Question

e. Select all the correlations that are significant when controlling the family-wise error rate at 0.05 using the Bonferroni correction. Gore percentage $ Bush percentage Gore percentage & Buchanan percentage Gore percentage & Nader percentage Gore percentage & Total registered voters Gore percentage & Turnout percentage Bush percentage & Buchanan percentage Bush percentage & Nader percentage □ Bush percentage & Total registered voters ם Bush percentage & Turnout percentage Buchanan percentage & Nader percentage Buchanan percentage & Total registered voters Buchanan percentage & Turnout percentage Nader percentage & Total registered voters Nader percentage & Turnout percentage Total registered voters & Turnout percentage # Florida-2000 6-Multivariate-JMP Δ ▼ Multivariate Δ Correlations Gore_Pct Bush_PctBuchanan_Pct Nader_Pct Total_Votes Total_Reg 0.2721 0.2498 0.4670 0.4719 0.2573 -0.2971 -0.4540 -0.4583 .0000 -0.3797 -0.3878 0.3802 0.3797 1.0000 0.0841 0.0708 0.3878 0.0841 1.0000 0.9983 0.3802 0.0708 0.9983 1.0000 GorePct Bush Pct Buchanan_Pct 0.2721 0.2573 Nader Pct Total_Votes Total_Reg 1.0000 0.9982 0.9982 1.0000 0.2498 0.2971 0.4670 -0.4540 0.4719 0.4583 Scatterplot Matrix 60 50 Gore Pct 40 30 20 60 Bush_Pct 30 Buchanan Pc 05 Nader Pct 500000 Total_Votes 200000 100000 800000 600000 400000 200000 Total_Reg 20 40 60 30 45 60 0 0.51 1.5 0.5 200000 0

Answer 1

Hypotheses to test whether correlation is significant would be-

H₀: Correlation is not significant

H_a: Correlation is significant

Considering the p-values given in the 2nd table, we compare p-values with the level of significance 0.05

After comparsion we see that the correlations which have p-values less than 0.05 are -

Gore percentage $ Bush percentage
Gore percentage & Buchanan percentage
Gore percentage & Nader percentage
Gore percentage & Total registered voters
Bush percentage & Buchanan percentage
Bush percentage & Nader percentage
Bush percentage & Total registered voters
Buchanan percentage & Nader percentage
Buchanan percentage & Total registered voters
Nader percentage & Turnout percentage
Total registered voters & Turnout percentage

In these cases as p-value is less than 0.05 so null hypothesis is rejected at 5% level of significance and hence correlation is significant.

All other cases except these do not have significant correlation.