Is it legitimate to claim a planned linear trend as statistically significant if the omnibus test for the data is non significant?
An investigator conducted a five-group study where the groups represent equally spaced levels of a quantitative factor. Data are obtained for 15 participants in each group. The following sample means are obtained: The value of mean square within (MSw) equals 150. a. Assume that the investigator has planned to test only the linear trend. Is the trend statistically significant at the .05 level? b. Is the omnibus test of group differences statistically significant? In other words, can the null hypothesis be rejected? c. Why is the observed F value so much larger for the linear trend than for the omnibus test? d. What are the implications of your answer to part c for the potential benefits of testing a planned linear trend instead of testing the omnibus null hypothesis? e. Is it legitimate to claim a planned linear trend as statistically significant if the omnibus test for the data is non significant?