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Analysis of data in research


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Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making.

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Analysis of data in research

  1. 1. Presented by Abhijeet Birari UNIT V ANALYSIS OF DATA
  2. 2. ANALYSIS OF DATA Collection of Data Analysis of Data Draw Logical Inferences
  3. 3. STATISTICAL SOFTWARE PACKAGES Follow the link >>> sticalSoftwarePackages.html
  4. 4. Statistical Package for Social Sciences
  5. 5. WHAT IS SPSS? • SPSS Statistics is a software package used for statistical analysis. • SPSS can be used for: – Processing Questionnaire – Reporting in tables and graphs – Analyzing • Mean, Median, Mode • Mean Dev & Std. Dev., • Correlation & Regression, • Chi Square, T-Test, Z-test, ANOVA, MANOVA, Factor Analysis, Cluster Analysis, Multidimensional Scaling etc. • Founded in 1968 and acquired by IBM in 2009.
  6. 6. 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
  7. 7. 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.
  8. 8. 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
  9. 9. ANOVA (Analysis of Variance)
  10. 10. INTRODUCTION • Significance of difference between means of two samples can be judged using: – Z test (>30) – T test (<30) • Difficulty arises while measuring difference between means of more than 2 samples • ANOVA is used in such cases • ANOVA is used to test the significance of the difference between more than two sample means and to make inferences about whether our samples are drawn from population having same means Significance of difference of IQ of 2 divisions Z test or T Test Significance of difference between performance of 5 different types of vehicles ANOVA
  11. 11. 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
  12. 12. WHY ANOVA INSTEAD OF MULTIPLE T TEST? • If more than two groups, why not just do several two sample t-tests to compare the mean from one group with the mean from each of the other groups? • The problem with the multiple t-tests approach is that as the number of groups increases, the number of two sample t-tests also increases. • As the number of tests increases the probability of making a Type I error also increases.
  13. 13. ANOVA HYPOTHESES • The Null hypothesis for ANOVA is that the means for all groups are equal. • The Alternative hypothesis for ANOVA is that at least two of the means are not equal.
  15. 15. What is 1-way ANOVA and 2-way ANOVA? • If we take only one factor and investigate the difference among its various categories having numerous possible values, it is called as One-way ANOVA. • In case we investigate two factors at the same time, then we use Two-way ANOVA Training Type Productivity Advanced 200 Advanced 193 Advanced 207 Intermediate 172 Intermediate 179 Intermediate 186 Beginners 130 Beginners 125 Beginners 119 One-way ANOVA 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-way ANOVA
  16. 16. HOW ANOVA WORKS? • Three methods used to dissolve a powder in water are compared by the time (in minutes) it takes until the powder is fully dissolved. The results are summarized in the following table: • It is thought that the population means of the three methods m1, m2 and m3 are not all equal (i.e., at least one m is different from the others). How can this be tested?
  17. 17. • One way is to use multiple two-sample t-tests and • compare Method 1 with Method 2, • Method 1 with Method 3 and • Method 2 with Method 3 (comparing all the pairs) • But if each test is 0.05, the probability of making a Type 1 error when running three tests would increase. • Better method is ANOVA (analysis of variance) • The technique requires the analysis of different forms of variances – hence the name. Important: ANOVA is used to show that means are different and not variance are different.
  18. 18. • ANOVA compares two types of variances • The variance within each sample and • The variance between different samples. • The black dotted arrows show the per-sample variation of the individual data points around the sample mean (the variance within). • The red arrows show the variation of the sample means around the grand mean (the variance between).
