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MAS
Prof. DONNO
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2ndEXAM
FALL 2OOO
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Name
I.D.#
- Headaches are very common ailments.^ Most^ people^ usually^ can^ control^ them^ with
over-the-counter pills. For a^ few^ others,^ however,^ headaches are^ debilitating^ rind
almost gnbearable.^ A major hospital^ decided^ to^ conduct^ a^ research^ on^3 new^ pills^ to
measure their effectiveness. An^ index^ that^ goes^ from^ =50 to^ +50^ is^ used.^ Negative
values indicate that tlie headache^ is^ actually^ getting worse.^ Positive^ values^ indicate^ an
improvement. The ideal score^ is +50. Patients^ for^ this^ test^ were^ selected at^ random.^ In
total, ttre sample is composedby l2males^ and^12 females.^ ihe^ goat is to determine^ if there is a dffircnce between^ pills^ in^ treating^ headaches.
Results are prwided on the separate MINITAB^ printout^ labeled^ as
PLLS FOR HEADAirms (^) iI Dataentered include: INDEX-PILL TY"E-^ SEX.^ i In answering (^) a{ questions use g:^ ,05.^ Three^ Models^ are^ shown: MODEL I : dne-Way Analysis of^ Varianc€^. MODEL II : Two-Way ntoct< Design^ (NO^ Interaction)^ i MODEL III:' Two-Way Factorial^ (with^ Interaction)
In answering thefollowing questions, sdlect^ and^ use^ only^ the^ printout^ thizt y (^) ou c ons id er appr opr igte (^) for (^) .this qp eriqgept^ ;
Which did you select?...J.x?.:'}.14/.r..?..P.!C.c.!:;..r -'-.
,what is^ the^ NuttHypothesis^ Ho? seteci^ oo.,^ ..)l'9...!)ifr.t3.r..*........... Ifo: (^) No difference due to treatments, (factors)^ tNO^ l)ifference IIo: Treatments, (factons), do make a^ difference^ )^ Differencel
Should PILL TYPE be considered^ a^ F'ACTOR^ or^ a^ BLOC^ XZ^ ..(1M...
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I I I
Shoulh SEX be considered a^ FACTOR or^ a^ BLOCK?^ .-$..tg.iK^
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a { 1
I I{ {j ! I
V
(/
y/
'How
many degrees of freeilom for^ PILLS^?^ -.....2..-.^ For^ SEX?^ ....!....... oar/ _ o, \ilhat is the Mean Square, (MS),^ for^ PILLS?^ .....qp-.'-g.-J...^ For^ SEX?^ ...Y........"
TVhat is the F-v
appears to
What is the (^) P-value for PILLS?..i?.9.1...
What is the P-value for SEX? ..o.t33?l
Hence, Reject Ho?^ YES..... /
r/
Hence, R6ject Ho?^ YES..:..
/ NO.......
NO.......
Based on X'isherts Painvise Comparisonsr^ w
1 versus 3 2 versus^3
- The same hospital is also conducting^ a^ research^ on new treatments^ used^ to control^ the woist (^) cases of headaches: MIGRANE HEADACHES.^ They^ are^ testing^4 new drugs, (mixtures),^ all^ of which^ require^ to^ be^ injected.^ It^ is^ also^ important to determine the dose. They decided to test the four'drugs by^ injecting^ them^ once^ per^ week^ or^ twice per week (If one i4jection aweek^ is^ used,^ the^ input variable SCHEEDULE^ is^ :^ 1, if two injections are given, the^ input variable^ SCHEDULE;2)
To measure results, they used the^ same^ index^ as^ for^ the previoug Problem. (From^ -50^ for
badreaction to +50forperfectresults).^ +
Data entered include: INDEX (^) - SCHEDI'JLE^ - MIXTURE.^
j
Please, note that the variable MIXTURE^ is^ identiffing^ the^ DRUG^ number.
In answering (^) all questions use o =.05. Two^ Models^ are^ shown: MODELI' (^) : Two-WayFactgrial (withlnteraction)^ i MODEL II : Two-Way Block Design^ (No^ Interaction)^ ; In arrywertng thefollowing questions, select^ the^ printoht^ that^ you consider appropriatefor this etcperirnent; (Witlt or^ witltout^ interaction?) Wh ich did you (^) s elect?... .11 ::.. ?. P.^ t:'1^ ..F.^ !.?.?.'.^ t^ #
In Analysis of (^) vari4nce, what is the^ Null^ Hypothesis^ Ho? Select on": ... .,. .01.e..D.fu-.{$.q3'........ IIo: No difference due to treatments,^ (factors) tNO^ Difference IIo: (^) Treatments, (factors), do make a^ difference^ )^ Difference
/1. Should SCIIEDULE be considered^ a^ FACTOR or^ a^ BLOCK?^ ..f.+-?:.'. al ' (^) should MIXTURE be considered a FAcroR or a BLoc K? ....t+?.!.... 4 tto (^) -"oy degrees of freedom for MIXTURE?^ ..3.,.^ For^ SCHEDULE? ...{....
