Applied Research Methods New
-
Upload
muhammad-ali -
Category
Documents
-
view
221 -
download
0
Transcript of Applied Research Methods New
-
7/24/2019 Applied Research Methods New
1/175
Applied Research MethodsCourse code: MGT-808
by
Prof. Dr. Zahid Hussain
Depart ent of Mana!e ent"ciences.Preston #ni$ersit%& 'sla a(ad.
-
7/24/2019 Applied Research Methods New
2/175
Research Concepts)Meanin! ofResearch
Meanin!: Research is an art of scienti*cin$esti!ation +hich refers to a search of,no+led!e. Research is also s%ste ati ed e ortto !ain ne+ ,no+led!e. Research is an acade ic
acti$it% and is actuall% a /ourne% of disco$er%. "o& Research is an ori!inal contri(ution to thee istin! stoc, of ,no+led!e 1in $arious*elds)spheres of acti$ities2 for its ad$ance ent.
The ter Research also refers to the s%ste atic
ethod 1s2 consistin! of identif%in! the pro(le &for ulatin! h%pothesis& collectin! the facts ordata& anal%sin! the data 3 reachin! to certainconclusion1s2.
-
7/24/2019 Applied Research Methods New
3/175
Signifcance o research: 4ollo+in! are thesi!ni*cance of conductin! a research:
1i2 Research pro$ides the (asis for nearl% all!o$t. policies in our econo ic)5usiness)trades%ste . Throu!h research& one can ad$isealternati$e policies and can as +ell e a ine theconse6uencies of each of these alternati$es.
Research has its special si!ni*cance in sol$in!$arious operational 3 plannin! pro(le s of(usiness 3 industr%. 7perational research refersto the application of athe atical& lo!ical 3
anal%tical techni6ues to the solution of (usinesspro(le s of cost ini i ation or of pro*ta i i ation or +hat can (e ter ed as
opti i ation pro(le s.
-
7/24/2019 Applied Research Methods New
4/175
Research is e6uall% i portant for socialscientists in stud%in! social relationship and insee,in! ans+ers to $arious special pro(le s. 'naddition to these& the si!ni*cance of researchcan also (e understood ,eepin! in $ie+ thefollo+in! points
To those students +ho are to +rite a Master sor Ph.D thesis& research a% ean a careerisor a +a% to attain hi!h position in the socialstructure
To professionals& research a% ean a source
of li$elihood. To anal%st and intellectuals& research a%ean the !enerali ation of ne+ theories.
-
7/24/2019 Applied Research Methods New
5/175
Thus, research is the foundation ofknowledge for the sake of knowledge andimportant source of providing guidelines forsolving di erent business, governmental andsocial problems. It is a sort of formal trainingwhich enables to understand the newdevelopment in ones eld in a better way.
M7T'9AT'7 ' R;";ARCH: 't is often as,ed that +h% the people conduct
Research< This 6uestion is of funda entali portance and so e of the possi(le oti$esof research a% (e one or ore of the
follo+in!: 1i2 Desire to !et a research de!ree)certi*cate
alon! +ith its conse6uential (ene*ts.
-
7/24/2019 Applied Research Methods New
6/175
Desire to !et intellectual /o%. Desire to (e of ser$ice to societ%. Desire to !et respecta(ilit%. Ho+e$er& this is not a co plete list of
factors oti$atin! people to underta,eresearch studies.
Major Types o Research 1i2 Applied $s 4unda ental research.1ii2=uantitati$e $s =ualitati$e research.
1iii2 5usiness $s "ocial research. These are de*ned as (elo+:
1i2 Research can either (e applied 1oraction2 research or funda ental 1(asicor pure2 research.
-
7/24/2019 Applied Research Methods New
7/175
Applied research ai s at sol$in! an i ediate1current2 pro(le facin! a societ% or a(usiness) industrial or!anisation. >hereas
funda ental research is concerned +ith!enerali ation and for ulation of a theor%.
'n si ple +ords& !atherin! ,no+led!e for,no+led!e s sa,e is called ?pure or ?(asic
research@ +hile research concernin! so e(asic pheno enon or relatin! to pureMathe atics are e a ples of funda entalresearch.
"i ilarl%& research studies concernin! hu an(eha$ior carried out +ith a $ie+ to a,e!enerali ations a(out hu an (eha$ior are also
-
7/24/2019 Applied Research Methods New
8/175
e a ples of funda ental research& (utresearch ai ed at certain conclusions
1sa%& a solution2 facin! a concrete socialor (usiness pro(le is an e a ple ofapplied research.
5oth (asic 3 applied research ha$e to (ecarried out in a scienti*c anner so thatthe *ndin!s or results !enerated (% thecan (e relied upon to e ecti$el% sol$e thepro(le in$esti!ated. 't is& ho+e$er&possi(le that so e applied research a%ha$e so e shorter ti e fra e than so e(asic research.
-
7/24/2019 Applied Research Methods New
9/175
1ii2 =uantitati$e $s =ualitati$e Research:=uantitati$e research is (ased on
easure ent of 6uantit% or a ount. 't is
applied to pheno ena that can (ee pressed in ter s of 6uantit%. =uantitati$eresearch atte pts precise easure ent ofso ethin!.
'n (usiness research& 6uantitati$eethodolo!ies usuall% easure consu er(eha$ior& ,no+led!e& opinions& or attitudes."uch ethodolo!ies ans+er 6uestions
related to ho+ uch& ho+ an%& ho+ often&+hen and +ho. ote sur$e% is considered ado inant ethodolo!% of 6uantitati$eresearch.
-
7/24/2019 Applied Research Methods New
10/175
7n the other hand& =ualitati$e research isconcerned +ith 6ualitati$e pheno enon&i.e. a pheno enon relatin! or in$ol$in!
6ualit% or ,ind. =ualitati$e researchincludes& perception of people to+ards li,e3 disli,e of an% (rand& +ord associationtests and si ilar other pro/ecti$e
techni6ues. 1iii2 5usiness and "ocial Research:
5usiness research can (e descri(ed as as%ste atic and or!anised e ort to
in$esti!ate a speci*c pro(leencountered in the +or, settin!& +hichneeds a solution. 't co prises a series ofsteps that are desi!ned 3 e ecuted +ith
the !oal of *ndin!
-
7/24/2019 Applied Research Methods New
11/175
Ans+ers to the issues that are of concernto the Mana!er in the +or, en$iron ent."peci*call%& (usiness research can (ede*ned as an or!anised& s%ste atic& data-(ased& o(/ecti$e scienti*c in6uir%& orin$esti!ation into a speci*c pro(le &underta,en +ith the purpose of *ndin!ans+ers or solutions to it.
'n essence& research pro$ides thenecessar% infor ation that !uideMana!ers to a,e infor ed decisions tosuccessfull% deal +ith pro(le s. Theinfor ation pro$ided could (e the result ofa careful anal%sis of data !athered *rst-hand or of data that are alread% a$aila(le1in't a% (e noted that data can (e6uantitati$e or 6ualitati$e
-
7/24/2019 Applied Research Methods New
12/175
1in the co pan%& industr%& archi$es& etc.2. 'ta% (e noted that data can (e 6uantitati$e
or 6ualitati$e.
Generally business research can beundertaken or two purposes:
. To sol$e a current pro(le faced (% theMana!er in the +or, settin! that is called
applied research. B. To !enerate a (od% of ,no+led!e a(out
ho+ to sol$e pro(le s that could (e occurredin or!anisations. This is called (asic research
or funda ental research. 't is also ,no+n aspure research. ; a ple of h%pothesis: ; perience is
positi$el% related to /o( perfor ance.
-
7/24/2019 Applied Research Methods New
13/175
02/16/16 13
Definition of Various Concepts used in Research
Variable
QualitativeVariable
Quantitative Variable
DiscreteVariable
ContinuousVariable
-
7/24/2019 Applied Research Methods New
14/175
Variable:
Any characteristic of interest which takes on different values is called variable. Forexample: production, cost, temperature, sale of a market, consumption, price of a
commodity at different locations etc.Variable is broadly divided into qualitative
and quantitative variables.
Qualitative and Quantitative Variables
A variable is defined to be qualitative which is not capable of numerical measurement
but one can feel the presence or absence of a particular phenomena. For
example, honesty, beauty, race, like and dislike, pass or fail, gender
classification etc.
A variable is defined to be quantitative which is capable of numerical measurement.
For example, cost of production, price of a commodity, monthly consumption of
households etc.
02/16/16 14
Definition of Various Concepts used in Research
-
7/24/2019 Applied Research Methods New
15/175
Discrete and Continuous Variables
A variable is said to be discrete if it takes isolated integral values or a
variable which take the values on umps is called a discrete
variable. For example, number of rooms in a house, number of
students in the class, number of !anks in different cities, si"e of a
household, number of shops in a market etc.
A type of variable which takes all possible values with in a giveninterval#range $a, b%. For example, consumption, production,
temperature, monthly sale of a market, height, weight and age etc.
02/16/16 15
Definition of Various Concepts used in Research
-
7/24/2019 Applied Research Methods New
16/175
Classif% the $aria(les as discrete orcontinuous 1i2 The a ount of il, produced (% a co+.
1ii2The nu (er of heads in the toss of coins. 1iii2The life ti es of tele$ision tu(es produced (%
"on%. 1i$2The nu (er of petals on a o+er.