  19. 19. STEPS FOR USING ANOVA Null Hypothesis H0 : μ1= μ2= μ3=………= μk Alternate Hypothesis Ha : μ1≠ μ2 ≠ μ3 ≠ ……… ≠ μk 1. Calculate mean of each sample (x̄1, x̄2, x̄3…… x̄k) 2. Calculate mean of sample means: Where k=Total number samples 3. Calculate Sum of 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 Null and Alternate Hypothesis Step 2 : Compute Variance Between the samples k XXXX X K  .......321 22 33 2 22 2 11 )(......)()()( xxnxxnxxnxxnSS kkbetween 
  20. 20. 1. Calculate Sum of Square within the samples: SSTotal = SSBetween + SSWithin Step 3 : Compute Variance Within samples 22 33 2 22 2 11 )(....)()()(   kkiiiiiiiiwithin xxxxxxxxSS Step 4 : Calculate total variance Step 5 : Calculate average variance between and within samples 1  k SS MS Between between kn SS MS within within   N=Total no of items in all samples K=Number of samples
  21. 21. Step 6 : Calculate F-ratio within between MS MS Fratio  Step 7 : Set up ANOVA table Source of variation Sum of squares (SS) Degree of freedom (d.f) Mean Squares F-Value (Calculated) Between Samples SS Between k-1 MS Between= SS Between/k-1 F=MS Between/MS Within Within Samples SS Within n-k MS Within= SS Within/n-k Total SS Total n-1
  22. 22. Decision Rule: Reject H0 if  Calculated value of F > Tabulated value of F  Otherwise accept H0 Or Accept H0 if  Calculated value of F < Tabulated value of F  Otherwise reject H0 Step 8 : Look for Table value of F  Steps: 1. Find out two degree of freedom (one for between and one for within) 2. Denote x for between and y for within [F(x,y)] 3. In F-distribution table, go along x columns, and down y rows. The point of intersection is your tabulated F-ratio
  23. 23. EXAMPLE • Set up an analysis of variance table for the following per acre production data for three varieties of wheat, each grown on 4 plots and state if the variety differences are significant. • Test at 5% level of significance
  24. 24. H0 = The difference between varieties is not significant Ha = The difference in varieties is significant
  25. 25. Interpretation: Calculated Value of F < Table Value of F ∴ Accept Null Hypothesis Difference in wheat output due to varieties is not significant and is just a matter of chance.
  26. 26. EXAMPLE • Ranbaxy Ltd. has purchased three new machines of different makes and wishes to determine whether one of them is faster than the others in producing a certain output. • Four hourly production figures are observed at random from each machine and the results are given below: • Use ANOVA and determine whether machines are significantly different in their mean speed. Observations M1 M2 M3 1 28 31 30 2 32 37 28 3 30 38 26 4 34 42 28
  27. 27. EXAMPLE
  28. 28. EXAMPLE
  29. 29. TWO WAY ANOVA
  30. 30. TWO WAY ANOVA • Two-way ANOVA technique is used when the data are classified on the basis of two factors. • For example, the agricultural output may be classified on the basis of different varieties of seeds and also on the basis of different varieties of fertilizers used. • Two types of 2-way ANOVA – Without repeated values – With repeated values
  31. 31. STEPS IN 2-WAY ANOVA 1 2 3
  32. 32. STEPS IN 2-WAY ANOVA SS for residual or error = total SS – (SS between columns + SS between rows) 4 5 6
  33. 33. STEPS IN 2-WAY ANOVA 7
  34. 34. Prepare ANOVA Table STEPS IN 2-WAY ANOVA 8
  35. 35. EXAMPLE
  37. 37. WHAT IS RESEARCH PROPOSAL? A research proposal is a document that provides a detailed description of the intended program. It is like an outline of the entire research process that gives a reader a summary of the information discussed in a project.
  38. 38. WHAT IS RESEARCH PROPOSAL? • Research proposal sets out – Broad topic you want to research – What is it trying to achieve? – How would you do research? – What would be time need? – What results it might produce?
  39. 39. PURPOSE OF RESEARCH PROPOSAL • Convince others that research is worth • Sell your idea to funding agency • Convince the problem is significant and worth study • Approach is new and yield results
  40. 40. ELEMENTS OF RESEARCH PROPOSAL Introduction Statement of Problem Purpose of the Study Review of Literature Questions and Hypothesis The Design – Methods & Procedures Limitations of the Study Significance of the Study References
  42. 42. Color of Bike Look Masculine/Feminine Mileage Price Maintenance Cost Power Speed Control Weight Brand Ease of delivery Financial Assistance Offer/Discounts Tyre size Disc Brake Smooth Handling Service Centers Design Cost Technical Comfort FACTORS Unobserved Observed
  43. 43. FACTOR ANALYSIS “Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.”
