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8/3/2019 Friedman Test-Comparing All Treatments With a Control
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5/5/12
Statistical Methods andAdvanced Application
Multiple ComparisonProcedure For Use With
Friedman Test( Comparing All TreatmentsWith A Control )
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Learning Outcome
At the end of this lesson studentshould be able to:
Compute all treatments with acontrol and compare of two ormore treatments, of which one iscontrol condition by usingFriedmens Test.
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Case A Case B Case C
H0 : Mj M0 H0 : Mj M0 H0 : Mj = M0
H1 : Mj < M0 H1 : Mj > M0 H1 : Mj M0
Hypotheses
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t
Test Statistic
Treatment
Block 0 1 k
1 X10 X11 X1k
2 X20 X21 X2k: : : :
: : : :
b Xb0 xb1 Xbk
Signed differences ,dij = xij-xi0Number of minuses sign,rjNumber of pluses sign,b -rj
Continue
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Decision Rule
Case A
Reject H0 if the number of + sign critical value.
Case B
Reject H0 if the number of - sign critical value.
Case CReject H0 if the number of - sign or
number of + sign (smaller) criticalvalue.
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CASE HYPOTHESIS TESTSTATISTIC
DECISION
A
H0 : Mj M0H1 : Mj < M0
dij = xij -xi0rj= No. ofpluses
Reject H0 if thenumber of +sign critical
value.
B
H0 : Mj M0H1 : Mj > M0
dij = xij -xi0
rj = No. ofminuses
Reject H0 if thenumber of -sign critical
value.
C
H0 : Mj = M0
H1 : Mj M0
dij = xij -xi0
rj= No. ofminuses or
Reject H0 if the
number of -sign or number
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Example
A paint manufacturer wished tocompare three newly proposed withthe standard formula currently in
use for manufacturing a particulartype of house paint. The responsevariable was a composite score that
incorporated several properties thatmeasure paint quality. Since theeffective quality of paint is affectedby the surface to which it is applied,the company researches applied
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Table7.13FORMULA
SURFACE 0( Standard)
1 2 3
A 13 25 17 25
B 12 27 15 25
C 15 29 19 23
D 14 21 9 13
E 13 31 27 21Number of
minuses sign, rj
Number of pluses
sign, b - rj
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Solution
Hypotheses:
Case B:
Formula 1
H0 : M1 M0
H1 : M1 > M0 (claim)
Formula 2
A high score indicates a higherquality
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FORMULA
SURFACE 0( Standard) 1 2 3
A 13 25(+12) 17(+4) 25(+15)
B 12 27(+15) 15(+3) 25(+13)
C 15 29(+14) 19(+4) 23(+8)
D 14 21(+7) 9(-5) 13(-1)E 13 31(+18) 27(+14
)21(+8)
Number ofminuses sign, rj
0 1 1
Number of 5 4 4
Table7.13
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An experimentwise error rate, =0.10
Refer table A.15 for
k = 3 (treatment)
b = 5 (surfaces)Critical Value = 0
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Decision:
Formula 1
Since 0 0 (critical value)
Reject H0Formula 2
Since 1 > 0 (critical value)
Do not reject H0
Formula 3
Since 1 > 0 (critical value)
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Conclusion:
Formula 1There is enough evidence to
support the claim
that a high score indicates higherquality.
Formula 2
There is not enough evidence to
support the claim that a high score
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Exercise 1
Syme and Pollard* conducted an
experiment to investigate the
effect of different motivation levels
on measures of food-gettingdominance in the laboratory rat.
The data shown in Table 7.10 are
the amounts of food in gramseaten by eight male hooded rats
following 0 as control condition 24
and 72 hours of food deprivation.
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Table 7.10 : Amount of food, grams, eatenby eight rats under three levels of food
deprivation
Subject Hours of food deprivation0 24 72
1 4.5 5.9 13.9
2 15.3 8.1 12.63 9.6 8.1 8.1
4 7.2 8.6 6.8
5 6.8 8.1 14.3
6 4.7 5.9 4.2
7 10.1 9.5 14.5
8 9.3 7.9 7.9
i 2
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Exercise 2
A paint manufacturer wished to
compare three newly proposed with
the standard formula currently in use
for manufacturing a particular type
of house paint. The response variable
was a composite score thatincorporated several properties that
measure paint quality. Since the
effective quality of paint is affected
T bl 7 13
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Table 7.13
Surface
Formula
0 1 2 3
A 13 25 12 11
B 12 27 10 9
C 15 29 13 12
D 14 21 9 13
E 13 31 11 10
E i 3
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Exercise 3
Syme and Pollard* conducted an
experiment to investigate the effect ofdifferent motivation levels on measures offood-getting dominance in the laboratoryrat. The data shown in Table 7.10 are the
amounts of food in grams eaten by eightmale hooded rats following 0 as controlcondition 24, 72 and 96 hours of fooddeprivation. A higher amount of food
indicates more effects to the three levelsof food deprivation.
Let = 0.05
*Syme, G. J., and J. S. Pollard, The Relation between Differences inLevel of Food Deprivation and Dominance in Food Getting in the Rat,
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Link to youtube :
http://www.youtube.com/watch?v=gI
http://www.youtube.com/watch?v=gI0xQcLIplA&feature=youtu.behttp://www.youtube.com/watch?v=gI0xQcLIplA&feature=youtu.be8/3/2019 Friedman Test-Comparing All Treatments With a Control
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Thank you..
http://www.youtube.com/watch?v=gI0xQcLIplA&feature=youtu.behttp://www.youtube.com/watch?v=gI0xQcLIplA&feature=youtu.behttp://www.youtube.com/watch?v=gI0xQcLIplA&feature=youtu.beRecommended