Experiments with a Single Factor

1
Experiments with a Single Factor

• Means Comparisons

MeansCompare.ppt
ã D.A. Schaub, Univ. of Florida
2
Comparing Treatment Means Tukeys Test

• Suppose we wish to compare the results of our
  treatments
• This will show us if there is a statistically
  significant difference in the tensile strength as
  affected by Cotton
• Our hypothesis is

3
Tukeys Test
Tukeys test uses the distribution of the
studentized range
For equal sample sizes, 2 means are different if
the absolute value of their sample differences
exceeds
See text pp. 97-98
4
Tukeys Test (cont.)
Assuming that a0.05, and knowing that a5 and
dfE20
From App. Table VIII
5
Using Tukeys Test

• To use this test (and the ones following), we
  need to compare the average tensile strength for
  each setting of cotton

6
Calculating Treatment Average Differences

• Since (-5.6) is greater than our test value of
  5.37, then we can
• conclude that there IS a statistically
  significant difference in
• tensile strength between 15 and 20 cotton
  fibers.

The rest of the treatment differences should be
compared to our test value, (not just adjoining
percentage values, but ALL pairs) to see if there
are other significantly different variations in
TS based on cotton.
7
Comparing Treatment Means Fishers Least
Significant Difference (LSD)

• This procedure uses the t statistic for testing
  H0mimj

See text pp. 99-100
8
Testing LSD

• Assuming a0.05, the LSD test value is
• We now compare all pairs of treatment averages,
  as we did in the Tukeys test
• Notice that this test is less severe, (i.e., more
  differences in treatment means) than TukeysThis
  can lead to more Type I errors

9
Comparing Treatment Means Duncans Multiple
Range Test

• The third test that well discuss is the Duncans
  Multiple Range Test
• For this test, we need to first arrange the
  treatment averages in ascending order
• Then we calculate the standard error

And then use this number to calculate unique test
values
10
Duncans Test (cont.)

• Then using Duncans values for ra(p,f) (Appendix
  Table VII), we calculate a-1 significant test
  ranges
• The ra(p,f) are found for p2,3,,a with an
  agreed-upon a level, and f degrees of freedom for
  error
• The observed differences are compared, beginning
  with the largest versus the smallest compared
  with the Ra value, and continuing on

11
Summary of Multiple Comparisons of Treatment Means

• You may use any of the three procedures (Tukeys,
  Fishers LSD, or Duncans test) to compare
  treatment means to each other.
• Dunnetts test (available in Minitab)may be used
  to compare treatments to a control value
• Hsus MCB test (also available in Minitab)
  compares each mean only with the best among all
  of the other ones.