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DATA PROCESSINGand STATISTICAL
TREATMENT
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TREATMENT
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Exampe!
• “How efective is the teaching o ProessorSnape in Mathematics to ElectricalEngineering students?
x x
20 x ! "0 #! x$ %0 x % ! &0
#!2'0$(00
0 x 2 ! "0 #! 2)' or%
(0 x ( ! (0 *muchefective+
,otal- (00 2'0
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DATA PROCESSING
• .onverting inormation eithermanuall/ or / machine into1uantitative and 1ualitative orms)
Categorization
Coding
Tabulation ofData
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DATA MATRI"
• Presentation o data usuall/ intaular orm)
• ives picture o the results o thestud/)
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#ni$ariate Matrix
• 3nvolves onl/ one variale)
Scale :
9- Like extremely 6- Like sligtly
!- Like "ery muc #- $eiter like nor dislike%- Like moderately &- Dislike sligty
%&ait'Attri(&tes
Mi)*s+ L&nc+eon Meat
Mean Descripti$eInterpretation
Color %'%# Like "ey muc
(dor !')# Like "ey muc
*la"or !'+, Like "ey muc
Texture !',, Like "ey muc
eneral .cce/tability !'0, Like "ey muc
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,i$ariate Matrix• 3nvolves two variales)
SC.L1 :
#- 2ery "ery serious /roblem +- Serious /roblem )- not a /roblem at all
&3 2ery serious /roblem 0- less serious /roblem
-O,.RELATEDPRO,LEM
S
STAFF N#RSESPRI/ATE 0OSPITALS GO/ERNMENT
0OSPITALS
Mean Interpretation Mean Interpretation
( 2)( Less serious /roblem 2) less serious /roblem
2 %)2 Serious /roblem %)% Serious /roblem
% %)0 Serious /roblem ) 2ery serious /roblem
%) Serious /roblem %)& 2ery serious /roblem4 )2 2ery serious /roblem 2)0 less serious /roblem
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M&ti$ariate Matrix• Has three or more variales in the
tale)
Scale:
9- Like extremely 6- Like sligtly!- Like "ery muc #- $eiter like nor dislike
%&ait'Attri(&tes
L&nc+eon Meat
Mil56sh7falMean
oat6sh7falMean
Siganid7falMean
Sardines7falMean
.olor 8)8 8)& 8)4 8)(
7dor ")0 ")0 8)% 8)2
9lavor ") ")2 8)& 8)'
,exture ")( ")0 8)" 8)8
eneral:cceptailit/ ")% ")0 8)8 8)4
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D#MM1 TA,LES
• ;sed in planning< summari=ing<
organi=ing and anal/=ing the data onhow the diferent variales difer witheach other)
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-o(Performance
0ospitas
Pri$ate Go$ernment Tota
Fre2&enc'
Percent Fre2&enc'
Percent Fre2&enc'
Percent
O&tstanding
/er'Satisfactor'
#nsatisfactor'
Tota (84 (00 (24 (00 %00 (00
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STATISTICAL TREATMENT
• ;sing :rithmetic mean in scaling)
> ver/ much efective
% > much efective 2 > efective
( > not efective at all
INCORRECT STATISTICAL
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INCORRECT STATISTICALTOOL
• Percentage in scale options * % 2 (+is incorrect or inappropriatestatistical tool to scale options)
8)4 @ ver/ much efective 4)0 @ much efective
28)4 @ efective
20)0 @ not efective at all
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;A3B:C3:,E
S,:,3S,3.:D
,CE:,MEA,M3;ED< A7C;ED :A )
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:rithmetic Mean
• ,he appropriate statistical tool or;nivariate prolems
Example-
*&
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Experimental Cesearch
• Example Prolem-
• “Fhat is the acceptailit/ o theGavor o 6sh urger rom ofal ooneless mil56sh? 7 the %0panellists who evaluated the productusing the &@point Hedonic Scale< 4
rated li5e extremel/ or &I 2% rated li5ever/ much or "I and 2 li5e moderatel/or 8)
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&@point Hedonic Scale
& @ li5e extremel/
" @ li5e ver/ much
8 @ li5e moderatel/
' @ li5e slightl/
4 @ neither li5e or disli5e
@ disli5e slightl/
4 votes
2% votes
2 votes
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9ormula o weighted arithmetic
mean-
Fhere- Feighted arithmetic mean
Sum o all the products o and xI where is there1uenc/ o each weight and x is the weight
Sum o all the re1uenc/$suJects
•
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iven-
4 & 2% "
2 8
*li5e ver/ much+
•
Solution-
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7r can e written asL)
x x
4 & 4
2% " ("
2 8 ( ,otal %0 2%
*li5e ver/ much+uantitative mean
ualitative description
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Nata Processing Mechanisms
3nput > 3s the evaluation o the %0panellists-
4 panellists rated &I 2%
