Question

Use minitab to solve the following:

5. The following data are the wing stroke frequencies for samples of two species of Euglossine bees. Four bees from one species and six from the next:

Wing Stroke Frequencies:

Euglossa Mandibularis Friese	Euglossa Imperialis Cockerell
235	180
225	169
190	180
188	185
	178
	183

1. Under what condition is the median a better measure of center than the mean?
2. At the 0.05 level of significance, is there any difference in the median wing stroke frequency of the two species?
3. What assumption is necessary for the test to be valid?

Answer 1

a)

The median is the value in the center of the data. Half of the values are less than the median and half of the values are more than the median. It is probably the best measure of center to use in a skewed distribution.

b)

Mann-Whitney Test and CI: Friese, Cockerell

           N Median
Friese     4 207.50
Cockerell 6 180.00

Point estimate for η1 - η2 is 30.50
95.7 Percent CI for η1 - η2 is (5.01,56.01)
W = 34.0
Test of η1 = η2 vs η1 ≠ η2 is significant at 0.0142
The test is significant at 0.0139 (adjusted for ties)

c)

A very general formulation is to assume that:

1. All the observations from both groups are independent of each other,
2. The responses are ordinal (i.e., one can at least say, of any two observations, which is the greater),