## Tuesday, August 30, 2016

### Hypothesis Testing Problem for Senate Polls

Hypothesis Testing Problem for Senate Polls

Question:   The table below has data on the margin in percentages Republican Candidate minus Democratic candidate for all polls up to August 29, 2016 in the major Senate battles for 2016.   Test the hypothesis that the mean difference in the Republican minus Democratic margin percentage is zero versus the null hypothesis that this margin is not zero.

Do we reject the null hypothesis?   Would we have rejected the null hypothesis if we had employed a one-tailed test rather than a two-tailed test?

 Recent Senate Poll Results State Republican minus Democrat  Senate Candidate Margin Ohio 15 Ohio 8 Ohio 7 Ohio 9 Ohio 5 Ohio 5 Ohio 4 Penn 7 Penn -3 Penn -4 Penn -2 Penn -1 Penn 1 Penn -7 Florida 5 Florida 5 Florida 6 Florida 2 Florida 13 Florida 3 Wisc -11 Wisc -13 Wisc -10 NC 5 NC 2 NC -2 NC 4 Iowa 7 Iowa 9 Iowa 10 Iowa 10 Iowa 10 Iowa 1 Iowa 7 Nevada 0 Nevada 1 Nevada 2 Nevada -2 Arizona 13 Arizona 2 Arizona 9 Colorado -16 Colorado -15 Colorado -15 Colorado -13 Colorado -6

Analysis:   I conducted the test in Excel.   See calculations in the table below.

 Hypothesis Test Results Count 46 STD 7.996 Average 1.457 Z-score 1.235 p-value Z score 0.217

The two-tailed p-value for the two-tailed test is 2 x (1-NORMSDIST(Z-SCORE))

At 0.217 this p-value suggests we cannot reject the null hypothesis at any conventional critical value.

The one-tailed test that Republicans are outpacing Democrats would have a p-value greater than 0.10.  Again we would end up accepting the null hypothesis of no difference.

Comments: it is somewhat remarkable that the Republican Average Senate vote is larger than the Democratic Average Senate vote in this sample because most of the states in the sample are blue states that Obama won twice and many of the Republican incumbents are still in their first term and only got elected in 2010, a very good year for Republicans.   The Democrats might manage to take back the Senate because the Republicans must defend a lot of seats in blue states but Democratic Senate candidates are running worse than expected in Ohio, Florida, and Nevada, all states where Hillary Clinton has a big lead.

A discussion of polling data on a state-by-state level and some of my political insights can be found in the following post.