1$2Hourl% te perature of 'sla a(ad recorded (% Met.7Ece. 1$i2Total e!!s laid (% a hen in a onth. 1$ii2 A ount of C G)petrol *lled in cars at a pu p. 1$iii2 The %earl% inco e of a uni$ersit% professor. 1i 2Ti e ta,en to score the *rst !oal in a foot(all
atch 1 2 o. of !oals scored in each of F0 foot(all atches.
-
7/24/2019 Applied Research Methods New
17/175
&. 'ependent Variable
(. )ndependent Variable
*. +oderating Variable
. +ediating or )ntervening Variable
02/16/16 17
Other Variables in Research
-
7/24/2019 Applied Research Methods New
18/175
Dependent and Independent Variables
A type of variable which is influenced by other variable#variables is called
dependent variable. )t is also called random or stochastic variable. -
A variable which depends on one or more other variables is called dependent
variable. -
A variable of primary interest that lends itself for investigation as a function of
other cause variables is known as dependent variable.
02/16/16 18
Other Variables in Research
-
7/24/2019 Applied Research Methods New
19/175
For example, in economics, consumption of a commodity $say apple%
depends upon the income, household si"e, and price etc of the
commodity.
)n this example, consumption of apple is a dependent variable whichwill vary from one family to other family/ while the other variables
like income, household si"e and price are independent variables.
A variable which influence a dependent variable in either direction
$positive or negative% is called independent variable.
02/16/16 19
Other Variables in Research
-
7/24/2019 Applied Research Methods New
20/175
Moderating Variable:
A variable which modify the original relationship is called moderating variable.-r
A variable that has a strong contingent or contributory effect on the relationship
between dependent and independent variables, is called moderating
variable.For example, Amount of study in terms of study hours affect the grades, however,
those student consulting quality information for the purpose may even
perform much better as compared to others students. )n this example, it is
evident that quality information is a moderating variable which is notconsidered in the research study but have contributory effect on the final
grades, so called moderating variable.
02/16/16 20
Other Variables in Research
-
7/24/2019 Applied Research Methods New
21/175
Moderating Variable:A variable which modify the original relationship is called moderating variable.
-r
A variable that has a strong contingent or contributory effect on the relationship
between dependent and independent variables, is called moderatingvariable.
For example, Amount of study in terms of study hours affect the grades,
however, those student consulting quality information for the purpose may
even perform much better as compared to others students. )n this example,it is evident that quality information is a moderating variable which is not
considered in the research study but have contributory effect on the final
grades, so called moderating variable.
02/16/16 Dr. Yousaf Hayat 21
Other Variables in Business Research
Amount of Study hours
(Independent var !
"inal #rade$est score
(Dependent var !
Quality Information
(%oderatin# var !
-
7/24/2019 Applied Research Methods New
22/175
Intervening Variable:A variable that surfaces between the time the independent variable starts
operating to influence the dependent variable and its impact is felt on it, is
called intervening variable.
02/16/16 22
Amount of Study hours
(Independent var !
"inal #rade&$est score
(Dependent var !
Input 'no led#e In %emory
(Intervenin# var !
Other Variables in Research
-
7/24/2019 Applied Research Methods New
23/175
Research Process Research process consists of series of actions
or steps necessar% to e ecti$el% carr% outresearch and the desired se6uencin! of thesesteps. 't a% (e noted that the nu (er of stepsdescri(ed (% di erent authors)researchers$aries (et+een to 0. Ho+e$er& researchprocess in$ol$es a se6uence of hi!hl% inter-related acti$ities& therefore& research oftenfollo+s a !eneral pattern. The follo+in!steps)sta!es +ell descri(e a research process.
. De*ne research pro(le )Research o(/ecti$es. B.Re$ie+ the literature or iterature sur$e%.
-
7/24/2019 Applied Research Methods New
24/175
. 4or ulate h%potheses. I. Research Desi!n 1includin! sa ple desi!n2. F. Collectin! the data 1e ecution2. . Anal%sin! the data 1Test h%potheses if an%2. J. 'nterpret and report.
1. Research roble!: 'n research process& the *rst 3 fore ost step
happens to (e that of selectin! 3 properl%de*nin! a research pro(le . i,e a edical
doctor& a researcher ust e a ine all thes% pto s 1presented to hi or o(ser$ed (%hi 2 concernin! a pro(le (efore he candia!nose correctl%.
-
7/24/2019 Applied Research Methods New
25/175
't is pertinent to ention that scienti*c research!enerall% starts +ith a (road area pro(le area+ith a de*nite ai or purpose. 'n (usiness& theresearch process in$ol$es translatin! the(usiness decision situation into speci*cresearch o(/ecti$es.
The (road pro(le area is identi*ed throu!h theprocess of o(ser$in! 3 focusin! on the speci*c
situation. A pro(le does not necessaril% i pl%that so ethin! is seriousl% +ron! +ith a currentsituation that needs to (e recti*ed. "o ee a ples of (road area pro(le are: 4re6uentproduction interruptions& lac, of interest ofe plo%ees in their +or,& trainin! pro!ra areperhaps not as e ecti$e as anticipated or thesales $olu e of a product is droppin! and so on.
-
7/24/2019 Applied Research Methods New
26/175
To *nd solutions for identi*ed pro(le s& a pro(lestate ent that states the !eneral o(/ecti$e of theresearch should (e de$eloped. 't eans once +e
ha$e identi*ed the (road area pro(le area& itneeds to (e narro+ed do+n to a speci*c pro(lestate ent after so e preli inar% infor ation is!athered (% researcher.
4or e a ple& if it is o(ser$ed that a co pan% islosin! custo ers& the preli inar% infor ation!atherin! in$ol$es the see,in! of infor ation indepth& of +hat is o(ser$ed. This could (e done (% aliterature re$ie+ 1literature on custo er s+itchin!2
or (% tal,in! to se$eral people in the +or, settin!&to clients 1+h% do the% s+itch2& or to other rele$antsources& there(% !atherin! infor ation on +hat ishappenin! and +h%.
-
7/24/2019 Applied Research Methods New
27/175
Thus +e !et an idea of the situation andconse6uentl% this allo+s us to de$elop a speci*cpro(le state ent.
The research pro(le underta,en for stud% ust(e carefull% selected. Help a% (e ta,en fro aresearch !uide in this connection. e$ertheless&e$er% researcher ust *nd his o+n sal$ation forresearch pro(le cannot (e (orro+ed. A researchpro(le ust sprin! fro the researcher s indli,e a plant sprin!in! fro its o+n seed. 'f our e%esneed !lasses& it is not the optician alone +hodecides a(out the nu (er of lens +e re6uire. >e
ha$e to see oursel$es 3 ena(le hi to prescri(efor us the ri!ht nu (er (% cooperatin! +ith hi . Thus& a research !uide can at the ost onl% help aresearcher choose a su(/ect.
-
7/24/2019 Applied Research Methods New
28/175
't is desira(le to a,e a !ood pro(le state ent(ecause pro(le state ent introduces the ,e%pro(le that is addressed in the researchpro/ect. A pro(le state ent is clear& precise 3to the point state ent of the speci*c issue that aresearcher +ishes to in$esti!ate. There are three,e% criteria to assess the 6ualit% of the pro(lestate ent: it should (e rele$ant& feasi(le 3interestin!. A fe+ e a ples of +ell-de*nedpro(le state ent are:
Has the social edia ad$ertisin! essa!eresulted in enhanced recallhat are the e ects of do+nsi in! on the lon!-ran!e !ro+th patterns of co paniesednesda%& there
a% (e no one a(sent. Ran!e fro ?0 to ?all(ein! .. 1iii2 Moti$ation: The le$els of oti$ation of e (ers
in the class or in a +or, tea i!ht ta,e on $ar%in!$alues ran!in! fro L$er% lo+ to L$er% hi!h . Thus
oti$ation is a $aria(le. ; ercises: A researcher +ants to increase the
perfor ance of (an, e plo%ees in a particular
-
7/24/2019 Applied Research Methods New
36/175
5ranch. >hat is the dep. 9ar. in this caseor,in! h%pothesis is atentati$e assu ption ade in order to dra+out 3 test its lo!ical or e piricalconse6uences. As such the anner in +hichresearch h%potheses are de$eloped isparticularl% i portant since the% pro$ide thefocal point for research. The de$elop ent of+or,in! h%pothesis pla%s an i portant role.
H%pothesis should (e $er% speci*c 3 li ited topiece of research in hand (ecause it has to (etested.
-
7/24/2019 Applied Research Methods New
43/175
Directional and nondirectionalh%potheses
>hile descri(in! the relationship (et+een t+o $ari-
a(les or co parin! t+o !roups& ter s such aspositi$e& ne!ati$e& ore than& less than& 3 the li,eare used& then these are directional h%potheses ()cthe direction of the relationship ()+ the $aria(les1O positi$e)-ne!ati$e2 is indicated. 4or e a ple& seethe follo+in! state ent:
LThe !reater the stress e perienced in the /o(&the lo+er the /o( satisfaction of e plo%ees .
"i iarl%& the nature of the di erence ()+ t+o !roups
on a $aria(le 1 ore than)less than2 is postulated as:L>o en are ore oti$ated than en .
