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research methods and statistics

AbdulRashidAdamsSeguir

Analysis of data in researchAbhijeet Birari

Anova; analysis of variancePriyamvada Saarsar

Analysis of variance anovaResearch Scholar - HNB Garhwal Central University, Srinagar, Uttarakhand.

Tugasan kumpulan anovapraba karan

Statr session 19 and 20Ruru Chowdhury

Statistics for Anaesthesiologistsxeonfusion

- 1. Presented by Abhijeet Birari UNIT V ANALYSIS OF DATA
- 2. ANALYSIS OF DATA Collection of Data Analysis of Data Draw Logical Inferences
- 3. STATISTICAL SOFTWARE PACKAGES Follow the link >>> http://www.coedu.usf.edu/main/departments/me/MeasurementandResearchStati sticalSoftwarePackages.html
- 4. Statistical Packagefor SocialSciences
- 5. WHAT IS SPSS? • SPSSStatisticsis asoftware package used for statistical analysis. • S P S Scan be used for: – Processing Questionnaire – Reporting in tables andgraphs – Analyzing • Mean, Median, Mode • Mean Dev& Std. Dev., • Correlation & Regression, • ChiSquare,T-Test,Z-test,ANOVA, MANOVA, FactorAnalysis, ClusterAnalysis, Multidimensional Scalingetc. • Founded in 1968 and acquired by IBM in 2009.
- 7. WHAT IS HYPOTHESIS? “The statement speculating the outcome of a research or experiment.” • H0=There is no difference in performance of Div. A, B and C in Semester I • Ha=Business Communication subject has been effective in developing communication skills of students • H0=Biometric system has not improved the attendance of faculties • Ha=Excessive fishing has affected marine life • H0=There is no significant difference in salary of males and females in particular organization. Here, H0=Null Hypothesis Ha=Alternate Hypothesis
- 8. WHAT IS LEVEL OF SIGNIFICANCE When null hypothesis is true, you accept it. When it is false, you reject it. 5% level of significance means you are taking 5% risk of rejecting null hypothesis when it happens to be true. It is the maximum value of probability of rejecting H0 when it is true.
- 9. TYPES OF STATISTICAL TESTS Tests Meaning When it is used Statistical tests used Parametric Tests Based on assumption that population from where the sample is drawn is normally distributed. Used to test parameters like mean, standard deviation, proportions etc. • T-test • ANOVA • ANCOVA • MANOVA • Karl Pearson Non parametric Tests Don’t require assumption regarding shape of population distribution. Used mostly for categorical variable or in case of small sample size which violates normality. • Chi Square • Mann-Whitney U • Wilcoxon Signed Rank • Kruskal-Wallis • Spearman’s
- 10. ANOVA (Analysis of Variance)
- 11. INTRODUCTION • Significance of difference between means of two samples can bejudged using: – Ztest (>30) – Ttest (<30) • Difficulty ariseswhile measuring difference between means of morethan 2samples • ANOVAis usedin suchcases • ANOVAis usedto test the significance of the difference between morethan two sample means and to makeinferences aboutwhether our samples are drawnfrom population havingsame means Significanceofdifferenceof IQof 2 divisions Ztest orTTest Significanceof differencebetweenperformanceof 5 differenttypesofvehicles ANOVA
- 12. WHEN TO USE ANOVA? Compare yield of crop from several variety of seeds Mileage of 4 automobiles Spending habits of five groups of students Productivity of 4 different types of machine during a given period of time Effectiveness of fitness programme on increase in stamina of 5 players
- 13. WHY ANOVA INSTEAD OF MULTIPLE T TEST? • If more than two groups,why notjust doseveraltwo samplet-tests to compare the meanfrom one group with the mean from each of the other groups? • The problem with the multiple t-tests approach isthat asthe number of groups increases,the number of two samplet-tests also increases. • Asthe number of tests increasesthe probability of making aType I error also increases.
- 14. ANOVA HYPOTHESES • The Null hypothesis for ANOVAisthat the meansfor allgroups are equal. • TheAlternative hypothesis for ANOVAisthat at least two of the meansare not equal.