If applicable, how many'degrees of freedom^ fiir^ tne^ INTER^ i,CTION?^ ..?...
What id the Mean Square, (MS),^ for^ MD(TIIREI^ .!.1Jr.11^ For^ SCI{EDLLE?^ .).T.,.Y)
What (^) is the F-vahie foTMIXTLRE? ,..J,:l:3:{.....
ili/ What (^) is the P-value for SCIIEDULE? (^) ':(A). Hence, Rejebt^ Ho?^ YES....^ NO...
If the XNTERACTION is applicable, is^ it^ signilicantly^ + 0?^ y.rJ.
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*a/'^ f
,rd -'
.f'.k \in \
Refer to the printout^ labeled^ INJECTIONS^ FOR^ ffBnpeCI{ES
lVhat is the P-value for MD(TURE? :.:Y:...^ Hence, Reject^ Ho?^ YES....^ NO."-
/1,
One-way Analysis of Variance Analysis, of Variance for Index Source DF SS MS Pill. "^ L77.25 (^) ' -Error (^) 169. 37 Total 346.
t i PILLS FOR HEADACHES
I I
I
t
t
Y
Two-way Analysis (^) of Variance (Block^ Design:^ No^ Interaction) Analysis of Variance for Index source DF ss Ms PiIl sex I o. 3g D,Zb Error k,^ L69.00 (^) I ,q{ Total 23 346.
Two-way Anatysis of Variance (Two Factors^ with^ Interaction)
P
- 001
P
t !- j
Analysis of Source PiIl Sex Interaction" Error TotaI
Variance
DF
1
-9.
for fndex SS t77 ,
- 38
Flsher's Painrvise Gomparisons Intervals for (column^ level mean)^ (row^ level^ mean)
cl c2 c lndex Pill Sex 1 23 ,l^ M 2 -18^1 M 3 17 1 M 4 20 '1^ M 5 27 2 M .6 23 2 M 7 21 2 M 8 28 2 M 9 23 3 M 10 21 3 M 11 24 3 M 12 16 3 M 13 20 1 F" 14 17 1 F 15 16 1 F 16 19 1 F 17 29 2 F
t8 23 2 F
19 27 2 F 20 25 2 F 21 27 3 F .22 19 3 F 23 20 3 F 24 22 3 F
i'" I
INJECTIONS FOR HEADACHES
Two-way Analysis (^) of Variance (Two Factors^ with^ lnteraction)
Source DF SS MS^ F^ P Schedule I 14. Mi.xture t^ SAt. A Interaction L^ 548. Error 23 804. 8 2q.?
Tota1 39 L949.
Schedule Mean i 1 9.s 2 to.1'
Mixture Mean (^1) 13. 2 LO.z 3 L2.
- (^) 3.
{
Two-way Analysis (^) of Variance (Blcick^ Design: No^ Interaction)
Source (^) DF SS l$S F (^). P Schedule L4 .4 0.^37 0.^ 54 6 Mixture'" 581-.8 5.92^ 0. Error (^) 1353. Total (^39) L949. S ,
. Schedule Mean (^1) 9. (^2) LO.
Mixture Mean r. (^) 13- 2 LO',. (^3) t2. (^4) 3,
{ d , I 1 1
j l
cl (^) c2 (^) c Index Scedule (^) Mixture (^1 17 1 ) (^2 6 1 ) (^3 10 1 ) (^4 12 1 ) (^5 14 1 ) (^6) -18 2 1 7 9 .2 (^1) 8 17 2 ,, (^9 21 2 ) (^10 15 2 ) (^11 24 1 ) (^12 15 1 ) (^13 10 1 ) (^14 16 1 ) (^15 14 1 ) 16 -2 (^2 ) (^17 0 2 ) (^18 17 2 ) (^19 2 2 ) (^20 6 2 ) (^21 14 1 ) (^22 9 1 ) (^23 12 1 ) (^24 0 1 ) (^25 6 1 ) (^26 20 2 ) (^27 16 2 ) (^28 12 2 ) (^29 17 2 ) (^30 18 2 ) (^31 10 1 ) 32 -1^1 (^33 0 1 ) (^34 3 1 ) 35 '-1^1 36 -2^2 37 7 2 4 (^38 10 2 ) 39 6 2 4 (^40 7 2 )