  44. 44. EXAMPLE Academic ability of student Quantitative Ability Verbal Ability 1. Maths Score 2. Computer Program Score 3. Physics Score 4. Aptitude Test Score 1. English 2. Verbal Reasoning Score
  45. 45. PURPOSE OF FACTOR ANALYSIS • To identify underlying constructs in the data. • To reduce number of variables • To reduce redundancy of data (E.g. Quantitative Aptitude)
  46. 46. APPLICATION OF FACTOR ANALYSIS • Market Segmentation • Product Research • Advertising Studies • Pricing Studies
  47. 47. Friendliness of Staff Time Spent in Line-up Assistance via Telephone Service Observed Unobserved X1 X2 X3 F1
  48. 48. X1 X2 X3 X4 F1 F2 F3 F4 a1 b1 c1 d1
  49. 49. WAYS OF FACTOR ANALYSIS 1. Confirmative Factor Analysis – Factors and corresponding variables are already known – On the basis of literature review or past experience/expertise 2. Exploratory Factor Analysis – Algorithm is used to explore pattern among variables – Then factors are explored – No prior hypothesis to start with
  50. 50. 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
  51. 51. STEPS IN FACTOR ANALYSIS Formulate the Problem Construct the Correlation Matrix Determine the method of Factor Analysis Determine Number of Factors Estimate the Factor Matrix Rotate the Factors Estimating Practical Significance
  53. 53. 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.
  54. 54. DEFINITION “Discriminant analysis is a multivariate statistical technique used for classifying a set of observations into pre defined groups.”
  55. 55. OBJECTIVE • To understand group differences and to predict the likelihood that a particular entity will belong to a particular class or group based on independent variables.
  56. 56. PURPOSE • To classify a subject into one of the two groups on the basis of some independent traits. • To study the relationship between group membership and the variables used to predict the group membership.
  57. 57. 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 anthropometric variables. • High or low performer on the basis of skill. • Juniors or seniors category on the basis of the maturity parameters.
  58. 58. ASSUMPTIONS 1. Sample size – Should be at least five times the number of independent variables. 2. Normal distribution – Each of the independent variable is normally distributed. 3. Homogeneity of variances / covariances – All variables have linear and homoscedastic relationships.
  59. 59. ASSUMPTIONS • Outliers – Outliers should not be present in the data. DA is highly sensitive to the inclusion of outliers. • Non-multicollinearity – There should be any correlation among the independent variables. • Mutually exclusive – The groups must be mutually exclusive, with every subject or case belonging to only one group.
  60. 60. ASSUMPTIONS • Variability – No independent variables should have a zero variability in either of the groups formed by the dependent variable.
  61. 61. To identify the players into different categories during selection process.
  63. 63. DEFINITION • “Cluster analysis is a group of multivariate techniques whose primary purpose is to group objects (e.g., respondents, products, or other entities) based on the characteristics they possess.” • It is a means of grouping records based upon attributes that make them similar. • If plotted geometrically, the objects within the clusters will be close together, while the distance between clusters will be farther apart.
  64. 64. CLUSTER VS FACTOR ANALYSIS  Cluster analysis is about grouping subjects (e.g. people). Factor analysis is about grouping variables.  Cluster analysis is a form of categorization, whereas factor analysis is a form of simplification.  In Cluster analysis, grouping is based on the distance (proximity), in Factor analysis it is based on variation (correlation)
  65. 65. 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 measured for each respondents on 0-10 scale.
