Question

SOLVE WITH SPSS ONLY

We wish to assess the effect of three different track surfaces on sprinter speed. Six world-class sprinters are asked to run five 100m dashes on each of the three track surfaces. Their average times are recorded below. USE SPSS NO EXCEL NO HAND

Surface 1 Surface 2 Surface 3

Sprinter 1 9.85 10.00 10.04

Sprinter 2 9.90 10.07 10.16

Sprinter 39.89 9.99 10.17

Sprinter 4 9.88 9.98 10.04

Sprinter 5 9.81 10.03 10.10

Sprinter 6 9.81 9.95 10.12

Using the sprinters as blocks, discuss the differences between the track surfaces as suggested by SPSS. Give a statement to be tested, identify the random variables involved and the assumptions you make about them, state the hypotheses to be tested, ask SPSS to run the analysis for you, including a post hoc, and then discuss the outcome. Describe the critical region(s) upon which you base your decisions. Include any SPSS output in your discussion.

Answer 1

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
Sprinter 1	3	29.89	9.963333333	0.010033333
Sprinter 2	3	30.13	10.04333333	0.017433333
Sprinter 3	3	30.05	10.01666667	0.020133333
Sprinter 4	3	29.9	9.966666667	0.006533333
Sprinter 5	3	29.94	9.98	0.0229
Sprinter 6	3	29.88	9.96	0.0241
Surface1	6	59.14	9.856666667	0.001586667
Surface2	6	60.02	10.00333333	0.001746667
Surface3	6	60.63	10.105	0.00319
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	0.017383333	5	0.003476667	2.282275711	0.124965406	3.32583453
Columns	0.187033333	2	0.093516667	61.38949672	2.423E-06	4.102821015
Error	0.015233333	10	0.001523333
Total	0.21965	17

Tukey's hsd=CR=Qa* MSE/cn'

=0.11 (For 0.05 significance level)

X1-X2=	-0.08
X1-X3=	-0.053333333
X1-X4=	-0.003333333
X1-X5=	-0.016666667
X1-X6=	0.003333333
X2-X3=	0.026666667
X2-X4=	0.076666667
X2-X5=	0.063333333
X2-X6=	0.083333333
X3-X4=	0.05
X3-X5=	0.036666667
X3-X6=	0.056666667
X4-X5=	-0.013333333
X4-X6=	0.006666667
X5-X6=	0.02

Since critical value is more than all the differences, there is no significant difference between any of the pairs

To run randomized block design anova in spss, please see the steps below: -

a) Select Analyze > General Linear Model > Univariate

b) Insert dependent and independent variables and also select Tukey as the post hoc test

c) Click Continue and OK