the predictive success of each variable. Using the information from a statistical data program (even excel can do this reasonably well), we can arrive at a predictive equation for the most logical expectation conditional on the information we have at our disposal.

The data will find the coefficients- the “B’s”- and also determine the likelihood that each “B” is a significant predictor. In this case, I suspect B3 would not be statistically significant.

In part three, I will discuss an example of student achievement data from a nation-wide sample and how conditional expectations can be used to inform decisions in many fields.

### The Rise of Big Data… From Moneyball to the Classroom and Back Again

This is the first of a three-part series of posts discussing the importance of data analysis and introducing readers to the importance and value in statistical and econometric analysis.

Last Sunday, Steve Lohr wrote a great piece in the New York Times explaining the importance of “big data” in today’s society. He explained that increasingly “businesses make sense of an explosion of data- Web traffic and social network comments, as well as software and sensors that monitor shipments, suppliers and customers- to guide decisions, trim costs and lift sales.”

The explosion of data Lohr is referring to is accessible to any field- not just a profit maximizing business- and when used properly, that data can be used to enhance and enrich any institution. Clearly businesses utilize data to inform their decisions, but increasingly, political campaigns, public health officials and advertising agencies are innovating their traditional practices by developing methods and metrics based on data analysis.

The most glorified example is illustrated in the book and recent film “Moneyball,” written by Michael Lewis describing the revolution in baseball by Billy Beane and the Oakland Athletics. The short story is that the team began to analyze players using complex statistical analyses instead of traditional benchmarks. Billy Beane is not the only front office executive to develop and exploit new statistical methods; the general manager of the Houston Rockets, Daryl Morey wrote a piece for Grantland.com regarding the “stats movement in sports” and how the success of Moneyball has transcended sports and become impacted countless industries.

Morey briefly describes how statistical analyses have entered the realm of education: the Gates foundation is gathering data to evaluate teachers. But Morey and the Gates foundation are only scratching the surface. Education at all levels is ripe for a takeover of objective data analyses. Statistics currently used within schools to evaluate programs or students rely on static data. Static data consists of the most basic statistics we remember from high school: averages and percents. New data- big data- is about how information, records, numbers move over time and how a fact or figure can be broken down to find relationships and meaning behind the numbers.

Consider a static piece of data such as: In a specific district, 28% of parents are unhappy about their child’s school. This does not tell an administrator much- probably only something that she already knows. But, a deeper look into the data could reveal important information such as “of the 28% of parents who are unhappy, 70% of their students play a varsity sport.” This has more value; specifically, there is a trend among unhappy parents.

The next two posts will dig deeper into the “why” and “how” of how data can be used to improve decision making. At the most basic level, data can help shape expectations, specifically conditional expectations given some sort of observed trend in the data. I will explain the concept of conditional expectation in part two.