-
7/24/2019 Applied Research Methods New
44/175
7n the other hand& nondirectional h%potheses arethose that do postulate a relationship ordi erence& (ut o er no indication of direction ofthese relation- ship s or di erences. 'n other+ords& thou!h it a% (e speculated that there is asi!ni*cant relationship ()+ t+o $aria(les& +e a%not (e a(le to sa% +hether the relationship is
positi$e or ne!ati$e. 4or e a ple& see thefollo+in! state ent)h%pothesis: LThere is arelationship ()+ /o( and satisfaction
i,e+ise& e$en if +e can assu e that there +ill (e
di erences ()+ t+o !roups on a particular$aria(le& +e a% not (e a(le to sa% +hich !roup+ill (e ore 3 +hich less on that $aria(le. 4ore a ple& see the
-
7/24/2019 Applied Research Methods New
45/175
follo+in! h%pothesis:LThere is a di erence ()+ the +or, ethic
$alues of ;uropean and Asian e plo%ees . ondirectional h%potheses are for ulated either
()c the relationships or di erences ha$e ne$er(een e plored 3 hence there is no (asis forindicatin! the direction& or ()c there ha$e (een
con ictin! *ndin!s in pre$ious research studies onthe $aria(le. 'n so e studies a positi$erelationship i!ht ha$e (een found& +hile inothers a ne!ati$e relationship i!ht ha$e (eentraced. Hence& the current researcher i!htonl% (e a(le to h%pothesi e that there is a si!-ni*cant relationship & (ut the direction a% not (eclear. 'n such cases& the h%potheses can (e stated
-
7/24/2019 Applied Research Methods New
46/175
ondirectionall%. >hene$er the direction of the relationship is ,no+n&
it is (etter to de$elop directional h%potheses. &hat 's ( )ypothesis* 7rdinaril%& +hen one tal,s
a(out h%pothesis& one si pl% eans a ereassu ption or so e supposition to (e pro$ed ordispro$ed. 5ut for a researcher h%pothesis is afor al 6uestion that he intends to resol$e. Ah%pothesis can (e de*ned as a tentati$e& %ettesta(le& state ent& +hich predicts +hat %oue pect to *nd in %our e pirical data. H%potheses
are deri$ed fro theor% on +hich %our conceptualodel is (ased 3 are often relational in nature."e$eral testa(le state ents or h%potheses can (edra+n fro theoretic. fra e+or,.
-
7/24/2019 Applied Research Methods New
47/175
)ypothesis+ ,ull and (lternate)ypotheses : 'tis pertinent to note that a h%pothesis can (ede*ned as a testa(le state ent of therelationship a on! $aria(les. A h%pothesis canalso test +hether there are di erences ()+ t+o!roups 1or a on! se$eral !roups2 +ith respect to
an% $aria(le or $aria(les. To e a ine +hether or notthe assu ed relationship s or di erences e ist&these h%potheses can (e set as propositions asunder:
; plo%ees +ho are ore health% +ill ta,e sic, lea$eless fre6uentl%.
'f e plo%ees are ore health%& then the% +ill ta,esic, lea$e less fre6uentl%.
-
7/24/2019 Applied Research Methods New
48/175
"tudents +ho recei$e counsellin! +ill sho+ a!reater increase in creati$it% than students notrecei$in! counsellin!.
The auto o(ile A is perfor in! as +ell asauto o(ile 5.
ull and Alternate H%potheses: 'f +e are toco pare ethod A +ith 5 a(out its superiorit% 3
if +e proceed on the assu ption that (othethods are e6uall% !ood& then this assu ption
is ter ed as the null h%pothesis. As a!ainst this&+e a% thin, that the ethod A is superior or the
ethod 5 is inferior& it is ter ed as alternate oralternati$e h%pothesis. A null h%pothesis 1H 02 is ah%pothesis set up to (e re/ected in order tosupport an alternate h%pothesis&
-
7/24/2019 Applied Research Methods New
49/175
la(eled H A. >hen used& the null h%pothesis ispresu ed true until statistical e$idence& inthe for of a h%pothesis test& indicatesother+ise. A null h%pothesis shouldal+a%s (e precise such as La dru! isine ecti$e in curin! a particular
disease or Lthe di erence ()+ the t+o teachin!
ethods is null or ero
Lad$ertisin! does not a ect sales L en 3 +o en (u% e6ual a ounts of
shoes
-
7/24/2019 Applied Research Methods New
50/175
Moderator 3 ediator $aria(les 'n !eneral ter s& a oderator is a 6ualitati$e 1e.!.
se & race& class2 or 6uantitati$e 1e.!.& le$el of re+ard2$aria(le that a ects the direction and)or stren!th ofrelation ()+ an independent 3 a dependent $aria(le.
Mediator $aria(le: 'n !eneral& a !i$en $aria(le a%(e said to function as a ediator to the e tent that itaccounts for the relation ()+ the predictor 3 depen-dent $aria(le. >hereas oderator $aria(les specif%+hen certain e ects +ill hold& ediators spea, toho+ or +h% such e ects occur.
Another +a% to thin, a(out this issue is that a ode-rator $aria(le is one that in uences the stren!th of a
-
7/24/2019 Applied Research Methods New
51/175
relationship ()+ t+o other $aria(les& and aediator $aria(le is one that e plains the
relationship ()+ the t+o other $aria(les.
-
7/24/2019 Applied Research Methods New
52/175
02/16/16 52
RESEARC DESI!"
-
7/24/2019 Applied Research Methods New
53/175
After the researcher has for ulated theresearch pro(le & he or she ust de$elop
the research desi!n as part of the researchdesi!n sta!e. A research desi!n is aaster plan that speci*es the ethods 3
procedures for collectin! 3 anal%sin! the
needed infor ation.
-
7/24/2019 Applied Research Methods New
54/175
02/16/16 54
'ecisions regarding what, where, when, how much, by what means concerning
an inquiry or a research study constitutes a research design. #R
esearch design is the arrangement of conditions for collection and analysis of
data in a manner that aims to combine relevance to the research purpose
with economy in procedure. )n fact, the research design is the conceptual
structure within which research is conducted. )t constitutes the blueprint
for the collection, measurement and analysis of data. +ore explicitly, the
design decisions happen to be in respect of:
%eanin# of Research Desi#n
% i # f R h D i#
-
7/24/2019 Applied Research Methods New
55/175
02/16/16 55
$i%. what is the study about0
$ii%. why is the study being made0
$iii%. where will the study be carried out0
$iv%. what type of data is required0
$v%. where can the required data be found0
$vi%. what periods of time will the study include0
$vii%. what will be the sample design0
$viii%. what techniques of data collection will be used0
$ix%. how will the data be analy"ed0
$x%. in what style will the report be prepared0
%eanin# of Research Desi#n
% i # f R h D i#
-
7/24/2019 Applied Research Methods New
56/175
02/16/16 56
1eeping in view the above $i% to $x%, one may split the overall research design into the
following parts:
$a%&2he sampling design which deals with the method of selecting items to be observed
for the given study/
$b%&2he observational design which relates to the conditions under which the
observations are to be made/
$c%.2he statistical design which concerns with the question of how many items are to be
observed and how the information and data gathered are to be analy"ed/ and
$d%&2he operational design which deals with the techniques by which the procedures
specified in the sampling, statistical and observational designs can be carried out.
%eanin# of Research Desi#n
I t t " t f R h D i#
-
7/24/2019 Applied Research Methods New
57/175
02/16/16 57
I'portant features of a research design are:
&. )t is a plan that specifies the sources and types of informationrelevant to the research problem.
(. )t is a strategy specifying which approach will be used for gathering
and analy"ing the data.
*. )t also includes the time and cost budgets since most studies are done
under these two constraints.
In su' up , a research design must at least contain a clear statement of the
research problem, procedures and techniques used for gatheringinformation#data, the population to be studied, and the methods to be
used in processing and analy"ing the data.
Important "eatures of Research Desi#n
-
7/24/2019 Applied Research Methods New
58/175
02/16/16 58
!efore going to conduct a research, a research design is needed because it
facilitates the smooth sailing of the various research operations,
thereby making research as efficient as possible yielding maximal
information with minimal expenditure of effort, time and money.
For example, to construct an economical and attractive construction of ahouse, one should consult an architect or an expert for making a map
so that all the necessary things for its construction are highlighted.
3imilarly, we need a research design or a plan in advance of data collectionand analysis methods for research pro ect keeping in view the
ob ectives, time and labours required.
)eed for Research Desi#n
f
-
7/24/2019 Applied Research Methods New
59/175
02/16/16 59
2herefore, 4 esearch design stands for advance planning of the
methods to be adopted for collecting the relevant data and the
techniques to be used in their analysis, keeping in view the
ob ective of the research and the availability of staff, time and
money5. 2he research design helps the researcher to organi"e his
ideas in a form whereby it will be possible for him#her to look for
flaws and inadequacies. 6ithout proper and accurate research
design, it will be difficult to provide a comprehensive review ofthe proposed study $research%.
)eed for Research Desi#n
"eatures of a *ood Desi#n
-
7/24/2019 Applied Research Methods New
60/175
02/16/16 60
Following are the features of a good research design:
&. Flexible (. Appropriate *. 7fficient . 7conomical and so on
8enerally, the design which minimi"es bias and maximi"es the reliability of the
collected data and analy"ed is considered a good design. 2he design which
gives the smallest experimental error is supposed to be the best design inmany investigations.
3imilarly, a design which yields maximal information and provides an opportunity
for considering many different aspects of a problem is considered most
appropriate and efficient design in respect of many research problems.
eatures of a *ood Desi#n
" f * d D i#
-
7/24/2019 Applied Research Methods New
61/175
02/16/16 61
An appropriate research design for a particular research problem
usually involves the consideration of the following factors:
the means of obtaining information
the availability and skills of the researcher and his staff, if any
the ob ectives of the problem to be studied
the nature of the problem to be studied
the availability of time and money for conducting a research
"eatures of a *ood Desi#n
D l i # R h l
-
7/24/2019 Applied Research Methods New
62/175
02/16/16 62
Arrange'ent of ideas in the for' of an e(peri'ental plan is called a research plan& Research plan
contains the following prere)uisites:
esearch ob ectives should be clearly stated in line.
