Philosophy - Philosophy Course Notes

Scientific Reasoning

Lecture 13

Sep 25, 2007

Remember: Not all cogent arguments are valid arguments.

One goal of these three lectures is to give enough information to understand reports of scientific studies.  People often try to use scientific information to further their own agendas.

I. Correlation

A. What is Correlation?

1. Correlations exist in a given group or population.

2. Values of variables are what are claimed to be correlated. (A variable is a general property which every member of the population has.)

3. Make sure each member of population does not have more than one value for a variable.  (Cannot be married and unmarried.)

4.  Need to know the proportion of a population that has a given property.  (Num with property / Total population)

A correlation is a claim about two values of two different variables.

Find # of population with property X.  Find subgroup in X with property Y.  Find subgroup in non-x with property Y.  If x group has more than non-x group then is positively correlated.  If less than non-x group, negatively correlated.

5. What do you need to know to understand a claim of correlation?

i. What population is being talked about.

ii. What are the two variables and values can they each have?

iii. Is a positive or negative correlation being claimed?

B. What is Good Evidence That a Correlation Exists

Two main restrictions on determining if correlations exist:

1. Some populations are very large. (no resources to do a study.)

2. Populations are often scattered, hard to get access to.

To get around these problems:

1. Instead of studying entire population, study a sample.

2. Ensure your sample is representative of the whole population.

3. Randomness helps to ensure representativeness.

C. Randomness in Context of Correlations

1. Not a property of actual sample

2. It is a property of the way you choose the members that make up that sample.

D. When is a sample randomly selected?

1. Every time you have a chance to choose a member for the sample, every member of the population has a chance to be selected.

2. This gives the greatest likelihood of having a representative sample.

3. Given your restraints, make your sample as large as possible.

4. The bigger your sample, less likely to get skewed results and exact same %.

5. Far less like if bigger sample, to get proportion that is very different from real value.

6. The closeness to the real number is usually expressed as a margin of error.  3%, 19 times out of 20

(how close to real number, arbitrarily chosen 'accuracy factor')

E. Rules of Thumb for Remembering Margins of Error

1. If 25 members in sample, confidence level 25%.

2. Sample size less than 100, margin of error 105.

3. Sample size of 100, margin of error 5%.

4. With 2000 sample size, margin of error 2%.