Answered: One vital goal of science is to figure…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Part 1: Correlation

One vital goal of science is to figure out causes. To determine causation is not easy, because we have to be able to distinguish causation from mere association. If two sets of values are related, we call that a correlation in statistical analysis. (If the values of each data source rise together we say they have a positive correlation. If the value of one source rises as the other falls, we call that a negative correlation.) For example you might notice that the more rainfall an area gets, the taller the trees are. The height of trees and the mean rainfall are positively correlated. In this case it is reasonable to suppose that the increased rainfall causes the trees to be taller, but you would have to document that in a controlled experiment.

What if you noticed that people with stomach ulcers have a higher incidence of a certain bacterium living in their stomachs? The correlation could be due to the bacterium causing the ulcers, or the ulcers might provide a good place for the bacteria to live. You could not say which way causation goes. Or it might be that eating certain foods both causes ulcers and introduces the bacteria.

Popular interpretations of science often get this issue wrong. Consider this Figure:

What are four possible types of explanations for the correlation shown in this graph--or any correlation between two sets of data? There are infinite specific explanations involving organic foods and autism. I am looking for general explanations that are not specific to these issues. One of them would be organic food causes autism.