This document summarizes key concepts in causal and statistical reasoning. It discusses cause and effect relationships, associations versus causal relationships, and fallacies involving false correlations. It also outlines philosopher John Stuart Mill's methods for determining causation, including the method of agreement, method of difference, joint method, and method of concomitant variation. Finally, it discusses aspects of statistical studies such as sample size, diversity, and margin of error, as well as the forms and strength of statistical arguments.

1. Chapter Eight Roll the Dice: Causal & Statistical Reasoning Second Thoughts, 4 th ed. Wanda Teays McGraw-Hill Higher Ed. © 2010. Wanda Teays. All rights reserved .

2. Cause & Effect Reasoning Cause and effect reasoning is all around us. It is common in medicine and health. For example : “ Young women who took the commonly used epilepsy drug phenytoin for one year showed significant bone loss compared to women taking other epilepsy drugs,” according to a study published in the April 29, 2008, issue of Neurolog y We also see cause and effect reasoning about social problems and natural phenomena (e.g., weather conditions, environmental changes, and so on). Cause and effect arguments present us with probability, not certainty. This asserts that the antecedent conditions, if true, cause the supposed effect to happen.

3. Associations vs. Causal Relationships An association between two thinks means they are connected in some way—but the nature of that connection may be in doubt. For example, some think there is an association between cell phone use and brain cancer—but no causal relationship has yet to be established. Let’s see what it can mean to posit a causal relationship . Watch for any claims asserting a relationship between two things where is said to cause (or be a causal condition) of the other. The word “cause” need not be present, so long as the relationship is made apparent. This can be done simply using the word “effect” or “effect of” or the equivalent.

4. False Correlations False correlation: When a connection is drawn between two things, but the one is not clearly the cause of the other. For example, the Post Hoc fallacy, that something is the cause of something else simply because it precedes it E.g., I ate a chocolate bar and went hiking in the woods. That night I got a rash—it must have been the chocolate!

5. Mill’s Methods Philosopher John Stuart Mill set forth a systematic way to look at cause and effect arguments. His methods are known as: (1) The Method of Agreement; (2) The Method of Difference; (3) The Joint Method; and (4) The Method of Concomitant Variation. METHOD OF AGREEMENT: Here we seek to determine the cause of an event by examining all the cases where the event occurs and then look for a common factor. For example, when a group of people become ill we often look for a common factor, such as exposure to a toxic chemical or spoiled food.

6. Mill’s Method of Difference With the method of difference we compare two cases—one where the effect (or event) occurs and one where it doesn't occur. We then look at the antecedent conditions for these two cases to determine what is different. In light of the differences, we then select the probable cause. For example, you have two primroses. You plant one in the sun and one in the shade. You put fertilizer on both of them and water them regularly. The plant in the sun grows beautifully and has lots of blossoms. The primrose planted in the shade has keeled over and the leaves have curled up. What’s different?

7. Mill’s Joint Method A more high-powered approach would be to combine the two methods, looking at what is similar and what is different. This is what is done with the joint method . For example, you plant twenty fields of corn. Fifteen fields produce wonderful, tasty corn and five fields only have dried, shriveled corn. The fields with the wonderful corn are next to a pasture. The five fields with crummy corn are not only near a chemical dump, but people throw their trash into the fields. This suggests that the common location of the successful fields figures into getting good quality corn. Furthermore, both the chemical waste dump and the piles of trash landing on the struggling plants suggest a probable cause for these fields of corn doing so poorly.

8. Method of Concomitant Variation This last method is for cases that are not all or nothing, but where an effect occurs in degrees. With the method of concomitant variation we might have increasing or decreasing amounts of some effect (like pollution in a city or disease patterns in a population). It's not that you are ever without the effect, but that its presence is a matter of percentage. An example of the use of concomitant variation is with the study of mosquito populations and health concerns. The West Nile virus is a potentially lethal disease transmitted by mosquitoes. The bite of an infected mosquito can be deadly for the victim. Since the West Nile virus appeared on the East Coast in 1999, and by January, 2009 had infected humans in all but nine states. So, in ten years the disease has become a health concern beyond one state’s borders. With the method of concomitant variation, researchers can study the varying rates of the spread of the disease.

9. Statistical Reasoning Arguments based on statistical studies are inductive arguments, since they draw an inference based on a sample group, where the evidence is partial at best. Statistical reasoning always entails a degree of probability—never certainty—in the relationship between the premises and the conclusion. We need to know how to properly use statistical studies to recognize the strong arguments and not be fooled by the weak ones.

10. Statistical Studies A statistical study has several factors: One, a targeted population about whom we want information and, Two, the sample group we intend to study as a a microcosm of the larger group. In certain sorts of statistical studies, such as medical experiments, psychological testing, or pharmaceutical studies, research protocol may call for a control group as a basis of comparison. This group is used to compare relative responses, for example, to a medical treatment or drug regimen, in order to eliminate other factors. I

11. Three Key Aspects of a Statistical Study Date  What is the date of the study? Is it still relevant? Size  How big was the sample group? Diversity  How diverse is the sample population? Is it representative of the target population? Study old? May no longer be relevant. Sample size too small? May end up a Hasty Generalization (fallacy) Sample group not diverse enough? May end up Biased Statistics (fallacy)

12. Diversity of Sample Two Major Ways to get Sufficient Diversity in A Sample Study Representative Sample. A representative sample is obtained by trying to match thesample groupwith the target population. Try to keep a balance of the major aspects to consider (like gender, age, race, religion, education, class, geography). Random sample. A random sample is not obtained by carefully orchestrating a sample group taking into account the relevant factors (like age, gender, nationality, class). In a random sample, each member of the target population has an equal chance of being studied. We get a random sample by using some numerical means (like every third person is polled, every tenth voter is interviewed) with a sufficient quantity. Hopefully this will generate enough diversity to reflect the target population.

13. Margin of Error The margin of error is indicated as a ± x, where x is some small number. The smaller the margin of error is the better. In well-orchestrated studies like those we see in the Gallup Poll, the margin of error is usually ±2 or 3 percent. A margin of error over 5% may indicate a less reliable study. Mathematician Matthew Delaney considers a 5% margin of error hard to achieve and, therefore, it may be unrealistic to think a study can achieve this level of accuracy.

14. Two Forms of Statistical Arguments Form of a statistical syllogism x% of A is a B. p is an A. Therefore, p is a B. FOR EXAMPLE: 46% of short women like spike heels. Bibi Marimba is short. So she’ll like spike heels. Form of an inductive generalization x% of A's polled (or sampled) are Bs. Therefore, x% of all As are Bs. FOR EXAMPLE: 73% of donut-lovers prefer jellies to creams. Chuck loves donuts. Therefore, Chuck must prefer jellies over cream donuts

15. Strong Statistical Syllogisms The strength of a statistical syllogism is directly proportional to the percentage. The closer to 100% in an affirmative claim, the better the argument. Basically, 85% and up is pretty strong, the higher the better. But the lower the percentage more questionable is the truth of the conclusion. FOR EXAMPLE: 92% of tall men have big feet. PaoGasol is a tall man. Therefore, he probably has big feet. Pretty good! 49% of short women have well-manicured nails. Jolene is short. Therefore, she probably has well-manicured nails. Not very impressive!