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Nescriptive Cesearch
• Example Prolem-
• 7 the 200 staf nurses in private andgovernment hospitals in 3loilo .it/< 24staf nurses said ver/< ver/ serious or4I 40 said ver/ serious or I (00<serious or %I (4< less serious or 2I (0<
not at all or ()
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iven-
24 (4 4 2 40 (0 (
(00 %
*serious+
•
Solution-
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7r can e written asL)
x x
24 4 (24
40 200
(00 % %00
(4 2 %0
(0 ( (0
,otal 200 ''4
*serious+
uantitativmean
ualitative description
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Nata Processing Mechanisms
3nput > 3s the responses o staf nurses-
24 said 4I 40
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O3B:C3:,E
S,:,3S,3.:D ,CE:,MEA,
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Experimental Cesearch
• Statistical tools are-
t@test
linear correlation
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,he t@test
• ormula-•
Fhere- @ mean o the 6rst variale @ mean o the second variale @ variance o @ variance o@ total numer o operations @ total numer o operations o 6rst variale o second variale
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Steps in using t@test
Step () 9ind the arithmetic mean o each variale
Step 2) Solve the variance *+ o each variale *and+
Step %) .ompute the t@value using the t@test ormula
Step ) et the degrees o reedom *d+ / using
this ormula- d ! A@( I i A is the same or the twovariales
d ! Q @2 I i A is diferent or the two variales
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Example-
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Dinear .orrelation
•
Fhere-@ .orrelation etween # and R @ ,otal numer o cases@ Sum o variale # @ Sum o s1uared # variale@ Sum o variale R @ Sum o s1uared R variale @ Sum o the product # and R
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Steps in using Dinear .orrelation
Step () 9ind the sum o # and R
Step 2) S1uare all # and R values
Step %) Sum and
Step ) 9ind the product o # and RStep 4) et the sum o the product #R
Step ') :ppl/ the ormula o linear correlation
•
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Example-
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Nescriptive Cesearch
• Statistical tools areI
Dinear .orrelation
=@test
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Dinear .orrelation
•
Fhere- @ Spearman rho @ Sum o the s1uared diferences etween
ran5sA @ Aumer o cases
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,he Steps are as ollow-
Step () Can5 the values rom highest to lowest inthe 6rst se o variale *#+ and mar5 them
Step 2) Can5 the second set o values *R+ in thesame manner as in Step ( and mar5 them
Step %) Netermine the diference in ran5s or ever/pair o ran5s)
Step ) S1uare each diference to get
Step 4) Sum the s1uare diference to 6nd
Step ') .ompute the Spearman rho *+
•
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,he =@test
•
Fhere- Z > =@test@ Percentage o 6rst group o suJects or 6rst variale@ Percentage o second group o suJects or second variale
@ Pooled percentage o andQ ! ( @ P @ Aumer o cases or the 6rst variale @ Aumer o cases or the second variale
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M;,3B:C3:,ES,:,3S,3.:D ,CE:,MEA,
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Multivariate
Experimental Cesearch 9@test or :A7B: *anal/sis o variance+I
rus5al@Fallis 7ne@wa/ :nal/sis oBariance< andI
9riedmanTs ,wo@wa/ :nal/sis oBariance / Can5s)
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9@test as Statistical
,ool in MultivariateExperimental
Cesearch 3nvolves three or more
independent variales asasis o classi6cation)
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Ta(e 34564 Cesults on the Efect o 9ish Meal< ,rash 9ishOread Meal and 9ish Silage as Supplemental 9eedsupon the rowth o rouper .ultured in 9ish .ages or
,hree replications *9ictitious Nata+
S&ppementaFeeds
Repications 7)g8 Tot
a7) g8
5 9 :
Fis+ Mea 7T58
Tras+ Fis+ 7T98
,read Mea 7T:8
8
(0
(4
('
'
&
(2
(%
4
4
&
(%
("
2
%'
2
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Form&a for F.test!
Fhere-
9 !9@test
MSC ! Mean S1uare or
Ceplication
MS ,rt ! Mean S1uare or ,reatment
MSE !Mean S1uare or Error
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Step 54
Partition o sum os1uares or replication<treatment< error< total
/ using theappropriate ormula)
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S&m of S2&ares forRepication 78
SSC ! @ .9 I .9 !
