This article involves using the Fisher exact and the chi-square test to determine whether state budget challenges more frequently pertain to the states that typically vote as “red”, “blue” or “purple”. There is a general notion that states in the biggest fiscal messes are the “blue” democratic states, generally because these states tend to have more significant unfunded (or underfunded) state employee pensions, and are more generous with social programs. However, a statistical analyses disproves the notion that there is a relationship between states in the largest fiscal messes and their political tendency; i.e., whether it is a blue, red or purple (battleground) state. The data tables and additional detail are contained in my more complete article on these chi-squar and fisher tests.
We previously described three different “solutions” to three states’ financial crises, and provided a list of the top ten states (i) projecting the largest shortfalls for fiscal year 2012, and (ii) with the largest 2012 projected shortfalls relative to their most recent budget. The classification of red, blue and purple (i.e., battleground) states was determined by compiling average margins of victory in the last five presidential elections. Three of these past elections were won by Democrats, Bill Clinton in 1992 and 1996, and Barack Obama in 2008; two were won by Republican George W. Bush in 2000 and 2004.
Both the Fisher exact and the chi-square test the hypothesis that the two groups (i.e., voting tendency and largest budget shortfall) are unrelated. The two tests are summarized as follows:
- The chi-square compares the “actual” values (values that actually were observed) with the “statistically expected” values (calculated values based on the sum of actual values that one would expect assuming the hypothesis is valid). Based on the difference between the actual value and the statically expected value, the test result either accepts or rejects the hypothesis with a certain confidence level. Here is our online interactive chi-square calculator.
- The Fisher exact test calculates the probability of getting deviations as extreme as the “actual” values (values that actually were observed) under the hypothesis that political tendency and largest budget shortfalls are not related. Based on the probability result, the test result either accepts or rejects the hypothesis with a certain confidence level.
Stated otherwise, (i) using the chi-square test, the actual values are NOT significantly different than the statistically expected values at the 95 percent confidence level, and (ii) using the Fisher exact test, differences in largest budget shortfall states between political tendency is NOT extreme enough to be considered “beyond chance” or “random”. Importantly, these results remain despite the way the data is “sliced and diced” (e.g., use the top 5, top 15, top 20 states rather than top 10). Essentially, this means that one can successfully assert with 95 percent confidence that there is no relationship between those states with the largest 2012 budget shortfall and their political tendency.