3tated the problem explicitly so that one may know what information is to be obtained for
solving the problem.
7ach ma or concept which a researcher wants to measure should be defined in operational terms
in context of the research problem.
2he plan should contain the methods to be used in solving the problem.
2he plan must contain the details of the techniques to be adopted. For example, if interview
method is used for data collection it should be written as such. 9rocedure for quantifying the data
must also be given.
niverse of the population, sampling plan, selection of appropriate sample si"e etc should be
selected in such a way that all these are feasible.
9rocessing of data should also be a part of the sampling plan.
esults of the pilot test, if any, should be reported. 2ime and cost budgets for the research pro ect
should also be prepared and laid down in the plan.
Developin# a Research +lan
Important Concepts Relatin# $o Research Desi#n
-
7/24/2019 Applied Research Methods New
63/175
02/16/16 63
!efore starting the research design, it would be appropriate to explain various concepts
for easy understanding relating to design. )t includes the following: 'ependent and independent variables:
7xtraneous variable:
esearch hypothesis:
7xperimental and non;experimental testing of hypothesis: 7xperimental and
-
7/24/2019 Applied Research Methods New
64/175
Research H%pothesis >hen a prediction or h%pothesised relationship is
to (e tested (% scienti*c ethods& it is ter ed asresea-rch h%pothesis. The research h%pothesis is apredicti$e state ent that relates a dependent$aria(le to a dependent $aria(le. #suall% a
research h%pothesis ust contain& at least& oneindependent 3 one dependent $aria(le. Predicti$estate ent +hich are not to (e o(/ecti$el% $eri*edor the relationships that are assu ed (ut not to(e tested& are not ter ed research h%pothesis.
- peri!ental / control group: 'n ane peri ental h%pothesis-testin! research +hen a!roup is e posed
-
7/24/2019 Applied Research Methods New
65/175
To usual conditions& it is ter ed a ?control!roup & (ut +hen a !roup is e posed to so e
no$el or special condition& it is ter ed an?e peri ental !roup . 4or e a ple& suppose aresearcher rando l% selects F0 students fro a!roup of students +ho are to ta,e a course instatistics 3 then di$ides the into B !roups (%rando l% assi!nin! BF to !roup A& the usualstudies pro!ra & 3 BF to !roup 5& the specialstudies pro!ra . Here& the !roup A can (ecalled a control !roup 3 the !roup 5 ane peri ental !roup. 'f (oth !roups A 3 5 aree posed to special studies pro!ra & then (oth!roups +ould (e ter ed ?e peri ental !roups .
R h h d 3 h
-
7/24/2019 Applied Research Methods New
66/175
Research ethods 3 researchethodolo!%
't is i portant to e plain the di erence ()+ research
ethods 3 research ethodolo!%.Research ethoda% (e understood as all those ethods)techni6ues
that are used for conduction of research. Researchethods or techni6ues& thus& refer to the ethods
the researchers use in perfor in! research operatio-ns. 'n other +ords& all those ethods +hich are used(% the researcher durin! the course of stud%in! hisresearch pro(le are ter ed as research ethods.
R;";ARCH M;TH7D7 7GN: Research ethodolo!% is
a +a% to s%ste aticall% sol$e the research pro(le .'t a% (e understood as a science of stud%in! ho+
research is done scienti*call% 'n it +e stud% the
-
7/24/2019 Applied Research Methods New
67/175
research is done scienti*call%. n it +e stud% the$arious steps that are !enerall% adopted (% aresear-cher in stud%in! his research pro(le
alon! +ith the lo!ic (ehind the . 't is necessar%for the researcher to ,no+ not onl% the researchethods)techni6ues (ut also the ethodolo!%.
>e can sa% that research ethodolo!% has
an% di ensions 3 research ethods doconstitute a part of the research ethodolo!%. The scope of research ethodolo!% is +iderthan that of research ethods. Thus& +hen +e
tal, of research ethodolo!% +e not onl% tal, ofresearch ethods (ut also consider the lo!ic(ehind the ethods +e use in the conte t of ourstud%.
-
7/24/2019 Applied Research Methods New
68/175
=uantitati$e 3 =ualitati$e desi!ns The 6uantitati$e-6ualitati$e classi*cation is
dependent on criteria: 1i2 the purpose of stud%& 1ii2Ho+ the $aria(les are
easured@ 3 1iii2 ho+ the infor ation is anal%sed. The stud% is classi*ed as 6ualitati$e if: the purpose
of the stud% is pri aril% to descri(e a situation&pheno- enon& pro(le or e$ent@ the infor ation is!athered throu!h the use of $aria(les easuredon no inal or ordinal scales 16ualitati$e
easure ent scales2@ 3 if anal%sis is done toesta(lish the $ariation in the situation&pheno enon or pro(le +ithout 6uantif%in! it.
The description of an o(ser$ed
-
7/24/2019 Applied Research Methods New
69/175
situation& the historical enu eration of e$ents& anaccount of the di erent opinions people ha$ea(out an issue& 3 a description of li$in! conditionsof a co unit%& are e a ples of 6ualitati$eresearch.
7n the other hand& if +e +ant to 6uantif% the$ariat-ion in a pheno enon& situation& pro(le orissue& if infor ation is !athered usin!predo inantl% 6uantit-ati$e $aria(les& 3 if theanal%sis is !eared to ascertain the a!nitude ofthe $ariation & the stud% is classi*ed as
6uantitati$e stud%. ; a ples of 6uantitati$easpects of a research stud% are: Ho+ an% peopleha$e a particular pro(le < Ho+ an% people holda particular attitudehere the o(ser$er has a predeter ined set ofcate!ories of acti$ities or pheno enon to (estudied& it is a structured o(ser$ational stud%.
7n the other hand& at the (e!innin! of a stud%& itis possi(le that the o(ser$er has no de*nite ideas
re!ardin! the particular aspects that need focus.7(ser$in! e$ents as the% occur a% also (e a partof the plan& as in an% 6ualitati$e studies. 'n suchcases & the o(ser$er +ill record practicall%e$er%thin! that is o(ser$ed. "uch a stud% is anunstructured o(ser$a-tional stud%. #nstructuredo(ser$ational studies are clai ed to (e thehall ar, of 6ualitati$e research.
" th th d f i % d t
-
7/24/2019 Applied Research Methods New
82/175
"o e other ethods of pri ar% datacollection include & consu er panels@ usin!
echanical de$ices@ throu!h pro/ecti$etechni6ues@ and depth inter$ie+s etc.
'nter$ie+ Method
-
7/24/2019 Applied Research Methods New
83/175
nter$ie+ Method The inter$ie+ ethod of collectin! data in$ol$es
presentation of oral-$er(al sti uli 3 repl% in ter sof oral-$er(al responses. This ethod can (e usedthrou!h personal inter$ie+s and& if possi(le&throu!h telephone inter$ie+s.
1a2 Personal interviews : Personal inter$ie+ ethod
re6uires a person ,no+n as the inter$ie+er as,in!6uestions !enerall% in a face-to-face contact to theother person or persons. At ti es the inter$ie+ee
a% also as, certain 6uestions 3 the inter$ie+erre-sponds to these& (ut usuall% the inter$ie+erinitiates the inter$ie+ 3 collects the infor ation.
This sort of inter$ie+ a% (e in the for of directpersonal
in$esti!ation or it a% (e direct oral in$esti!ation.
-
7/24/2019 Applied Research Methods New
84/175
( Structured !nstructured Interviews : The ethod of collectin! infor ation throu!h
perso-nal inter$ie+s is usuall% carried out in astructured +a%. As such +e call the inter$ie+s asstructured interviews. "uch inter$ie+s in$ol$e theuse of a set of predeter ined 6uestions 3 of hi!hl%standardised techni6ues of recordin!. As a!ainst it&the unstructur" ed interviews are characterised (%a e i(ilit% of app-roach to 6uestionnin!.#nstructured inter$ie+s do not follo+ a s%ste ofpre-deter ined 6uestions 3 standardisedtechni6ues of recordin! infor ation.
1(2 Telephone interviews# This ethod of collectin!infor ation consists in contactin! respondents on
telephone itself. 't is not a $er% +idel% used
-
7/24/2019 Applied Research Methods New
85/175
pethod& (ut pla%s i portant part in industrial
sur$e%s & partic-ularl% in de$eloped re!ions.
"ollection o 0ata through 2uestionnaires : This ethod of data collection is 6uite popular&
parti-cularl% in case of (i! en6uires. 't is (ein!adopted (% pri$ate indi$iduals& research
+or,ers& pri$ate 3 pu(lic or!anisations 3 e$en(% !o$ern ents. 'n this ethod a 6uestionnaireis sent 1usuall% (% post2 to the person concerned+ith a re6uest to ans+er the 6uestions 3 return
the 6uestionnaire. A 6uestionna-ire consists of anu (er of 6uestions printed or t%ped in ade*nite order on a for or set of for s.
The ethod of collectin! data (% ailin! the
-
7/24/2019 Applied Research Methods New
86/175
The ethod of collectin! data (% ailin! the6uestio-naires to respondents in ost e tensi$el%e plo%ed in $arious econo ic 3 (usiness sur$e%s.
