LydiaLe@UTS-Learning Arguments-Evidence and Intuition

The Simpson Paradox

Simpson’s Paradox

What is Simpson's Paradox?

According to the Statistics How To (2016), the Paradox is named after the statistician who discovered something unusual in the 1960s that statistics can be wrong, and the paradox is that averages can be misleading. For learning the definition, the Board of Education Commonwealth of Virgina (2009) states that Simpson’s paradox refers to the fact that aggregate proportions can reverse the direction of the relationship seen in the individual parts.

References

Board of Education Commonwealth of Virgina (2009). Mathematics Standards of Learning Curriculum Framework 2009: Probability and Statistics. Retrieved 13/4/2016 from

http://www.doe .virginia.gov/testing/sol/frameworks/mathematics_framewks/2009/framewk_probability_statistics.pdf

Statistics How To (2016). What is Simpson’s Paradox?: Overview. Retrieved 13/4/2016 from

http://www.statisticshowto.com/what-is-simpsons-paradox/

Some different sources of information for understanding about the Simpson's Paradox are collected as follows:

References / Sources & Author/s

About the Simpson's Paradox

Simpson's paradox illustrates that the effect of an omission of a categorical explanatory variable Z can have on the measure of association between a categorical explanatory variable X and a categorical response variable Y.

https://www3.nd.edu/~busiforc/handouts/Other%20Articles/simponsparadox.html

Simpson's paradox, or the Yule-Simpson effect, is a phenomenon noted in statistics, which states:

”The ratio of success of several sub-populations can be reversed in the ratio of success of the population as a whole.”

This effect has been noticed to occur in Bernoulli Trials, especially in social science, medicine and baseball batting averages.

It is not this statement by Homer Simpson:

”To alcohol! The cause of, and solution to, all of life's problems.”

http://rationalwiki.org/wiki/Simpson's_paradox

Simpson's paradox, also known as the Yule–Simpson effect, is a paradox in probability and statistics, in which a trend appears in different groups of data but disappears or reverses when these groups are combined.

It is sometimes given the impersonal title reversal paradox or amalgamation paradox.

According to Pearl (2014), Simpson’s paradox is often presented as a compelling demonstration of reasons that the statistics are needed . It is a reminder of how easy it is to fall into a web of paradoxical conclusions when relying solely on intuition, unaided by rigorous statistical methods.

Pearl, J. (2014). Understanding Simpson’s Paradox. Retrieved 10 April 2016 from http://ftp.cs.ucla.edu/pub/stat_ser/r414.pdf

Simpson's paradox occurs when groups of data show one particular trend, but this trend is reversed when the groups are combined together. Understanding and identifying this paradox is important for correctly interpreting data.

Simpson’s paradox refers to the reversal in the direction of an X versus Y relationship when controlling for a third variable Z.

http://www.math.grinnell.edu/~mooret/reports/SimpsonExamples.pdf

An association between a pair of variables can consistently be inverted in each subpopulation of a population when the population is partitioned... The arithmetical structures that invalidate that despite intuitions to the contrary, then a discussed argument is invalid. Such arguments pose deep problems for inferences from statistical regularities to conclusions about causal relations. Robust associations between variables can mask underlying causal structures that, when made explicit, expose the associations to be causally spurious.

Simpson's paradox occurs when a sample is composed of separate classes with different mean values of a statistical value.

Simpson’s paradox refers to the apparent contradiction, in which the trend of the whole can be different from or the opposite of the trend of the constituent parts.

http://www.brookings.edu/blogs/social-mobility-memos