  66. 66. HOW DO WE MEASURE SIMILARITY? • Proximity Matrix of Euclidean Distance Between Observations Observation Observations A B C D E F G A --- B 3.162 --- C 5.099 2.000 --- D 5.099 2.828 2.000 --- E 5.000 2.236 2.236 4.123 --- F 6.403 3.606 3.000 5.000 1.414 --- G 3.606 2.236 3.606 5.000 2.000 3.162 ---
  67. 67. HOW DO WE FORM CLUSTERS? • Identify the two most similar(closest) observations not already in the same cluster and combine them. • We apply this rule repeatedly to generate a number of cluster solutions, starting with each observation as its own “cluster” and then combining two clusters at a time until all observations are in a single cluster. • This process is termed a hierarchical procedure because it moves in a stepwise fashion to form an entire range of cluster solutions. It is also an agglomerative method because clusters are formed by combining existing clusters.
  68. 68. AGGLOMERATIVE PROCESS CLUSTER SOLUTION Step Minimum Distance Unclustered Observationsa Observation Pair Cluster Membership Number of Clusters Overall Similarity Measure (Average Within-Cluster Distance) Initial Solution (A)(B)(C)(D)(E)(F)(G) 7 0 1 1.414 E-F (A)(B)(C)(D)(E-F)(G) 6 1.414 2 2.000 E-G (A)(B)(C)(D)(E-F-G) 5 2.192 3 2.000 C-D (A)(B)(C-D)(E-F-G) 4 2.144 4 2.000 B-C (A)(B-C-D)(E-F-G) 3 2.234 5 2.236 B-E (A)(B-C-D-E-F-G) 2 2.896 6 3.162 A-B (A-B-C-D-E-F-G) 1 3.420
  69. 69. • 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 each step of the procedure until all are contained in a single cluster
  70. 70. USAGE OF CLUSTER ANALYSIS  Market Segmentation:  Splitting customers into different groups/segments where customers have similar requirements.  Segmenting industries/sectors:  Segmenting Markets:  Cities or regions having common traits like population mix, infrastructure development, climatic condition etc.  Career Planning:  Grouping people on the basis of educational qualification, experience, aptitude and aspirations.  Segmenting financial sectors/instruments:  Grouping according to raw material cost, financial allocation, seasonability etc.
  72. 72. EXAMPLE
  73. 73. MEANING • Concerned with understanding how people make choices 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 research technique that marketers use to determine what features a new product should have and how it should be priced.
  74. 74. • Suppose we want to market a new golf ball. We know from experience and from talking with golfers that there are three important product features: 1. Average Driving Distance 2. Average Ball Life 3. Price
  75. 75. TYPES OF CONJOINT ANALYSIS 1. Choice Based – Respondents select from grouped options
  76. 76. TYPES OF CONJOINT ANALYSIS 2. Adaptive Choice – It is used for studying how people make decisions regarding complex products or services – Packages adapt based on previous selections – It gets ‘smarter’ as the survey progresses
  78. 78. TYPES OF CONJOINT ANALYSIS 3. Menu-based 1. Respondents are shown a list of features and levels 2. They have to choose among options 3. Example: Airtel My Plan
  80. 80. 4. Full profile rating based – Display series of product profile – Typically rated on likelihood to purchase or preference scale
  81. 81. 5. Self explicate – Direct ask of features and levels – Each feature is presented separately for evaluation – Respondents rate all remaining features according to desirability
  82. 82. ADVANTAGES • Estimates psychological tradeoffs that consumers make when 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 • Used to develop needs based segmentation
  83. 83. DISADVANTAGES • Designing conjoint studies can be complex • With too many options, respondents resort to simplification strategies • Respondents are unable to articulate attitudes toward new categories • Poorly designed studies may over-value emotional/preference variables and undervalue concrete variables • Does not take into account the number items per purchase so it can give a poor reading of market share
  85. 85. 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.
  86. 86. MEANING • Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. • Multidimensional scaling is a method used to create comparisons between things that are difficult to compare. • The end result of this process is generally a two-dimensional chart that shows a level of similarity between various items, all relative to one another.
  87. 87. 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. • Gauging the effectiveness of advertising by identifying the brands position before and after a campaign. • Assessing the attitudes and perceptions of consumers. • Determine what attributes the brand owns and what attributes competitors own.
  88. 88. THANK YOU