friedman test-comparing all treatments with a control

8/3/2019 Friedman Test-Comparing All Treatments With a Control

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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.be


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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.be

friedman test-comparing all treatments with a control

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