Fhere- SSC ! Sum o S1uares or Ceplication
! Sum o the s1uared total o each
Ceplication ,rt ! Aumer o ,reatment
.9 ! .orrection 9actor
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S&m of S2&ares for Treatment Form&a 78
SS ,rt ! @ .9
Fhere-
SS ,rt ! Sum o S1uares or ,reatment
! Sum o the s1uared total o each ,reatment
C ! Aumer o Ceplication
.9 ! .orrection 9actor
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S&m of S2&ares for Tota 78 Form&a
SS , ! @ .9
Fhere- SS , ! Sum o S1uares or ,otal
! Sum o each value per
,reatment.9 ! .orrection 9actor
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S&m of S2&ares for Error Form&a78
! @ * Q +
Fhere- ! Sum o S1uares or Error
! Sum o S1uares or ,otal
! Sum o S1uares or Ceplication
! Sum o S1uares or ,reatment
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Step 94
Nivide the sum o s1uares
or replication< treatment<total and error with theircorresponding degrees oreedom< A>(< to get themean s1uares)
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9ormula-
MS !
Fhere-
MS ! Mean S1uare
SS ! Sum o S1uaresd ! Negrees o 9reedom
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MEAN S%#ARES FOR!
CEPD3.:,37A *M+M !
,CE:,MEA, *M+
M !
ECC7C *M+
M !
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Step :4
Nivide the mean s1uares orreplication *+ / the mean s1uaresor error *+ to get the 9@value orreplication *+I and divide the means1uares or treatment *+ / themean s1uares or error *+ to get the9@value or treatment *+)
! !
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Step ;4
Netermine i the computed 9@value issignifcant < i the computed 9@value ise1ual or greater than the taular 9@valueI and not signifcant, i the
computed 9@value is less than thetaular 9@value)
.B U ,B ! signi6cant where-
.B V ,B ! not signi6cant .B ! computed value
,B ! taular value
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9inding the taular 9<
d R and d Trt is the numeratorand d E is the denominator)
Example- d R ! 2I d Trt ! %I d E !'
ddenomin
ator
Aumerator2 %
' 4)()8'
(0)&2&)8"
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Step
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Freidman>s T?o.@a' ANO/A asStatistica Too for M&ti$ariate
Experimenta Researc+
is also a statistical toolused oth in experimentaland descriptive multivariate
research prolems)
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Form&a!
!
Fhere-
! 9reidmanTs two@wa/ :A7B:/ ran5s
! Sum o the ran5s
A ! Aumer o rows
! Aumer o columns
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Steps of t+e form&a is as
foo?s!
Step 54 Prepare a two@wa/ tale
consisting o rows and columns)Step 94 Enter the data in Step (
and ran5)
Step :4 Sum the ran5s in eachcolumn)
Step ;4 :ppl/ the ormula)
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SuJects
Methods o teaching
S: ;S: ,PS N:
# 9C # 9C # 9C # 9C
(2%4
'8"&(0
&0"""4&2"8
&4"084"%88
%
%)4%%
%%
%)4%
"4"%"0"8"2
&08280"084
((
()4(
()4
2(
()42(
&("8"4&%""
&'"(84"28&
2)4%)4
%)4%
"8"8"0&("2
&(84808&8'
22)4()42
()4
(2
()4(2
,otal %%)0 (%)4 %')4 (8)0
#r2 ! 2%)44 7Signi*cant8 d ! @( ! %
d )0(*%+
! (()%
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r&s)a.@ais One.@a' ANO/A asStatistica Too for M&ti$ariate
Experimenta Researc+another statistical tool used in multivariate
research prolems oth in experimental anddescriptive researches)
H ! @ %*A@(+Fhere-
H ! rus5al@FallisT anal/sis o variance /ran5s
A ! Aumer o cases in all samples comined
n ! Aumer o cases in each sample
! Sum o ran5s in each column
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Steps in getting t+e r&s)a.@ais> one.?a' ANO/A ('ran)s are as foo?s!
