Question

A highway safety institution conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In the institute’s 40-mph offset test, 40% of the total width of each vehicle strikes a barrier on the driver’s side. The barrier’s deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40mph. You are in the market to buy a family car and you want to know if the mean head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles (SUV’s). The data in the tables below were collected from the institute’s study. Use ?=.01. Large Family Cars 262 135 413 526 148 630 164 Passenger Vans 149 237 341 697 554 466 319 Midsize Utility Vehicles 225 216 146 255 402 596 395 State the null and alternative hypothesis. h_0: h_A: Calculate the sample standard deviation of each sample. Do we meet the requirement for these? Find the test statistic. F_0= Determine the P-value. p= State your conclusion. Would we perform post-hoc procedures for this data?

Answer 1

For a one-way ANOVA, you will probably find that just two tests need to be considered. If your data met the assumption of homogeneity of variances, use Tukey's honestly significant difference (HSD) post hoc test. Note that if you use SPSS Statistics, Tukey's HSD test is simply referred to as "Tukey" in the post hoc multiple comparisons dialogue box). If your data did not meet the homogeneity of variances assumption, you should consider running the Games Howell post hoc test.

Because post hoc tests are run to confirm where the differences occurred between groups, they should only be run when you have a shown an overall statistically significant difference in group means (i.e., a statistically significant one-way ANOVA result). Post hoc tests attempt to control the experimentwise error rate in the same manner that the one-way ANOVA is used instead of multiple t-tests. Post hoc tests are termed a posteriori tests.