Main Aspects of a Questionnaire : =uite often a 6uestionnaire is considered as a heart
of a sur$e% operation. Hence it should (e $er%caref-ull% constructed. 'f it is not properl% set up&
then the sur$e% is (ound to fail. This fact re6uiresus to stud% the ain aspects of a 6uestionnaire $i .&the $eneral form, %uestion se&uence %uestionformulation wording.
'. $eneral form# "o for as the !eneral for of a6ues-tionnaire is concerned& it can either (estructured or
unstructured 6uestionnaire. "tructured
-
7/24/2019 Applied Research Methods New
87/175
unstructured 6uestionnaire. tructured6uestionaires are those 6uestionnaires in +hichthere are de*nite& concrete 3 pre-deter ined
6uestions. >hen these characteristics are notpresent in a 6uestionnaire& it can (e ter ed asunstructured or non-structured 6uestionnaire.
B. %uestion se&uence# 'n order to a,e the
6uestion-naire e ecti$e 3 to ensure 6ualit% to thereplies rec-ei$ed& a researcher should pa%attention to the 6uestion-se6uence in preparin!the 6uestionnaire. The openin! 6uestions should(e such as to arouse hu an interest. =uestions ofa personal character or related to personal +ealthshould !enerall% (e a$oid-ed as openin! 6uestionsin a 6uestionnaire.
%uestion formulation wording :
-
7/24/2019 Applied Research Methods New
88/175
. %uestion formulation wording : >ith re!ard to this aspect of
6uestionnaire& the rese-archer should notethat each 6uestion ust (e $er% clear foran% sort of isunderstandin! can doirrepar-a(le har to a sur$e%. =uestions
should also (e i partial in order not to!i$e a (iased picture of the true state ofa airs.
Collection of "econdar% data
-
7/24/2019 Applied Research Methods New
89/175
Collection of econdar% data "econdar% data eans data that are alread% a$aila(le
i.e. the% refer to the data +hich ha$e alread% (eencollected 3 anal%sed (% so eone else. "econdar% dataare indispensa(le for ost or!anisational resea-rch
There are se$eral sources of secondar% data. "o ei portant sources are discussed (elo+:
1i3 Go$ern!ent / Se!i4go$ern!ent publications: There are an% !o$t. 3 se i-!o$t. or!anisations that
collect data on a re!ular (asis in a $ariet% of areas 3pu(lish it for use (% e (ers of the pu(lic 3 intere-st!roups. "o e co on e a ples are: the census& $ital
statistics re!istration& la(our force sur$e%s& healthreports& econo ic forecasts& de o!raphic
'nfor ation& Pu(lications of the "tatistics di$ision&
-
7/24/2019 Applied Research Methods New
90/175
( $M)o 4inance&4ood 3 A!riculture& 'ndustr%& la(our&the 4edural 3 pro$incial 5ureaus of "tatistics& "tate
5an, of Pa,istan& Central cotton co ittee& stoc,e chan-!e& Rail+a% 5oard 3 District councils etc. 1ii2 Research rganisations: Man% or!anisations collect 3 store a $ariet% of data
to support their operations: for e a ple& pa%rolldet-ails&copies of letters& inutes of eetin!s 3accounts of sales of !oods or ser$ices. Consu erresearch or!anisations collect data that are usedsu(se6uentl% (% di erent clients. Tradeor!anisations collect data fro their e (ers ontopics such as sales that are
-
7/24/2019 Applied Research Methods New
91/175
su(se6uentl% a!!re!ated 3 pu(lished. 1iii2 ;arlier research: 4or so e topics& an enor ous nu (er of research
studies that ha$e alread% (een done (% others canpro$ide %ou +ith the re6uired infor ation.
1i$2 Personal records: "o e people +rite historical 3 personal records
that a% pro$ide the infor ation %ou need. 1$2 Mass edia: Reports pu(lished in ne+spapers& a!a ines&
(oo,s etc. a% (e another source of data. 4ore a ple& 6ua lit% dail% ne+spapers contain a+ealth of data& inclu-din! reports a(out ta,e o$er(ids 3 co panies share
prices.
-
7/24/2019 Applied Research Methods New
92/175
p 1$i2 #ni$ersities 3 other 'nstitutions: Reports prepared (% research scholars 3 econo ists
etc. in uni$ersities 3 other such institutions indi erent *elds of acti$ities.
Pro(le s +ith usin! data fro "econdar% sources: >hen usin! data fro secondar% sources& the resea-
rcher ust (e careful as there a% (e certainpro(le- s +ith the a$aila(ilit%& for at 3 6ualit% ofdata. The e tent of these pro(le s $aries frosource to source. >hile usin! such data& so eissues %ou should ,eep in ind are:
1i2 9alidit% 3 relia(ilit% of data: The $alidit% ofinfor -tion a% $ar% ar,edl% fro source tosource.
The relia(ilit% can (e tested (% *ndin! out such
-
7/24/2019 Applied Research Methods New
93/175
The relia(ilit% can (e tested (% *ndin! out suchthin!s a(out the said data: 1a2 >ho collected thedata< 1(2 >hat are the sources of data< 1c2 >erethe% collected (% usin! proper ethods< 1d2 At+hat ti es +ere the% collected< 1e2 >as there an%(ias of the co plier< ote that the use ofinfor ation fro personal diaries& ne+spapers 3
a!a ines a% ha$e the pro(le of personal(ias. 1ii2 "uita(ilit% of data: The data that are suita(le for one en6uir% a% not
necessaril% (e suita(le in another en6uir%. Hence&if the a$aila(le data are found to (e unsuita(le&the% should not (e used (% the researcher.
1iii2 Ad 6 % f d
-
7/24/2019 Applied Research Methods New
94/175
1iii2 Ade6uac% of data: 'f the le$el of accurac% achie$ed in data is
found ina-de6uate for the purpose of presenten6uir%& the% +ill (e considered as inade6uate3 should not (e used (% the researcher.
1i$2 4or at:
5efore decidin! to use data fro secondar%sources it is e6uall% i portant to ascertainthat the data are a$aila(le in the re6uiredfor at. 4or e a ple& %ou i!ht need toanal% e a!e in the cate!ories B - & I-I8etc.& (ut in %our source the a!e a% (ecate!ori ed di erentl%& e.!.& B -BI& BF-B & etc.
-
7/24/2019 Applied Research Methods New
95/175
4ro all this +e can sa% that thealread% a$aila(le data should (e used(% the researcher onl% +hen he *ndsthe relia(le& suita(le and ade6uate.
l % " di R h
-
7/24/2019 Applied Research Methods New
96/175
; plorator% "tudies or Research; plorator% research is research conducted
for a pro(le that has not (een clearl%de*ned. 't i plies that not uch is ,no+na(out the situation at hand& or no infor ationis a$aila(le on ho+ si ilar pro(le s orresearch issues ha$e (een sol$ed in the past.'n such cases& e tensi$e preli inar% +or,needs to (e done to !ain fa iliarit% +ith thepheno ena in the situation and understand+hat is occurrin!& (efore +e de$elop a odel.; plorator% research is also
Qno+n as for ulati$e research ; plorator%
-
7/24/2019 Applied Research Methods New
97/175
Qno+n as for ulati$e research. ; plorator%research often relies on secondar% research
such as re$ie+in! literature and)or data& or6ualitati$e approaches such as infor aldecisions +ith consu ers& e plo%ees&
ana!e ent or co petitors& and ore
for al approaches throu!h in-depthinter$ie+s& focus !roups& pro/ecti$e ethod&case studies or pilot studies. ; tensi$einter$ie+s +ith an% people i!ht ha$e to(e underta,en to !et a handle on thesituation and understand the pheno enon.
"o e 6ualitati$e studies 1as opposed to
-
7/24/2019 Applied Research Methods New
98/175
o e 6ualitati$e studies 1as opposed to6uantitati$e data !athered throu!h
6uestionnaire& etc.2 +here data are collectedthrou!h o(ser$ation or inter$ie+s& aree plorator% in nature. >hen the data re$ealsso e pattern re!ardin! the pheno enon of
interest& theories are de$eloped andh%pothesis for ulated for su(se6uent testin!e.!.& a co pan% inter$ie+ed ana!ers toe plore the nature of ana!erial +or,.
5ased on the anal%sis of their inter$ie+eddata& the% for ulated theories of
ana!erial roles& the nature and
t%pes of ana!erial acti$ities and so on
-
7/24/2019 Applied Research Methods New
99/175
t%pes of ana!erial acti$ities and so on.; plorator% studies are also necessar% +hen
so e facts are ,no+n& (ut ore infor ationis needed for de$elopin! a $ia(le theoreticalfra e +or,. 4or instance +hen +e +ant to!et at the i portant factors that in uence
the de$elop ent of +o en in or!ani ations&pre$ious studies i!ht indicate that +o enare increasin!l% ta,in! on 6ualities such asasserti$eness& co petiti$eness 3independence. The results of e plorator%research are not usuall%
useful for decision a in! (% the sel$es&
-
7/24/2019 Applied Research Methods New
100/175
useful for decision a,in! (% the sel$es&(ut the% can pro$ide si!ni*cant insi!ht into a
!i$en situation. Althou!h the results of6ualitati$e research can !i$e so e indicationas to the L+h% & Lho+ and L+henso ethin! occurs& it cannot tell us Lho+
often or Lho+ an% . ; plorator% researchis not t%picall% !enerali a-(le to thepopulation at lar!e. 'nsu & e plorator% studies are i portant for
o(tainin! a !ood !rasp of the pheno enonof interest and ad$ancin! ,no+led!e throu!h
-
7/24/2019 Applied Research Methods New
101/175
su(se6uent theor% (uildin! andh%pothesis testin!. 'n si ple +ords&the o(/ecti$e of e plorator% research isto !ather preli inar% infor ation that+ill help de*ne pro(le s 3 su!!esth%potheses.