- 15. ONE WAY ANOVA AND TWO WAY ANOVA
- 16. What is 1-way ANOVA and 2-way ANOVA? Ifwe take only one factor and investigatethe difference among its various categories having numerous possible values, it is called asOne-way ANOVA. Incasewe investigatetwo factors at the sametime, then we useTwo-way ANOVA • • TrainingType Productivity Advanced 200 Advanced 193 Advanced 207 Intermediate 172 Intermediate 179 Intermediate 186 Beginners 130 Beginners 125 Beginners 119 One-wayANOVA Gender Educational Level Marks Male School 89 Male College 50 Male School 90 Male College 80 Female College 50 Female University 40 Female School 91 Female University 56 Two-wayANOVA
- 17. HOW ANOVA WORKS? • Three methods usedto dissolve a powder in water are compared bythe time (in minutes) it takes until the powder isfully dissolved. The results are summarized in the following table: • It isthought that the population means of the three methods m1, m2and m3are not all equal (i.e., at least one m is different from the others). How can this betested?
- 18. • Oneway isto use multiple two-sample t-tests and • compare Method 1with Method 2, • Method 1with Method 3 and • Method 2with Method 3 (comparing all the pairs) • But if eachtest is0.05,the probability of making aType 1error when runningthree tests would increase. • Better method isANOVA(analysis of variance) • Thetechnique requiresthe analysis of different forms of variances– hencethe name. Important:ANOVAis usedto showthat means are different and not variance are different.
- 19. • ANOVAcomparestwo types of variances • Thevariance withineachsample and • Thevariance between different samples. • The blackdottedarrows showthe per-sample variation of the individual data points aroundthe sample mean (the variancewithin). • The red arrowsshowthe variation of the sample meansaroundthe grand mean (thevariance between).
- 20. STEPS FOR USING ANOVA Null Hypothesis H0: μ1= μ2= μ3 =………=μk Alternate Hypothesis Ha : μ1≠ μ2≠ μ3≠ … … …≠ μk 1. Calculate meanof each sample (x ̄ 1, x ̄ 2, x ̄ 3……x ̄ k) 2. Calculate meanof sample means: Where k=Total number samples 3. Calculate Sumof Square between the samples: Where n1=Total number of item in sample 1 n2=Total number of item in sample 2 n3=Total number of item in sample 3 … … … … … … … … . Step 1 :State NullandAlternate Hypothesis Step2 :ComputeVariance Betweenthe samples X K k X1 X2 X3 ....... X SSbetween n1(x1 x) n2(x2 x) n3(x3 x) ...... nk(xk x) 2 2 2 2
- 21. 1. Calculate Sumof Squarewithin the samples: SSTotal=SSBetween+ SSWithin Step3 :ComputeVarianceWithin samples 2 2 2 2 SSwithin i(x1i x1) i(x2i x2) i(x3i x3) .... i(xki xk) Step4 :Calculatetotalvariance Step5 :Calculateaveragevariance betweenandwithin samples k SS Between MSbetween 1 SSwithin MSwithin n k N=Totalno of items in all samples K=Numberof samples
- 22. Step6 :Calculate F-ratio within between MS MS Fratio Step7 :Set upANOVAtable Sourceof variation Sumof squares(SS) Degreeof freedom (d.f) MeanSquares F-Value (Calculated) Between Samples S SBetween k-1 MSBetween= S SBetween/k-1 F=MSBetween/MS Within Within Samples S SWithin n-k MSWithin= S SWithin/n-k Total S STotal n-1
- 23. Decision Rule: Reject H0if Calculated value of F>Tabulated value of F Otherwise accept H Or Accept H0if Calculated value of F<Tabulated value of F Otherwise reject H 0 0 Step8 : Lookfor Tablevalueof F Steps: 1. Findout two degree of freedom (one for between and onefor within) 2. Denote xfor between and yfor within [F(x,y)] 3. In F-distribution table, go along x columns, and down y rows. Thepoint of intersection isyour tabulated F-ratio
- 24. EXAMPLE • Set up ananalysis of variance table for the following per acre production datafor three varieties of wheat, eachgrown on4 plots and state if the variety differences are significant. • Testat 5%level of significance
- 25. H0= The difference between varieties is not significant Ha=The difference in varieties is significant
- 26. Interpretation: Calculated Value of F<TableValue of F ∴Accept Null Hypothesis Difference inwheatoutputdueto varieties isnotsignificantandisjusta matter of chance.
