Question

Complete subsequent Tukey Tests and LSD tests on all significant effects and state your conclusions. When conducting post hoc tests for the type of infection x Time interaction, I want you to examine the effects of type of brain damage at each level of time.

1-2 Years                     3-5 Years                     7-10 Years

Postencephalitic                      71.7                             62.25                           50.00

Postmeningitic    82.0                             79.25                           60.0

Postoperative Control             71.75                           81.75                           89.75

Main Effect of Infection

Postencephalitic                      Postmeningitic                        Postoperative Control

   61.32                                    73.75                                                   81.08

Critical difference Tukey =

Critical difference LSD =

Conclusions Tukey:

Conclusions LSD:

Subsequent Tests for Infection x Time Interaction

Critical Difference Tukey =

Critical Difference LSD =

1-2 years

Conclusions: Tukey:

Conclusions: LSD:

3-5 years

Conclusions: Tukey:

Conclusions: LSD:

7-10 years

Conclusions: Tukey:

Conclusions: LSD:

Answer 1

Given,

1-2 Years                     3-5 Years                     7-10 Years

Postencephalitic                      71.7                             62.25                           50.00

Postmeningitic 82.0                             79.25                           60.0

Postoperative Control 71.75                           81.75                           89.75

Main Effect of Infection

Postencephalitic                      Postmeningitic                        Postoperative Control

   61.32                                    73.75                                                   81.08

The formula for Tukey HSD:

Where:

Mi – Mj is the difference between the pair of means. to calculate this, Mi should be larger than Mj

  MSw is the Mean Square Within, and n is the number in the group or treatment.

Groups count sum average variance

Postencephalitic                      3                           183.95 61.32 10.88

Postmeningitic 3 220.05 73.75 11.98

Postoperative Control 3                          243.24 81.08 9.01

X1 ? X2 = 61.32 ? 73.75 = -12.43

X1 ? X3 = 61.32 ?81.08= -19.76

X 2 ? X3 = 73.75 ?81.08 = ?7.33

F value: 2.616886?

P value: 0.152362?

The formula for the least significant difference is:

Where:
t = critical value from the t-distribution table
MSw = mean square within, obtained from the results of your ANOVA test
n = number of scores used to calculate the means

Critical Values for the Tukey Q Test

d.f. = N – K (ANOVA Error or Within d.f.) for ANOVA: Single Factor

d.f. = N – R*C (ANOVA Within d.f.) for ANOVA: Two-Factor With Replication

d.f. = (R – 1)*(C – 1) (ANOVA Error d.f.) for ANOVA: Two-Factor Without Replication

Number of Groups (Treatments) = K

Lsd result SS df MS F
Between	135.2882 2 67.6441 0.3527
Within	1150.5933 6 191.7656
Total	1285.8815 8

LSD 0

SS = Sum of Squares,	df = Degrees of Freedom
MS = Mean Squares,	F = F - Ratio Test
LSD = Fisherman's Least Significant Difference Main Effect of Infection Lsd result SS df MS F Between 199.5638 2 99.7819 -    Within 70.385 2 35.1925 - Total 199.5638 2 LSD 0 1-2 years

Lsd result SS df MS F
Between 0 0 - -
Within 70.385 2 35.1925
Total 70.385 2

LSD 0

3-5 years

Lsd result SS df MS F
Between 0 0 - -
Within 225.1667 2 112.5833
Total 225.1667 2

LSD 0

7-10 years

Lsd result SS df MS F
Between 0 0 - -
Within 855.0417 2 427.5208
Total 855.0417 2

LSD 0