; planator% "tudies and Research
-
7/24/2019 Applied Research Methods New
102/175
; planator% tudies and Research
"tudies that esta(lish causal relationships()+ $aria(les a% (e ter ed as e planator%research. ; planator% research is also ,no+nas casual research 1cause and e ect2.
; planator% research atte pts to classif%+h% and ho+ there is a relationship ()+ t+oaspects of a situation or pheno enon. Thist%pe of research atte pts to e plain& for
e a ple& +h% stressful li$in! results in heart-attac,s@ +h% a decline in ortalit% isfollo+ed (% a fertilit% decline@ or
ho+ the ho e en$iron ent a ects children s
-
7/24/2019 Applied Research Methods New
103/175
ho+ the ho e en$iron ent a ects children sle$el of acade ic achie$e ent. et us considerone other e a ple& +here %ou a% *nd that acursor% anal%sis of 6uantitati$e data on
anufacturin! scrap rates sho+s a relationship()+ scrap rates and the a!e of achine (ein!operated. %ou could !o ahead and su(/ect thedata to statistical tests such as correlation inorder to !et clearer $ie+ of relationship.Alternati$el%& or in addition& collect 6ualitati$edata to e plain the reasons +h% custo er of%our co pan% rarel% pa% their (ills accordin! tothe prescri(ed pa% ent ter s.
Cross-sectional $ersus lon!itudinal
-
7/24/2019 Applied Research Methods New
104/175
studies Cross-sectional studies: A stud% can (e underta,en
in +hich data are collected /ust once& perhaps o$era period of da%s& +ee,s or onths& in order toans+er a research 6uestion. "uch studies are calledone-shot or cross sectional studies. 4or e a ple& a
dru! co pan% desirous of in$estin! in research fora ne+ o(esit% pill & conducted a sur$e% a on!o(ese people to see ho+ an% of the +ould (einterest-ed in tr%in! the ne+ pill. This is a one-shotor cross-sectional stud% to assess the li,el% de andfor the ne+ product. The purpose of the stud% hereis to collect data that +ould (e pertinent to *ndin!the
ans+er to a research 6uestion. Data collection at
-
7/24/2019 Applied Research Methods New
105/175
ans er to a research 6uestion. Data collection atone point in ti e is suEcient.
on!itudinal studies: 'n so e cases& the researcher i!ht +ant to stud%
people or pheno enon at ore than one point inti e in order to ans+er the research 6uestion. 4orinstance& the researcher i!ht +ant to stud%
e plo-%ees (eha$ior (efore 3 after a chan!e inthe top ana!e ent& so as to ,no+ +hat e ectsthe chan!e acco plished. Here& ()c data are!athered at t+o di erent points in ti e& the stud% isnot cross sectional& (ut is carried lon!itudinalacross a period of ti e. "uch studies& as +hen thedata on depende-nt $aria(le are !athered at t+o or
ore points in
i h h 6 i &
-
7/24/2019 Applied Research Methods New
106/175
ti e to ans+er the research 6uestion& arecalled lon!itudinal studies.
A cross sectional stud% is e tre el% si plein desi!n. Nou decide +hat %ou +ant to
*nd out& identif% the stud% population&select a sa ple 1if %ou need to2& 3 contact%our respondents to *nd out the re6uiredinfor ation.
The incidence of H'9 positi$e cases in acountr%.
Collect data +hich ha$e not (eenor!ani ed nu ericall% are called raw data .4 l & h i!h f B0 d l%
-
7/24/2019 Applied Research Methods New
107/175
4or e a ple& the +ei!ht of B0 rando l%selected students 1recorded to the nearest
,.! 2 fro a uni$ersit% is !i$en as (elo+.
Main di$ision of statistics
-
7/24/2019 Applied Research Methods New
108/175
Main di$ision of statistics
1i2 Descripti$e "tatistics 1ii2 'nferential"tatistics
1i2 Descripti$e statistics is that (ranch ofstatistics +hich deals +ith concepts 3 ethodsconcerned +ith su ari ation 3 description ofthe i portant aspects of nu erical data. 'tconsists of condensation of data, their!raphical displa%s& co putation of nu erical6uantities such as speciali ed a$era!es& ratios&pro/ections 3 other easures +hich aid in
a,in! decisions.
1ii2 'nferential statistics or statistical
-
7/24/2019 Applied Research Methods New
109/175
1ii2 nferential statistics or statisticalinference co prisin! those ethods
concerned +ith the anal%sis of a su(set1sa ple2 of data leadin! to predictions orinferences a(out the entire set of data1population2.
't in$ol$es the esti ation of populationpara eters and testin! of statisticalh%pothesis. This area of statistics is (asedon pro(a(ilit% theor%& and lies in the heartof statistics. ote that lar!er !roup of data1or the +hole2 is called population and onl%a part of data is ,no+n as sa ple. Theseare de*ned (elo+.
Population and "a ples
-
7/24/2019 Applied Research Methods New
110/175
p p
A population or statistical population is acollection or set of all possi(leo(ser$ations +hether *nite or in*nite&ani ate or inani ate& rele$ant to so echaracteristic of interest. 'n e$er% da%
lan!ua!e& the +ord population eans allthe people in a speci*c area. Ho+e$er& the+ord population has a (roader eanin! instatistics. 4or e a ple& population of (an,accounts& all the houses in a cit%& all thestudents in a uni$ersit%& all the (oo,s in ali(rar%& all the patients in a hospital etc.
;ach indi$idual ite in a population is calledan ele!ent of the correspondin! population
-
7/24/2019 Applied Research Methods New
111/175
an ele!ent of the correspondin! population. "tatistical population a% (e real such as the
hei!ht of colle!e students or h%potheticalsuch as all the possi(le outco es fro thetoss of a coin or thro+ of a dice.
A sa ple is a part or su(set of a population.
o. of o(ser$ations in a *nite population iscalled the si e of the population-denoted (%.
't consists of so e o(ser$ations or +hole ofthe population. The no. of o(ser$ations in asa ple is called the si e of the sa ple isdenoted (% n.
The infor ation deri$ed fro sa ple
-
7/24/2019 Applied Research Methods New
112/175
data is used to dra+ conclusions a(outthe population for e a ple ..
PARAM;T;R 3 "TAT'"T'C A nu erical 6uantit% co puted fro a popn.
1i.e. data o(tained fro a popn.2 is called a
para eter& and is denoted (% Gree, letter 9alues of para eters are !enerall% un,no+n
(ut a% (e esti ated (% usin! certainesti ation ethod. 4or e a ple
A nu erical 6uantit% co puted fro asa ple& is called a statistic---- represented (%ordinar% atin letter.
The infor ation deri$ed fro sa ple
-
7/24/2019 Applied Research Methods New
113/175
data to dra+ conclusions a(outthe popn. 4or e a ple
9AR'A5 ; 3 C7 "TA T A characteristics that $aries fro indi$idual
to indi$idual in a popn. 4or e a ple& a!e isa $aria(le as it $aries fro person toperson. "i ilarl%& other e a ple are .
Gi$en set of all possi(le $alues fro +hichthe $aria(le ta,es on $alue . do ain
Constant: 'f the do ain of a $aria(lecontains onl% one $alue then the $aria(le isreferred . Constant or * ed $alue
RA D7M 9AR'A5 ;
-
7/24/2019 Applied Research Methods New
114/175
A $aria(le +hose $alue is o(tained (%chance---- or its $alue cannot (e e actl%
deter ined. 4or e a ple& suppose +e toss acoin t+ice and call heads on a toss a success10& &B2.
Here& the occurrence of a particular $alue is a
atter of chance& so the nu (er of heads is arando $aria(le. "i ilarl%& the su of dotso(tained +ith a pair of die ..e a ple of r.$.
=#A T'TA'9; A D =#A 'TAT'9; 9AR'A5 ; 9aria(les a% (e classi*ed into 6uantitati$e
and 6ualitati$e accordin! to the for ofcharacteristics of interest.
=uantitati$e $aria(le--------- nu erical $alue.
-
7/24/2019 Applied Research Methods New
115/175
uantitati$e $aria(le nu erical $alue.4or e a ple .
=ualitati$e $aria(le------not capa(le of ta,in!nu erical easure ents. 4or e a ple&education& intelli!ence ..A 6ualitati$echaracteristic is also called an Attri(ute.
Another de*nition: A characteristic +hich$aries onl% in a!nitude fro one indi$idualto another is called a 6uantitati$e $aria(le.