Step 54 Prepare a column tale)Step 94 Enter the data in Step (and ran5 the sample as a whole)
Step :4 :dd the ran5s in eachcolumn)
Step ;4 :ppl/ the ormula)
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H ! %)"4 Signi6cant d ! @(! d )0(*%+ ! (()%9ive Sows
Oirth Feight o Diters *5g+(
Ft) Can52
Ft) Can5%
Ft) Can5
Ft) Can54
Ft) Can5
%)% > %2%)0 > 2&
%)( > %0%)2 > %(%) > %%%)4 > %%)' > %4
()2 > ((() > (%
2)( > 202) > 2%2)' > 24()% > (22)2 > 2(
()" > (82)% > 22
%)& > %")( > 0
%)" > %8%)8 > %')0 > %&
()( > (02)" > 4
0)8 > '0)" > 80)4 > 0)& > "0) > %
0)2 > (0)% > 2()0 > &
2)& > 2"()8 > ('
2)" > 28()& > ("()4 > (()' > (42)0 > (&
2)8 > 2'2)4 > 2
9ive Sows
Oirth Feight o Diters *5g+(
Ft) Can52
Ft) Can5%
Ft) Can5
Ft) Can5
%)% > %2%)0 > 2&
%)( > %0%)2 > %(%) > %%%)4 > %%)' > %4
()2 > ((() > (%
2)( > 202) > 2%2)' > 24()% > (22)2 > 2(
()" > (82)% > 22
%)& > %")( > 0
%)" > %8%)8 > %')0 > %&
()( > (02)" > 4
0)8 > '0)" > 80)4 > 0)& > "0) > %
0)2 > (0)% > 2()0 > &
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C+i.s2&are 78 as a Statistica Too forM&ti$ariate Descripti$e Researc+
.hi@S1uare test are o man/ t/pes< orinstance< 2 x 2 tale< 2 x % tale< % x 2< % x%< and man/ others)
.hi@s1uare 2 x 2 tale *ourold tale+
@two discrete variales are involved)
@variales are usuall/ nominal)
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Form&a for C+i.S2&are
!
Fhere-
! .hi@S1uare
7 ! 7served re1uenc/
E ! Expected re1uenc/
Steps in so$ing
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Steps in so$ing
Step 54 7 ! CQ.
Step 94 E ! W*C+*.+X$AStep :4 7 > E
Step ;4 S1uare the Step %)
Step
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Anot+er form&a for 9 x 9 ta(e
!Fhere-
! .hi@s1uare
A ! Y o rows
D ! oserved re1uenc/ o cell D
P ! oserved re1uenc/ o cell P
M ! oserved re1uenc/ o cell M
. ! oserved re1uenc/ o cell .
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L P L P
M C M C
L P
M C
!
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RIEDMAN’
S TWO-WAY
ANOVA
BY RANKS AS STATISTICAL TOOL USED IN
MULTIVARIATE DESCRIPTIVE RESEARCH
BY: RONNIEL JAY MILLAN
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FRIEDMAN’S TWO-WAY ANOVA
-is used when the data from k related
samples consist of at least an ordinal
scale and have been drawn from the
same set of observation to different
population.
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FORMULA:
4ere:
5r 0 *riedman7s t8o-8ay .$(2. by ranks
$ $umber of ro8s
$umber of columns
Sum of ranks
STEPS FOR FRIEDMAN’S
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STEPS FOR FRIEDMAN’S
TWO-WAY ANOVA:
Step 1. Prepare a two-way table consisting
of rows and columns.
Step 2. Enter the data in Step 1 and rank.
Ranking is done horiontally and the lowestvalue ranks 1.
Step !. Sum the ranks in each column.
Step ". #pply formula.
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EXAMPLE
$hree different groups of sub%ects e&posed
to the same set of observations on the
ade'uacy of facilities and e'uipment infishery schools as perceived by key
officials( fishery teachers( and students.
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TABLE: *acilites and1ui/ment ey (fficials 5 *; *isery Teacers 5 *; Students 5 *;
)'*ising ground +')! 0 +'0, + +')) )
0'.uaculture
a//aratus
0'0% + 0'0, 0 0')# )
+'*is Ca/ture )'#& ) )'6+ + )'#% 0
&'*is nadeuate
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SOLUTION:
?0)0 @ 0%'#0 @ 0+'#0A 3 +B)0B+@)
?&&) @ %#6'0# @ ##0'0#A 3 +6B&
B)%&9'# 3 )&&
,',!!++ B)%&9'# 3 )&&
5r 0 )'%9 $ot Significant
df 3 ) df + - )
df 0 df ,')B0 9'0)EE
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KRUSKAL-
WALLI’S
ONE-WAY
ANOVA (H)BY RANKS AS STATISTICAL TOOL IN
MULTIVARIATE DESCRIPTIVE RESEARCH
(TIED OBSERVATIONS)
KRUSKAL WALLI’S
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KRUSKAL-WALLI’S
ONE-WAY ANOVA (H)
-is a rank-based nonparametric test that
can be used to determine if there are
statistically significant differences between
two or more groups of an independentvariable on a continuous or ordinal
dependent variable.
