Analysis of ResultsAnalysis of Results A lecture delivered to A lecture delivered to

participantsparticipants In In

Research Methodology And Use of Research Methodology And Use of Technologies In ResearchTechnologies In Research

On 16On 16thth Nov. (G.V.M. College of Edu.Sonepat) Nov. (G.V.M. College of Edu.Sonepat)

Prof. Rajbir SinghProf. Rajbir SinghDept. of PsychologyDept. of Psychology

M.D.U.RohtakM.D.U.Rohtak

Why Research ?Why Research ? In the behavioral sciences we conduct In the behavioral sciences we conduct

research in order to determine the research in order to determine the acceptability of hypotheses which we acceptability of hypotheses which we derive from our theories of behavior. derive from our theories of behavior. Having selected a certain hypothesis Having selected a certain hypothesis which seems important in a certain which seems important in a certain theory, we collect empirical data which theory, we collect empirical data which should yield direct information on the should yield direct information on the acceptability of that hypothesis. Our acceptability of that hypothesis. Our decision about the meaning of the data decision about the meaning of the data may lead us to retain, revise, or reject the may lead us to retain, revise, or reject the hypothesis and the theory which was its hypothesis and the theory which was its source.source.

TheoryTheory

HypothesisHypothesis

DataData

AnalysisAnalysisExhibit: Research as a process (Bidirectional)Exhibit: Research as a process (Bidirectional)

Frequently Asked Questions before analysisFrequently Asked Questions before analysis

1.When analysis?1.When analysis?When having data/information and to draw inferenceWhen having data/information and to draw inference2.What type of data?2.What type of data?Qualitative/Quantitative? Qualitative/Quantitative? 3.If qualitative what type?3.If qualitative what type?

Narratives Verbal Narratives Verbal Product Non-VerbalProduct Non-VerbalPerformancePerformance

4.If quantitative what is the Level of measurement ?4.If quantitative what is the Level of measurement ? Nominal, Ordinal, Interval and Ratio ScaleNominal, Ordinal, Interval and Ratio Scale

5. What Kind of Sample?5. What Kind of Sample?Large/Small:nLarge/Small:n1, .1, ....N=30,----N...N=30,----N

6.How the sample has been drawn?6.How the sample has been drawn?ProbabilityProbabilityNon-probabilityNon-probability

7. Estimation of population parameters? 7. Estimation of population parameters? µ, µ, σσ8. Verification of hypothesis, if any ?8. Verification of hypothesis, if any ?9. Correlational/ Experimental ?9. Correlational/ Experimental ?10.Parametric/Nonparametric ?10.Parametric/Nonparametric ?11.Univariate/bivariate/multivariate ?11.Univariate/bivariate/multivariate ?

ResultsResults

Analysis of DataAnalysis of DataA. Descriptive PresentationA. Descriptive Presentation n=1, Xs-listing, ordering, bunching, categorization n=1, Xs-listing, ordering, bunching, categorization X¯, Med., Percentile, Quartile etc.X¯, Med., Percentile, Quartile etc.Mode: Uni/bimodal/MultimodalMode: Uni/bimodal/MultimodalDistribution- frequencies, class intervalsDistribution- frequencies, class intervalsSD, Range,SESD, Range,SEMM

Graphic presentation- Bar diagrams, pie-charts etc.Graphic presentation- Bar diagrams, pie-charts etc.Histogram/polygonHistogram/polygon

Data transformation- monotonic , uni-Data transformation- monotonic , uni-directional,calculative destress: directional,calculative destress:

√√XX, 1, 1/ X,, log transformation, Arcsine / X,, log transformation, Arcsine transformation,transformation,

X+…, X-… etc.X+…, X-… etc. Normalization T-scalingNormalization T-scaling

B. Pre-Verification TestB. Pre-Verification Test

Test of deviation from normality-SK ,KuTest of deviation from normality-SK ,Ku Test of homogeneity- Bartlett's test, Cochran's Test of homogeneity- Bartlett's test, Cochran's testtest Test of homosedacity – Test of homosedacity –

Range restriction-Comparing distribution Range restriction-Comparing distribution Data scanning for assumptionsData scanning for assumptions

C. Verification of Hypothesis/ Goodness of fitC. Verification of Hypothesis/ Goodness of fit Statistical test yields a value that has associated probability alpha, Statistical test yields a value that has associated probability alpha,

the level of significance ( the p of committing type I error, i.e.; the level of significance ( the p of committing type I error, i.e.; rejecting Ho when it is true). Beta , the p of type II error, accepting rejecting Ho when it is true). Beta , the p of type II error, accepting Ho when it is infact false. Alpha is inversely related to beta, so to Ho when it is infact false. Alpha is inversely related to beta, so to reduce these errors, we must increase N.reduce these errors, we must increase N.

Sample mean and SD should be equal to population parameters. Are Sample mean and SD should be equal to population parameters. Are they or are not? Sampling distribution of various statistic has p of they or are not? Sampling distribution of various statistic has p of x¯ and SD to approximate of µ and x¯ and SD to approximate of µ and σσ. It is the process of . It is the process of estimation.estimation.

Applying a statistical testApplying a statistical test D.Post-hoc testsD.Post-hoc tests: individual comparisons, : individual comparisons,

Range statistics, sample effects e.g.; Range statistics, sample effects e.g.; Duncan’s test , Newman Keul’s test.Duncan’s test , Newman Keul’s test.

E. InterpretationE. Interpretation: Making a Statement: Making a StatementType –IV errorsType –IV errors

Some common Tests for verification of Some common Tests for verification of HypothesisHypothesis

Non-parametric Test Parametric univariate Non-parametric Test Parametric univariate MultivariateMultivariate

• Sign test, WilcoxenSign test, Wilcoxen XX22 t Manova t Manova

• Median test r FMedian test r F Canonical Canonical

• Mann-Whitney-U test R ClusterMann-Whitney-U test R Cluster

• Kruskal -Wallis-ANOVA Kruskal -Wallis-ANOVA ββ Discriminate Discriminate FunctionsFunctions

• Friedman’s ANOVAFriedman’s ANOVA Factor Factor AnalysisAnalysis

• Kendall’s coefficient Structural Kendall’s coefficient Structural Equation Equation

ModelingModeling Spearman’s rank correlation Spearman’s rank correlation