A characteristic +hich $aries onl% in 6ualit%
fro one indi$idual to another is called a6ualitati$e $aria(le or an attri(ute.
o. of outco es +hen a pair of die is
-
7/24/2019 Applied Research Methods New
116/175
rolled
51613 51673 51683 51693 516 3 516;3
1B& 2 1B&B2 1B& 2 1B&I2 1B&F2 1B& 2
1 & 2 1 &B2 1 & 2 1 &I2 1 &F2 1 & 2
1I& 2 1I&B2 1I& 2 1I&I2 1I&F2 1I& 2
1F& 2 1F&B2 1F& 2 1F&I2 1F&F2 1F& 21 & 2 1 &B2 1 & 2 1 &I2 1 &F2 1 & 2
Discrete and continuous
-
7/24/2019 Applied Research Methods New
117/175
$aria(les A discrete $aria(le is one that can ta,e
onl% o(tained (% a discrete set of inte!ersor +hole nu (ers& that is the $alues areta,en (% /u ps. 't is o(tained (% the
operation of countin!. 4or e a ple& theo. of (oo,s and /ournals in a li(rar%& .. A continuous $aria(le is one that ta,e on
an% $alue-fractional or inte!ral-+ithin a!i$en inter$al. A continuous $aria(le iso(tained (% the process of easure ent.4or e a ple& speed
of car& the te perature of 'sla a(ad etc.
i d $
-
7/24/2019 Applied Research Methods New
118/175
; peri ent and ;$ent The ter e peri ent eans a planned
acti$it% or process +hose results %ield a setof data. A sin!le perfor ance of ane peri ent is called a trial. An outco e of ane peri ent is called an e$ent. An e peri ent
+hich produces di erent results e$en thou!hit is repeated a lar!e nu (er of ti es underessentiall% si ilar conditions& is called arando e peri ent. 4or e a ple& tossin! ofa fair coin& dra+in! of a card fro a dec, ofFB pla%in! cards& thro+in! a dice etc
Pro(a(ilit%
-
7/24/2019 Applied Research Methods New
119/175
Pro(a(ilit%
A pro(a(ilit% is a nu (er +hich eansrelati$e fre6uenc% of occurrence o$er the lon!run or e presses a de!ree of (elief. 'nco on lan!ua!e& +e use the +ord chance
rather than pro(a(ilit%. >hen +e sa% the pro(a(ilit% that a tossedcoin +ill land head up is F0S 1or 0.F2& +e areusin! the relati$e fre6uenc% eanin! ofpro(a(ilit%.
Pro(a(ilit% al+a%s lies (et+een 0 and 1non-ne!ati$e2. ote 0 eans 0S 3 eans 00S.
"i ple Rando "a ple
-
7/24/2019 Applied Research Methods New
120/175
i ple Rando a ple
A si ple rando sa ple is one selected ina anner such that each ele ent of thepopulation has an e6ual chance of (ein!included in the sa ple.
Methods of selection of a ".R.". otter%s%ste )dra+& co puter etc.
".R. "a ples are i portant in the
de$elop ent of pro(a(ilit% and statisticalinference. "i ple rando sa ple 3rando sa ple are sa e.
Roundin! nu (ers
-
7/24/2019 Applied Research Methods New
121/175
Roundin! nu (ers The process of roundin! o or si pl%
roundin! a nu (er eans that a certainnu (er of di!its counted fro the left& areto (e retained and the last fe+ di!its are to(e 1i2 dropped in a deci al nu (er or 1ii2
replaced +ith eros in a +hole nu (er. >eadopt Lchoose the closer con$ention inroundin! as e plained (elo+:
'f +e +ish to round JI. 8 to three di!its (%droppin! the 8& +e a% +rite the roundednu (er as either JI. or JI.J& +e chooseJI.J (ecause it is closer to JI. 8.
Ho+e$er& if FF.FI is to (e rounded to three
-
7/24/2019 Applied Research Methods New
122/175
(di!its& +e +rite FF.F rather than FF. & +h%hen the di!it to (e dropped is e actl% F& orF follo+ed onl% (% eros& the acceptedpractice is to increase the last si!ni*cantdi!it (% one if it is odd& and to lea$eunaltered if it is e$en. 4or e a ple& thenu (ers I.F F and J .8F are rounded o si!ni*cant di!its as I.FI and J .8&respecti$el%. Thin, +h% ;'GHT 74 B0 "T#D; T"
-
7/24/2019 Applied Research Methods New
130/175
Weight
97.5
92.5
87.5
82.5
77.5
72.5
67.5
62.5
57.5
52.5
47.5
30
20
10
0
Std. Dev = 9.46
Mean = 67.8N = 120.00
Histo!ra )4re6uenc% pol%!on
-
7/24/2019 Applied Research Methods New
131/175
) p
H'"T7GRAM A D 7RMA C#R9;
74 >;'GHT 74 B0 "T#D; T"
-
7/24/2019 Applied Research Methods New
132/175
74 >; GHT 74 B0 T#D; T
Weight
97.5
92.5
87.5
82.5
77.5
72.5
67.5
62.5
57.5
52.5
47.5
30
20
10
0
Std. Dev = 9.46
Mean = 67.8
N = 120.00
or al distri(ution
-
7/24/2019 Applied Research Methods New
133/175
",e+ness 1de!ree of as% etr%2
-
7/24/2019 Applied Research Methods New
134/175
Graphical displa% of s,e+ness1s% etrical 3 positi$el% s,e+ed2
-
7/24/2019 Applied Research Methods New
135/175
Graphical displa% of s,e+ness1ne!ati$el% s e+ed2
-
7/24/2019 Applied Research Methods New
136/175
1ne!ati$el% s,e+ed2
4or or al distri(ution:
-
7/24/2019 Applied Research Methods New
137/175
a2 The inter$al -V 3 OV includes8.BJS of the cases)o(ser$ations.
The inter$al -BV 3 OBV includesF.IFS of the cases)o(ser$ations.
(2 The inter$al - V 3 O V includes.J S of the cases)o(ser$ations.
ote:- 4or oderatel% s,e+eddistri(ution the a(o$e percenta!eshold appro i atel%.
"cale of easure ents
-
7/24/2019 Applied Research Methods New
138/175
1 2 ,o!inal :- u (ers represent cate!ories. u (ers
do not re ect di erences in a!nitude.u (ers ser$e to distin!uish !roups.
; a ple:- "e & nationalit%& clinicaldia!nosis place of do icile.
1B2 rdinal :-u (ers indicate ran, order of
o(ser$ations. ; a ples:- "ocial class& le$el of
education& perfor ance e$aluation.
1 2 'nter$al :-u (ers descri(e the a!nitude of
-
7/24/2019 Applied Research Methods New
139/175
u (ers descri(e the a!nitude ofthe di erences a on! the thin!s. Here&
the ero point on the scale is ar(itrar%and does not correspond to thea(sence of the trait)characteristic (ein!
easured.
; a ple:- Te perature& calendar %ear1A.D.2 Ratio :-
u (ers represent e6ual units froa(solute ero. 7(ser$ations can (eco pared as ratio or percenta!es.
; a ples:- Distance& a!e& ti e& +ei!ht&(lood pressure.
H%pothesis Testin! 1 steps2
-
7/24/2019 Applied Research Methods New
140/175
"tate ent of null 3 alternati$eh%pothesis.
Decide upon le$el of si!ni*cance& W.
Test-statistic to (e used 1decision2. Critical re!ion or re!ion of re/ection. Co putation)Calculation. Result)interpretation.
'ndependent 3 dependent 1 Paired2 t-test 1Testin! h%pothesis a(out t+o
-
7/24/2019 Applied Research Methods New
141/175
eans2
; a ple: The s%stolic (lood pressure of 0+o en +ere recorded (efore and afterad inisterin! the dru! 1calciu channel(loc,er2. Test the h%pothesis 1at the FSle$el2 That the dru! a ects the a$era!e(lood pressure 7f +o en.
B sa ple t- test is used to test the e6ualit%of t+o population ean& i.e. H 0 :X UXB andH :X YXB
B.P. beforeB.P. beforetaking drugtaking drug
B.P. afterB.P. aftertaking drugtaking drug
Di erence dDi erence d ii
-
7/24/2019 Applied Research Methods New
142/175
g g(mm/Hg.)(mm/Hg.)
g g(mm/Hg.)(mm/Hg.)
128128 115115 1313115115 112112 331010 10!10! "1"1
128128 11#11# ##122122 115115 !!1$51$5 138138 !!
132132 121210#10# 105105 $$102102 10$10$ "2"2
11!11! 115115 22
t> ?d where d>9.@=s d 1=
-
7/24/2019 Applied Research Methods New
143/175
s d An n 1
/ standard de$iation o diBerence >s d> 9. ;;6t>59.@=3 8.87t tab >t =.=7 5C3 >7.7;7
Result:4 ) = is rejected which i!plies that drughas signifcant eBect in reducing the D. . owo!en.
(, E( T-ST: (, E( techniFue is used to testthe eFuality o !ore than two population!eans6 i.e.: ) =: 1> 7 >HH..> k .
%or this purpose6 %4test
-
7/24/2019 Applied Research Methods New
144/175
The follo+in! t+o $arieties of +heat +ere planted in 8di erent
localities. The %ields of these $arieties 1in Q. !2 arerecorded as
(elo+: Test the h%pothesis to test the e6ualit% ofean %ields for B $arieties.
%ariet& %ariet&11
2525 1515 33 3$3$ $0$0 1818 2!2! 3131
%ariet&%ariet& 2828 1$1$ $0$0 3#3# $3$3 2$2$ 2#2# 3333
+ere recorded as !i$en (elo+. Test +hether thereis an% si!ni*cant e ect of trainin! on (od% +ei!htor not.
'eig'eigtt
11 22 33 $$ 55 !! 88 ## 1010
BeforBeforee 5555 $$88 $5$5 22 $8$8 55## 3!3! $$00 $$88 5252
fterfter 55 5511
$8$8 00 5252 55!!
$5$5 $$ $$##
5555
R;GR;""'7
-
7/24/2019 Applied Research Methods New
145/175
; ;
'ntroduced (% ;n!lish 5io etrician&"ir 4rancis Galton in th centur%. Tendenc% to !oin! (ac, or re!ress
to+ards a$era!e1hei!ht e a ple2. To esta(lish
functional) athe atical relationship()+ one dependent and one or oreindependent $aria(les.