- 27. EXAMPLE • Ranbaxy Ltd. has purchasedthree new machinesof different makesand wishesto determine whether oneof them isfaster than the others in producingacertain output. • Four hourly productionfigures are observed at randomfrom each machine andthe results are given below: • UseANOVAand determine whether machinesare significantly different in their meanspeed. Observations M1 M2 M3 1 28 31 30 2 32 37 28 3 30 38 26 4 34 42 28
- 28. EXAMPLE
- 29. EXAMPLE
- 30. TWO WAY ANOVA
- 31. TWO WAY ANOVA • Two-wayANOVAtechnique is usedwhenthe data are classified onthe basis of two factors. • For example, the agricultural output may be classified onthe basis of different varieties of seedsand also onthe basis of different varieties of fertilizers used. • Twotypes of 2-wayANOVA – Without repeated values – With repeated values
- 32. STEPS IN 2-WAYANOVA 1 2 3
- 33. STEPS IN 2-WAYANOVA SS for residual or error = total SS – (SS between columns + SS between rows) 4 5 6
- 34. STEPS IN 2-WAYANOVA 7
- 35. STEPS IN 2-WAYANOVA PrepareANOVA Table 8
- 36. EXAMPLE
- 39. RESEARCH PROPOSAL
- 40. WHAT IS RESEARCH PROPOSAL? Aresearch proposal is adocument that provides adetailed description of the intended program. It is like an outline of the entire research processthat gives a reader a summary of the information discussed in a project.
- 41. WHAT IS RESEARCH PROPOSAL? • Research proposal sets out – Broadtopic you want to research – What is it trying to achieve? – How would you do research? – What would betime need? – What results it might produce?
- 42. PURPOSE OF RESEARCH PROPOSAL • Convince others that research is worth • Sellyour idea to funding agency • Convince the problem is significant and worth study • Approach is new and yield results
- 43. ELEMENTS OF RESEARCH PROPOSAL Introduction Statement of Problem Purposeof the Study Reviewof Literature Questionsand Hypothesis The Design– Methods & Procedures Limitationsof the Study Significanceof the Study References
- 44. FACTOR ANALYSIS
- 45. Colorof Bike Look Masculine/Feminine Mileage Price Maintenance Cost Power Speed Control Weight Brand Easeof delivery FinancialAssistance Offer/Discounts Tyre size Disc Brake Smooth Handling Service Centers Design Cost Technical Comfort FACTORS Unobserved Observed
- 46. FACTOR ANALYSIS “Factor analysis is astatistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.”
- 47. EXAMPLE Academicability of student QuantitativeAbility VerbalAbility 1. MathsScore 2. ComputerProgram Score 3. PhysicsScore 4. AptitudeTestScore 1. English 2. Verbal ReasoningScore
- 48. PURPOSE OF FACTOR ANALYSIS • Toidentify underlying constructs in the data. • To reduce number of variables • To reduce redundancy of data (E.g. Quantitative Aptitude)
- 49. APPLICATION OF FACTOR ANALYSIS • Market Segmentation • Product Research • Advertising Studies • Pricing Studies
- 50. Friendlinessof Staff TimeSpent in Line-up Assistancevia Telephone Service Observed Unobserved X1 X2 X3 F1
- 51. X2 X1 a1 b1 X3 X4 F1 F2 F3 F4 c1 d1
- 52. WAYS OF FACTOR ANALYSIS 1. Confirmative FactorAnalysis – Factors and corresponding variables are already known – Onthe basis of literature review or past experience/expertise 2. Exploratory FactorAnalysis – Algorithm is usedto explore pattern among variables – Thenfactors are explored – No prior hypothesisto start with
- 53. CONDITIONS FOR FACTOR ANALYSIS • Use interval or ratio data • Variables are related • Sufficient number of variables (min 4-5 variables for one factor) • Large no of observations • All variables should be normally distributed
- 54. STEPS IN FACTOR ANALYSIS Formulatethe Problem Constructthe Correlation Matrix Determinethe method of FactorAnalysis Determine Numberof Factors Estimatethe Factor Matrix Rotatethe Factors EstimatingPracticalSignificance
- 55. DISCRIMINANT ANALYSIS
- 56. EXAMPLE • Basketballer or volleyballer on the basis of anthropometric variables. • High or low performer on the basis of skill. • Juniors or seniors category on the basis of the maturity parameters.
