## Confounding Statistics Term Paper

When assessing academic studies, media members are often confronted by pages not only full of numbers, but also loaded with concepts such as “selection bias,” “p-value” and “statistical inference.”

Statistics courses are available at most universities, of course, but are often viewed as something to be taken, passed and quickly forgotten. However, for media members and public communicators of many kinds it is imperative to do more than just read study abstracts; understanding the methods and concepts that underpin academic studies is essential to being able to judge the merits of a particular piece of research. Even if one can’t master statistics, knowing the basic language can help in formulating better, more critical questions for experts, and it can foster deeper thinking, and skepticism, about findings.

Further, the emerging field of data journalism requires that reporters bring more analytical rigor to the increasingly large amounts of numbers, figures and data they use. Grasping some of the academic theory behind statistics can help ensure that rigor.

Most studies attempt to establish a **correlation **between two variables — for example, how having good teachers might be “associated with” (a phrase often used by academics) better outcomes later in life; or how the weight of a car is associated with fatal collisions. But detecting such a relationship is only a first step; the ultimate goal is to determine **causation**: that one of the two variables drives the other. There is a time-honored phrase to keep in mind: “Correlation is not causation.” (This can be usefully amended to “correlation is not *necessarily* causation,” as the nature of the relationship needs to be determined.)

Another key distinction to keep in mind is that studies can either explore observed data (**descriptive statistics**) or use observed data to predict what is true of areas beyond the data (**inferential statistics**). The statement “From 2000 to 2005, 70% of the land cleared in the Amazon and recorded in Brazilian government data was transformed into pasture” is a descriptive statistic; “Receiving your college degree increases your lifetime earnings by 50%” is an inferential statistic.

Here are some other basic statistical concepts with which journalism students and working journalists should be familiar:

- A
**sample**is a portion of an entire**population**. Inferential statistics seek to make predictions about a population based on the results observed in a sample of that population. - There are two primary types of population samples:
**random**and**stratified**. For a random sample, study subjects are chosen completely by chance, while a stratified sample is constructed to reflect the characteristics of the population at large (gender, age or ethnicity, for example). There are a wide range of sampling methods, each with its advantages and disadvantages. - Attempting to extend the results of a sample to a population is called
**generalization**. This can be done only when the sample is truly representative of the entire population. - Generalizing results from a sample to the population must take into account
**sample variation**. Even if the sample selected is completely random, there is still a degree of**variance**within the population that will require your results from within a sample to include a**margin of error**. For example, the results of a poll of likely voters could give the margin of error in percentage points: “47% of those polled said they would vote for the measure, with a margin of error of 3 percentage points.” Thus, if the actual percentage voting for the measure was as low as 44% or as high as 50%, this result would be consistent with the poll. - The greater the sample size, the more representative it tends to be of a population as a whole. Thus the margin of error falls and the
**confidence level**rises. - Most studies explore the relationship between two variables — for example, that prenatal exposure to pesticides is associated with lower birthweight. This is called the
**alternative hypothesis**. Well-designed studies seek to disprove the**null hypothesis**— in this case, that prenatal pesticide exposure is*not*associated with lower birthweight. - Significance tests of the study’s results determine the probability of seeing such results if the null hypothesis were true; the p-value indicates how unlikely this would be. If the p-value is 0.05, there is only a 5% probability of seeing such “interesting” results if the null hypothesis were true; if the p-value is 0.01, there is only a 1% probability.
- The other threat to a sample’s validity is the notion of
**bias**. Bias comes in many forms but most common bias is based on the selection of subjects. For example, if subjects self-select into a sample group, then the results are no longer**externally valid,**as the type of person who wants to be in a study is not necessarily similar to the population that we are seeking to draw inference about. - When two variables move together, they are said to be
**correlated**.**Positive correlation**means that as one variable rises or falls, the other does as well — caloric intake and weight, for example**. Negative correlation**indicates that two variables move in opposite directions — say, vehicle speed and travel time. So if a scholar writes “Income is negatively correlated with poverty rates,” what he or she means is that as income rises, poverty rates fall. **Causation**is when change in one variable alters another. For example, air temperature and sunlight are correlated (when the sun is up, temperatures rise), but causation flows in only one direction. This is also known as**cause and effect**.**Regression analysis**is a way to determine if there is or isn’t a correlation between two (or more) variables and how strong any correlation may be. At its most basic, this involves plotting data points on a X/Y axis (in our example cited above, vehicle weight and fatal accidents) looking for the**average causal effect**. This means looking at how the graph’s dots are distributed and establishing a**trend line**. Again, correlation isn’t necessarily causation.- The
**correlation coefficient**is a measure of linear association or clustering around a line. - While causation is sometimes easy to prove, frequently it can often be difficult because of
**confounding variables**(unknown factors that affect the two variables being studied). Studies require well-designed and executed experiments to ensure that the results are reliable. - When causation has been established, the factor that drives change (in the above example, sunlight) is the
**independent variable**. The variable that is driven is the**dependent variable**. **Elasticity**, a term frequently used in economics studies, measures how much a change in one variable affects another. For example, if the price of vegetables rises 10% and consumers respond by cutting back purchases by 10%, the expenditure elasticity is 1.0 — the increase in price equals the drop in consumption. But if purchases fall by 15%, the elasticity is 1.5, and consumers are said to be “price sensitive” for that item. If consumption were to fall only 5%, the elasticity is 0.5 and consumers are “price insensitive” — a rise in price of a certain amount doesn’t reduce purchases to the same degree.**Standard deviation**provides insight into how much variation there is within a group of values. It measures the deviation (difference) from the group’s mean (average).- Be careful to distinguish the following terms as you interpret results:
**Average**,**mean**and**median**. The first two terms are synonymous, and refer to the average value of a group of numbers. Add up all the figures, divide by the number of values, and that’s the average or mean. A median, on the other hand, is the central value, and can be useful if there’s an extremely high or low value in a collection of values — say, a Wall Street CEO’s salary in a list of people’s incomes. (For more information, read “Math for Journalists” or go to one of the “related resources” at right.) - Pay close attention to percentages versus percentage points — they’re not the same thing. For example, if 40 out of 100 homes in a distressed suburb have “underwater” mortgages, the rate is 40%. If a new law allows 10 homeowners to refinance, now only 30 mortgages are troubled. The new rate is 30%, a drop of 10 percentage points (40 – 30 = 10). This is
*not*10% less than the old rate, however — in fact, the decrease is 25% (10 / 40 = 0.25 = 25%). - In descriptive statistics,
**quantiles**can be used to divide data into equal-sized subsets. For example, dividing a list of individuals sorted by height into two parts — the tallest and the shortest — results in two quantiles, with the median height value as the dividing line.**Quartiles**separate data set into four equal-sized groups,**deciles**into 10 groups, and so forth. Individual items can be described as being “in the upper decile,” meaning the group with the largest values, meaning that they are higher than 90% of those in the dataset.