T+o ain ai s of re!ression are :
-
7/24/2019 Applied Research Methods New
146/175
T+o ain ai s of re!ression are :
a2 To esta(lish relationship a on!$aria(les. (2 Prediction of future $alues of the
response $aria(le.Deter inistic and pro(a(ilistic odels.Method of least s6uares 1esti ation ofpara eters2.;sti atin! a 3 ( usin! the for ulaederi$ed (% M ".
M "
-
7/24/2019 Applied Research Methods New
147/175
General e6uation of linear re!ression NiUWO[ \ O [ B\ BO............O [ , \ , O ] i
-
7/24/2019 Applied Research Methods New
148/175
1iU &B& & ..&n2
>here N is dependent $aria(le& \ & \B& ..\ , areindependent $aria(les& W is intercept& [ &[B& &[, arere!ression coeEcients 3 ] i s are the rando errors.Re!ression can (e linear or non-linear or cur$e-linear.
"i ple and ultiple linear re!ression."i ple correlation.Dia!nostic chec,in! of the *tted odel ore$aluatin! the 4it. 't is $er% i portant toin$esti!ate the structure of the residuals and thedata pattern throu!h !raphs.
Data of four !raphs
-
7/24/2019 Applied Research Methods New
149/175
4our di erent !raphs ha$in! sa esu ar% statistics
-
7/24/2019 Applied Research Methods New
150/175
'nterpretation of $arious de!rees ofcorrelation 1scatter dia!ra 2
-
7/24/2019 Applied Research Methods New
151/175
7(ser$ed 3 *tted data
-
7/24/2019 Applied Research Methods New
152/175
Multiple re!ression
-
7/24/2019 Applied Research Methods New
153/175
#suall% si ple re!ression is inade6uatein real +orld situation
Multiple re!ression is an e tension ofsi ple re!ression. NiUWO[ \ O [ B\ BO ] i1iU &B& & ..&n2.;sti ate W& [ 3 [B usin! M ".
.
Multiple re!ression
-
7/24/2019 Applied Research Methods New
154/175
Di ension Graph B
-
7/24/2019 Applied Research Methods New
155/175
Co on 9iolation in A!ricultural; peri ents
-
7/24/2019 Applied Research Methods New
156/175
; p(ariance heterogenity and )onnormality
>here the $ariance is functionall% related tothe ean.
#suall% associated +ith data +hosedistri(ution is not nor al. ; a ples 1i2 "uch as the o. of infestedplants per plot or the o. of lesion per leaf1 usuall% follo+ a Poissondistri(ution +here in " BU\2.
1ii2 "uch as percent sur$i$al of insects orpercent plants infected +ith a disease. Hereeach occurrence can onl% (e one of the t+opossi(le outco es 1e.!. ali$e or dead andinfested or not infested2. these follo+ a
(ino ial distri(ution
Data transfor ation
-
7/24/2019 Applied Research Methods New
157/175
't is the ost appropriate re edialeasure for $ariance hetero!eneit%+here the $ariance and ean arefunctionall% related 1see the !raphs2.
7ri!inal data are con$erted into a ne+scale resultin! in a ne+ data set that ise pected to satisf% the condition of
ho o!eneit% of $ariance. A fe+ datatransfor ation techni6ues aredescri(ed here.
Di erent t%pes of $ariancehetero!eneit% .
-
7/24/2019 Applied Research Methods New
158/175
ete o!e e t% .
#ogarith!ic trans or!ation. This transfor ation is ost appropriate
f d h d d d $i i i
-
7/24/2019 Applied Research Methods New
159/175
for data +here standard de$iation is
proportional to the ean. Thiscondition is !enerall% in data +herenu (ers and co$er a +ide ran!e of$alues. e.!. data on the nu (er ofinsects per plot.
To illustrate the procedure for appl%in!lo!arith ic transfor ation& +e usedata on the nu (er of li$in! lar$ae onrice plants treated +ith $arious rates ofan insecticide fro a RC5 e peri ent+ith four replications. The !raphs are!i$en !ear
"o e rules for choosin! the propertransfor ation scale for Sa!e datad i$ d f d i$ h
-
7/24/2019 Applied Research Methods New
160/175
deri$ed fro count data are !i$en here.
Rule1. 4or percenta!e data l%in! +ith theran!e of 0 to J0S& no transfor ation
is needed. Rule 7 .
4or percenta!e data l%in! +ith in the
ran!e of either 0 to 0S or J0 to 00S&(ut not (oth& the s6uare transfor ationshould (e used.
-
7/24/2019 Applied Research Methods New
161/175
Rule 8. 4or percenta!e data that do not
follo+ the ran!es speci*ed in either
rule or rule B& the arc sinetransfor ation should (e used.
"u!!ested readin! 'ntroduction to "tatistical theor%& part ' 3 Part ''
1B00 )l di i 2
-
7/24/2019 Applied Research Methods New
162/175
1B00 )latest edition2.
(% Prof. "her Muha ad Chaudhr% 3Dr. "hahid Qa al. "TAT'"T'C": Methods and Application 1B00F2
(% Dr. M. Af al (e!Qar$an 5oo, House& ahore.
"tatistical Methods and Data Anal%sis1;dition:B0002(% Dr. 4a6ir Muha ad& Qita( Mar,a 5ha+ana5a ar& 4aisala(ad.
A!riculture 3 applied statistics-' (% P.Q "ahu1B00J2& Qal%ani pu(lishers.5io statistical anal%sis I th edition (% K.H Zar&
ational (oo, foundation& 'sla a(ad"tatistical procedures for a!ricultural research
1 8I)latest edition2 (% Q A Go e 3 A A Go e
-
7/24/2019 Applied Research Methods New
163/175
-
7/24/2019 Applied Research Methods New
164/175
",e+ness
-
7/24/2019 Applied Research Methods New
165/175
Re!ression cur$es
-
7/24/2019 Applied Research Methods New
166/175
"cale of easure ents
o!inal !easure!ent:
-
7/24/2019 Applied Research Methods New
167/175
,o!inal !easure!ent:A no inal scale is one in +hich it ispossi(le to place the $aria(le intounordered cate!ories. 4or e a ple&
+e a% +ant to ,no+ ho+ uchpatients in a hospital areh%pertensi$e& dia(etic anic-depressi$e 3 ps%choneurotic& 3 so on.Data of this t%pe are fre6uentl%referred to as count data.
rdinal !easure!ent: An ordinal easure ent is one in+hich the results can (e ordered alon!a !i$en scale 7rdinal data are data
-
7/24/2019 Applied Research Methods New
168/175
a !i$en scale. 7rdinal data are data
that can (e ordered (ut do not ha$especi*c nu erical $alues. 4or e a ple&students or e plo%ees can (e !radedaccordin! to their perfor ance as
U; cellent& BU$er% !ood& U !ood&
IU satisfactor%& FU a$era!e. This isordinal $aria(le (ecause the di erent!rades &B& &I&F are ordered in thesense that !rade is (etter than B&+hich is (etter than !rade & -----& and
so on. Ho+e$er& +e cannot sa% thatthe di erence (et+een cate!ories and B is the sa e as the di erence(et+een !rades B and & ----& and soon. This is also called Ran, data.
'nter$al !easure!ent. An inter$al easure ent is one in +hich the
incre ents are consistent across the entirei ! l H $ & i h h li i i
-
7/24/2019 Applied Research Methods New
169/175
easurin! scale. Ho+e$er& it has the li itation
that it does not include true ero point. Theost co on e a ple is the te perature. Ano(/ect can (e e posed to 0 o 4ahrenheit& 0 o 4and 0 o 4. The actual di erence (et+een 0 o and 0 o is the sa e as (et+een 0 o and 0 o& (ut there is no true ero point in the scale& itcannot (e concluded that 0 o represents t+iceas uch heat as 0 o or that 0 o representsthrice as uch heat as 0 o. "uch a conclusion
+ould not (e correct. 't a% (e noted that inthe e a ple the ero point 1that is ar(itrar%2has a di erent eanin! for 4ahrenheit 3Celsius te peratures.
Ratio Measure!ent: The ratio easure ent is one in
+hich the inter$als are consistent
-
7/24/2019 Applied Research Methods New
170/175
+hich the inter$als are consistent
alon! the entire scale and there is atrue ero point. 4or e a ple& 5loodpressure and (od% +ei!ht are on
ratio scales 1or easure ent2(ecause the ero-point is +ell-de*ned in (oth instances. 'n case of(od% +ei!ht& +e can sa% that adi erence of l(s is actuall% t+ice aslar!e as a di erence of l(s.
-
7/24/2019 Applied Research Methods New
171/175
)istogra! o weight o 17= students:
-
7/24/2019 Applied Research Methods New
172/175
De*nition of "tatistics The +ord statistics see s to ha$e (een deri$ed
-
7/24/2019 Applied Research Methods New
173/175
(fro the atin +ord status or the 'talian +ordstatista. 5oth these +ords eans a politicalstate.
'n plural sense6 statistics refer to nu ericalfacts in an% *eld of stud%& These facts are
collected in s%ste atic anner +ith a de*nitepurpose in $ie+. 4or instance& statistics of (irths3 deaths& price statistics& a!ricultural statistics&statistics of cri es& statistics of road accidents&statistics of educational institutions etc.
'n singular sense. 't refers to the science ordiscipline that includes procedures 3techni6ues of collection& presentation& anal%sis3 interpretation of nu erical data.
-
7/24/2019 Applied Research Methods New
174/175
=uadratic ;6uation
-
7/24/2019 Applied Research Methods New
175/175