- 57. DEFINITION “Discriminant analysis is a multivariate statistical technique used for classifying aset of observations into pre defined groups.”
- 58. OBJECTIVE • To understand group differences and to predict the likelihood that a particular entity will belong to a particular class or group basedon independent variables.
- 59. PURPOSE • Toclassify asubject into one of the two groups on the basis of some independent traits. • Tostudy the relationship between group membership and the variables usedto predict the group membership.
- 60. SITUATIONS FOR ITS USE • When the dependent variable is dichotomous or multichotomous. • Independent variables are metric, i.e. interval or ratio. • Example: • Basketballer or volleyballer on the basis of anthropometricvariables. • Highor low performer onthe basis of skill. • Juniors or seniors category onthe basis of the maturity parameters.
- 61. ASSUMPTIONS 1. Samplesize – Should be at least five times the number of independent variables. 2. Normal distribution – Eachof the independent variable is normally distributed. 3. Homogeneityof variances/ covariances – All variables have linear and homoscedastic relationships.
- 62. ASSUMPTIONS • Outliers – Outliers should not be present in the data. DAis highly sensitive to the inclusion of outliers. • Non-multicollinearity – There should be any correlation among the independent variables. • Mutually exclusive – Thegroups must be mutually exclusive,with every subject or case belonging to only one group.
- 63. ASSUMPTIONS • Variability – No independent variables should have azerovariability in either of the groups formed bythe dependent variable.
- 64. Toidentify the playersinto different categories during selection process.
- 66. CLUSTER ANALYSIS
- 67. DEFINITION • “Cluster analysis is agroup of multivariate techniques whose primary purpose isto group objects (e.g., respondents, products, or other entities) based on the characteristicsthey possess.” • It is a meansof grouping records based upon attributesthat makethem similar. • If plotted geometrically,the objects within the clusters will be close together, while the distance between clusters will befarther apart.
- 68. CLUSTER VS FACTOR ANALYSIS Cluster analysis is about grouping subjects (e.g. people). Factoranalysis is about grouping variables. Cluster analysis is aform of categorization, whereas factor analysis is aform of simplification. In Cluster analysis, grouping is based on the distance (proximity), in Factoranalysis it is based on variation (correlation)
- 69. EXAMPLE • Suppose a marketing researcher wishes to determine market segments in a community based on patterns of loyalty to brands and stores a small sample of seven respondents is selected as a pilot test of how cluster analysis is applied. Two measures of loyalty- V1(store loyalty) and V2(brand loyalty)- were measuredfor each respondents on 0-10scale.
- 71. HOW DO WE MEASURE SIMILARITY? • Proximity Matrix of EuclideanDistance Between Observations Observation Observations A B C D E F G A B C D E F G --- 3.162 5.099 5.099 5.000 6.403 3.606 --- 2.000 2.828 2.236 3.606 2.236 --- 2.000 2.236 3.000 3.606 --- 4.123 5.000 5.000 --- 1.414 2.000 --- 3.162 ---
- 72. HOW DO WE FORM CLUSTERS? • Identify the two most similar(closest) observations not already in the samecluster and combine them. • Weapply this rule repeatedlyto generate a numberof cluster solutions, starting with each observation as its own “cluster” andthen combiningtwo clusters at atime until all observations are inasingle cluster. • This processistermed a hierarchical procedure becauseit moves in astepwise fashionto form an entire rangeof cluster solutions. It is also anagglomerative method becauseclusters areformed by combiningexisting clusters.
