Scientifically, you can't prove anything. You can deduce probabilities, such as that gravity most likely explains the phenomena of falling objects. In science, you can only disprove the hypothesis, which is done by finding exceptions to the rule or noting that there really isn't any difference between two sets of data (e.g. medical studies that try to show treatment improvements). If you can't disprove it, then it's likely, but not certain, that the hypothesis is true.
Many people have gotten in trouble by thinking correlations mean causation. Some people rely on the length of women's hem lines or which league wins the World Series or which political party wins the presidential election to predict if the stock market will increase or decrease the next year. Coincidences occur. Coincidences are not necessarily related. But many conspiracy theorists rely on coincidences and correlations.
I once related this story as an example of how Dan Brown's Da Vinci Code relied on coincidences and correlation to connect the dots in his story. "In this church, there are 3 stained glass windows. 3 blocks from here there is a war memorial. That war memorial mentions Col. Brown first. Col. Brown's descendant attends our church. Therefore, this church is a war mongerer." Anyone who looks at this would realize the erred logic here and that some information is missing in order to reach this conclusion.
In business, we shouldn't rely on coincidences and correlations. Yet, everyday we have the example of stock market reporting. Every statistically insignificant blip needs to have a cause ("such-and-such increased earnings and everyone is calmed about austerity discussions in pick-a-country-in-trouble"). Really? There is no reason to report any causes to normal variation. People purely report on coincidences. Likewise, when we report on improved results from one month to another and try to explain it, we're doing the same exact same thing. Unless the results are statistically significant and different, there's no reason to make a report. You cannot disprove the hypothesis that the results are from the same set of drivers as the previous month.
Two other examples: according to the IPCC, the international group charged with tracking climate change, the earth was warmer from approximately 1000 A.D. to 1400 A.D.--400 years of warmer, global temperatures than we have today. There is a coincidence that lately (in the past 200 years) we have increasing temperatures and more mechanization and industrialization and we have increasing temperatures. From that coincidence, most scientists believe in the causal link between industrialization and climate change. However, they're ignoring the other evidence. What industrialization or human effort caused the global roasting a millennium ago? And there was a lot fewer people back then--one tenth of what we have today. How did 600 million people create more carbon dioxide than 6 billion people with cars, planes, steel mills and lots of beef cattle? Are the causes similar for the two different millennia? How do we disprove that the causes for both periods of global warming are the same?
Here's the other: Wal-Mart is a large organization, hiring many people. Somewhere in this large organization would be someone who would say, "If everyone has an opportunity to be promoted and get pay increases through objective, non-biased criterion, then we would expect to see a similar demographic in our supervisory and management ranks as we see in our overall workforce." This person could be one (of many perhaps) that have to fill out Equal Employment Opportunity reports. It would be easy to test the hypothesis that the management ranks have a similar percentage of females in it as are in the workforce. If they can disprove that hypothesis, then they need to look for the factor that's causing a significant difference in percentages.
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