# ANOVA Testing

University of PhoenixResearch and Evaluation The Army would like to relocate me. My choices are Georgia, Arizona and California. I will determine the most cost efficient place to live. Since transportation is a necessity in todayÃÂs world I thought that I would start with the prices of gas. I would like to know if the mean gas prices are equal in all three states.

I will perform the Analysis of Variance (ANOVA) test. The reason I chose this particular test is because the data met all three requirements to perform the ANOVA. The requirements met were: ÃÂ1. the populations follow the normal distribution; 2. the population have equal standard deviations; 3. the populations are independentÃÂ (Lind, Marchal, & Wathen, 2004, P. 392).

Next I gathered 25 samples of gas prices from each state. I am using .05 as the level of significance. The data collected is as follows:ArizonaGeorgiaCalifornia\$1.65\$1.79\$1.99\$1.89\$1.82\$2.03\$1.89\$1.83\$2.04\$1.91\$1.84\$2.05\$1.92\$1.85\$2.09\$1.93\$1.86\$2.12\$1.94\$1.87\$2.15\$1.95\$1.87\$2.49\$1.95\$1.87\$2.85\$1.97\$1.87\$2.39\$1.97\$1.81\$2.03\$1.98\$1.85\$2.03\$1.98\$1.85\$2.03\$2.02\$1.76\$2.04\$2.02\$1.76\$2.79\$2.02\$1.77\$2.71\$2.03\$1.79\$2.49\$2.03\$1.86\$2.05\$2.05\$1.87\$2.55\$2.06\$1.87\$2.49\$2.07\$1.88\$2.03\$2.07\$1.89\$2.13\$2.09\$1.82\$2.15\$2.09\$1.94\$2.14\$2.11\$2.07\$2.37Using the above data it is determined thatH sub 0 is ÃÂµA = ÃÂµI = ÃÂµCH sub 1 is at least one mean is different.

The critical value is 2.03; therefore we can conclude that if the F calculation is greater than 2.03 the null is rejected.

The data analysis tool in excel was used for the ANOVA and the results are below:Anova:Single FactorSUMMARYGroupsCountSumAverageVarianceArizona2549.591.98360.009074Georgia2546.261.85040.003971California2556.232.24920.071949ANOVASource of VariationSSdfMSFP-valueF critBetween Groups2.06105921.03052936.374191.21E-113.123907Within Groups2.039856720.028331Total4.10091574From this I know that the SST is 2.06; the SSE is 2.03 and the SS Total is 4.10. This also shows that F = 36.37; therefore, the null is rejected. Their for I cannot conclude that all the means are equal.

Now to determine the best place to live since the means are not equal I determine which of the means were different. To figure this out I performed another test using Mega stat, shown below.

Post hoc analysisTukey simultaneous comparison t-values (d.f. = 72)GeorgiaArizonaCalifornia1.850...