THESIS consolidated report.pptx

8/20/2019 THESIS consolidated report.pptx

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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


6/102

DATA MATRI"

• Presentation o data usuall/ intaular orm)

• ives picture o the results o thestud/)


7/102

#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


8/102

,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


9/102

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%


22/102

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)


53/102

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)


68/102

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.


74/102

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


78/102

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


79/102

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.


81/102

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


82/102

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.


84/102

EXAMPLE:Teacing-orientedTeacers

.dministration-orientedTeacers

;esearc-oriented Teacers


85/102

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


87/102

SUBSTITUTING OF

FORMULA OF H-TEST

8ot Significant

df k 3 )

+ 3 )

0

df ,')B0 9'0)EE


88/102

-TEST OR

TWO-WAY

ANOVA

AS STATISTICAL TOOL IN MULTIVARIATE

EXPERIMENTAL RESEARCH

F-TEST OR TWO-WAY


89/102

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.


90/102

FORMULA:

4ere:

* *-test HS/ Hean suare for /anelists

HSs Hean suare for sam/les

HS1 Hean suare for error


91/102

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


94/102

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


96/102

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$ *


100/102

Com/utation of Sum of suares for 1rror *ormula BSS1

SS1 SST 3 BSS


101/102

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


102/102

THANK YOU

AND GOD

BLESS

Documents

THESIS consolidated report.pptx