Note that understanding statistical terms isn’t a license to freely salt your stories with them. Always work to present studies’ key findings in clear, jargon-free language. You’ll be doing a service not only for your readers, but also for the researchers.

**Related:** See this more general overview of academic theory and critical reasoning courtesy of MIT’s Stephen Van Evera. A new open, online course offered on Harvard’s EdX platform, “Introduction to Statistics: Inference,” from UC Berkeley professors, explores “statistical ideas and methods commonly used to make valid conclusions based on data from random samples.”

There are also a number of free online statistics tutorials available, including one from Stat Trek and another from Experiment Resources. Stat Trek also offer a glossary that provides definitions of common statistical terms. Another useful resource is “Harnessing the Power of Statistics,” a chapter in *The New Precision Journalism*.

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*A special thanks to Sudhakar**Raju of Rockhurst University for his invaluable contributions to this article. Keywords: training*

Last updated: April 7, 2015

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Design of Experiments > Confounding Variable

Watch the video or read the article below.

## What is a Confounding Variable?

A confounding variable is an “extra” variable that you didn’t account for. They can ruin an experiment and give you useless results. They can suggest there is correlation when in fact there isn’t. They can even introduce bias. That’s why it’s important to know what one is, and how to avoid getting them into your experiment in the first place.

A confounding variable can have a hidden effect on your experiment’s outcome.

In an experiment, the independent variable typically has an effect on your dependent variable. For example, if you are researching whether lack of exercise leads to weight gain, lack of exercise is your independent variable and weight gain is your dependent variable. Confounding variables are any other variable that also has an effect on your dependent variable. They are like extra independent variables that are having a hidden effect on your dependent variables. Confounding variables can cause two major problems:

Let’s say you test 200 volunteers (100 men and 100 women). You find that lack of exercise leads to weight gain. One problem with your experiment is that is lacks any control variables. For example, the use of placebos, or random assignment to groups. So you really can’t say for sure whether lack of exercise leads to weight gain. One confounding variable is how much people eat. It’s also possible that men eat more than women; this could also make sex a confounding variable. Nothing was mentioned about starting weight, occupation or age either. A poor study design like this could lead to bias. For example, if all of the women in the study were middle-aged, and all of the men were aged 16, age would have a direct effect on weight gain. That makes age a confounding variable.

## Confounding Bias

Technically, confounding isn’t a true bias, because bias is usually a result of errors in data collection or measurement. However, one definition of bias is “…the tendency of a statistic to overestimate or underestimate a parameter”, so in this sense, confounding *is* a type of bias.

**Confounding bias** is the result of having confounding variables in your model. It has a direction, depending on if it over- or underestimates the effects of your model:

- Positive confounding is when the observed association is biased away from the null. In other words, it overestimates the effect.
- Negative confounding is when the observed association is biased toward the null. In other words, it underestimates the effect.

## How to Reduce Confounding Variables

Make sure you identify all of the possible confounding variables in your study. Make a list of everything you can think of and one by one, consider whether those listed items might influence the outcome of your study. Usually, someone has done a similar study before you. So check the academic databases for ideas about what to include on your list. Once you have figured out the variables, use one of the following techniques to reduce the effect of those confounding variables:

- Bias can be eliminated with random samples.
- Introduce
**control variables**to control for confounding variables. For example, you could control for age by only measuring 30 year olds. **Within subjects designs**test the same subjects each time. Anything could happen to the test subject in the “between” period so this doesn’t make for perfect immunity from confounding variables.**Counterbalancing**can be used if you have paired designs. In counterbalancing, half of the group is measured under condition 1 and half is measured under condition 2.

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