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FORMULA:
4ere:
T t+ 3 t Bt is te number of tied obser"ations in a tied
grou/ of obser"ations$ $umber of obser"ations in all sam/les as a
8ole
FT Sum of all grou/ of ties
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FORMULA WITH TIES
STEPS FOR KRUSKAL-
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STEPS FOR KRUSKAL-
WALLI’S ONE-WAY ANOVA (H)
Step 1. Prepare a column table.
Step 2. Enter the data in Step 1 and rank the sample as a
whole.
Step !. #dd the ranks in each column.
Step ". Solve for the tie in scores by using formula )$ * t! + t,.
Step . #pply formula for tie scores as divisor.
Step . #pply formula for /ruskal-0allis ), tied observations.
Step 3. 4ompute for degrees of freedom )df, by using formula(
df * k + 1( wherek
stands for columns.Step 5. Refer to chi-s'uare tabular value in the appendi& of
any statistic book if -value is significant or not.
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EXAMPLE:Teacing-orientedTeacers
.dministration-orientedTeacers
;esearc-oriented Teacers
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COMPUTATION OF TIE
SCORES:
)2., $ * t! + t
* 26! + 26
$ * 3756
)7.6, $ * t! +
t* 1!! + 1!
$ * 215"
)"6., $ * t! + t
* 16! + 16
$ * 776
COMPUTATION OF
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COMPUTATION OF
FORMULA:
6.533"
SUBSTITUTING OF
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SUBSTITUTING OF
FORMULA OF H-TEST
8ot Significant
df k 3 )
+ 3 )
0
df ,')B0 9'0)EE
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-TEST OR
TWO-WAY
ANOVA
AS STATISTICAL TOOL IN MULTIVARIATE
EXPERIMENTAL RESEARCH
F-TEST OR TWO-WAY
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F-TEST OR TWO-WAY
ANOVA
-is the statistical used for multivariate
e&perimental research. 9t involves three or
more idependent variables as bases of
classification.
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FORMULA:
4ere:
* *-test HS/ Hean suare for /anelists
HSs Hean suare for sam/les
HS1 Hean suare for error
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STEPS FOR F-TEST
Step 1. Solve for the sum of s'uares for panelists( samples(
error( and total by using the appropriate formula below.
Sum of s'uares for Samples :ormula )SSS,
SSS *
0here;
SSs * Sum of s'uares for sample
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Sum of Suares for
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Sum of suares for total *ormula BSST
SST FFIi0 3 C*
4ere:
SST Sum for suares for total
FFIi0 Sum of eac "alue /er sam/le
C* Correction factor
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Sum of s'uares for Error :ormula )SSE,
SSE * SS$ + )SSP > SSS,
0here;
SSE * Sum of s'uares for error
SS$ * Sum of s'uares for total
SSP * Sum of s'uares for panelists
SSS * Sum of s'uares for samples
Step 2 ?ivide the sum of panelists samples error and total
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Step 2. ?ivide the sum of panelists( samples( error( and total
with their corresponding degrees of freedom( 8 + 1( to get
the mean s'uare by using the formula; @S*SSAdf.
Step !. ?ivide the mean s'uare for panelists by the mean
s'uare error to get the :-value of panelistsB and divide the
mean s'uare for samples by the mean s'uare error to get the
:-value for samples as shown in :ormula.
Step ". Refer to the :-distribution table in the appendi& of
any statistics book to determine if the :-value obtained is
significant or not.
Step . Prepare the #8CD# table by entering the values in
Steps 1( 2( and
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EXAMPLE:
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SOLUTION:
Com/utation of Sum of suares for Sam/les *ormula BSSS
SSS
SSS
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Com/utation of Sum of Suares for
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4omputation of Sum of S'uares for $otal )SS$,
SS$ *
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Com/utation of Sum of suares for 1rror *ormula BSS1
SS1 SST 3 BSS
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Source of
Dariance
?egrees of
freedom
Sum of
S'uares
@ean S'uare Cbserved
:
$abular :
1F
Samples 0 ,'& ,'0 )', !'6#EE
Panelists & +'6 ,'9 &'# %',)EE
Error ! )'6 ,'0
$otal )& #'!
THANK YOU
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THANK YOU
AND GOD
BLESS