- 73. AGGLOMERATIVEPROCESS CLUSTERSOLUTION Step Minimum Distance Unclustered Observationsa Observation Pair Cluster Membership Numberof Clusters OverallSimilarity Measure(Average Within-Cluster Distance) Initial Solution 1.414 2.000 2.000 2.000 2.236 3.162 (A)(B)(C)(D)(E)(F)(G) (A)(B)(C)(D)(E-F)(G) (A)(B)(C)(D)(E-F-G) (A)(B)(C-D)(E-F-G) (A)(B-C-D)(E-F-G) (A)(B-C-D-E-F-G) (A-B-C-D-E-F-G) 1 2 3 4 5 6 E-F E-G C-D B-C B-E A-B 7 6 5 4 3 2 1 0 1.414 2.192 2.144 2.234 2.896 3.420
- 75. • Dendogram: Graphical representation (tree graph) of the results of a hierarchical procedure. Starting with each object as a separate cluster, the dendogram shows graphically how the clusters are combined at eachstep of the procedure until all are contained in asingle cluster
- 76. USAGE OF CLUSTER ANALYSIS Market Segmentation: Splitting customers into different groups/segments where customers havesimilar requirements. Segmentingindustries/sectors: Segmenting Markets: Cities or regions having commontraits like population mix, infrastructure development, climatic condition etc. Career Planning: Grouping people on the basis of educational qualification, experience, aptitude and aspirations. Segmentingfinancialsectors/instruments: Grouping according to raw material cost,financial allocation, seasonability etc.
- 77. CONJOINT ANALYSIS
- 78. EXAMPLE
- 79. MEANING • Concerned with understanding how people makechoices between products or services or • Combination of product and service • Businesses can design new products or services that better meet customers underlying needs. • Conjoint analysis is a popular marketing researchtechnique that marketers useto determine what features a new product should have and how it should be priced.
- 80. • Supposewe want to market a new golf ball. We know from experience and from talking with golfers that there arethree important product features: 1. Average Driving Distance 2. Average Ball Life 3. Price
- 81. TYPES OF CONJOINT ANALYSIS 1. ChoiceBased – Respondentsselectfrom groupedoptions
- 82. TYPES OF CONJOINT ANALYSIS 2. Adaptive Choice – It is usedfor studying how people makedecisions regarding complex products or services – Packagesadapt basedon previous selections – It gets ‘smarter’ asthe survey progresses
- 83. TYPES OF CONJOINT ANALYSIS
- 84. TYPES OF CONJOINT ANALYSIS 3. Menu-based 1. Respondentsare showna list of features and levels 2. They haveto chooseamongoptions 3. Example:Airtel My Plan
- 85. TYPES OF CONJOINT ANALYSIS
- 86. 4. Full profile rating based – Display series of product profile – Typically rated on likelihoodto purchase or preferencescale
- 87. 5. Selfexplicate – Direct askof features and levels – Eachfeature is presented separately for evaluation – Respondents rate all remaining features accordingto desirability
- 88. ADVANTAGES • Estimates psychological tradeoffs that consumers makewhen evaluating several attributes together • Measures preferences at the individual level • Uncovers real or hidden drivers which may not be apparent to the respondent themselves • Realistic choice or shopping task • Usedto develop needs based segmentation
- 89. DISADVANTAGES • Designing conjoint studies can becomplex • With too many options, respondents resort to simplification strategies • Respondents are unable to articulate attitudes toward new categories • Poorly designed studies mayover-value emotional/preference variables and undervalue concrete variables • Does not take into account the number items per purchase so it cangive a poor reading of market share
- 90. MULTIDIMENSIONAL SCALING
- 91. EXAMPLE A researcher may give test subjects several varieties of apple and have them make comparisons on several criteria between two apples at a time. Once all the apples are directly compared to each other variety, the data is plotted on a graph that shows how similar one type is to another.
- 92. MEANING • Multidimensional scaling (MDS) is a meansof visualizing the level of similarity of individual casesof adataset. • Multidimensional scaling is a method usedto createcomparisons between things that are difficult to compare. • The end result of this process is generally atwo-dimensional chart that shows a level of similarity between various items, all relative to one another.
- 94. APPLICATIONS OF MDS • Understanding the position of brands in the marketplace relative to groups of homogeneous consumers. • Identifying new products by looking for white space opportunities or gaps. • Gaugingthe effectiveness of advertising by identifying the brands position before and after acampaign. • Assessingthe attitudes and perceptions of consumers. • Determine what attributes the brand owns and what attributes competitors own.
- 95. THANK YOU