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INTRODUCTION TO MULTIVARIATE STATISTICS Dr. Debdulal Dutta Roy, Ph.D. (Psy.) Psychology Research Unit Indian Statistical Institute Kolkata – 700 108 E-mail:ddroy@isical.ac.in (o) [email_address] http://www.isical.ac.in/~ddroy/abstract.html
Indian Statistical Institute (ISI), a unique institution devoted to the research, teaching and application of statistics, natural sciences and social sciences. Founded by Professor P.C. Mahalanobis in Kolkata on 17th December, 1931, the institute gained the status of an Institution of National Importance by an act of the Indian Parliament in 1959.
Research in Statistics and related disciplines is the primary activity of the Institute. Teaching activities are undertaken mainly in Kolkata, Delhi and Bangalore.
Purpose of multivariate statistics is to establish correlation among sets of variables.
True. But it’s purpose is not limited in determining relation among set of variables. It tends to control the effect of some intervening variables on relationship among sets of variables.
MVS refers to the set of statistical tools in order to find out pattern of relationship among the set of variables – Independent, dependent and intervening variables.
The definition suggests that MVS can not be used when the variables are not correlated with each other.
Therefore, before going for MVS, it is necessary to do correlation among them.
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List of Multivariate Statistical Tools Can we assess their perception, beliefs and attitudes ?
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List of Multivariate Research Questions on Women and Child development
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Multivariate Research Questions for Women & Child Development (Difference Perspective)
Multiple Regression
What is the predictive strength of poverty, inequality, war, criminal networks, ruthless demand for cheap labour and commercial sexual exploitation in predicting motivation to human trafficking ?
Factorial Design :
Does eating habit (DV) of women vary with age, education and socio-economic status (IV) ?
MANOVA
Does food belief of pregnant mother vary with religion ?
Discriminant function analysis ?
What is the predictive capacity of food attitude questionnaire to classify students in terms of their mid-day meal taking ?
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Multivariate Research Questions for Women & Child Development (Relation Perspective)
Canonical correlation
Is there any relation between awareness of nutrition and motivation to follow good food taking habits ?
Principal Component analysis
What is the meaning of good food taking motivation ?
Correspondence analysis
Can we map different districts of one state in terms of human trafficking ?
Cluster analysis
Is it possible to classify states in terms of immunization ?
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Some studies on Application of Multivariate statistics
Principal component analysis is a technique (1) to reduce the number of variables and (2) to detect structure in the relationships between variables, that is to classify variables . Therefore, PCA is applied as a data reduction or structure detection method. In principal component analysis, we seek linear composites of the original variables that display certain desirable properties, namely, scores that exhibit maximal variance, subject to being uncorrelated with previously computed composites.
Purpose: To determine principal components of school infrastructure perception.
Assumption: School infrastructure perception encompasses set of 13 variables – perception of students to school infrastructures as Classroom, Drinking Water, Toilet, Blackboard, Teachers, Book, Teaching learning materials, Friends, Games, Cultural Programs, Book bank, Mid-day Meal, and Health Check-up. Most of these infrastructures are available in rural schools. It is assumed that there would be some latent structure in perception of 13 variables.
Correspondence analysis is an exploratory multivariate technique that converts frequency table data into graphical displays in which rows and columns are depicted as points. It provides a method for comparing row or column proportions in a two-way or multiway table. CA investigates the magnitude and the substantive nature of association between the row and column categories of cross tabulation rather than to confirm or reject hypothesis about the underlying process.
These methods were originally developed in France by Jean-Paul Benzerci in the early 1960’s and 1970’s and it has gained importance in the classic text by Greenacre (1984).
Other names : correspondence mapping, perceptual mapping, social space analysis, correspondence factor analysis, principal components analysis of qualitative data, and dual scaling;
Cluster analysis helps to identify similar entities on the basis of characteristics they possess. It helps to classify objects or variables having functional homogeneity. The resulting object clusters should exhibit high internal homogeneity (within cluster) and high external homogeneity between any two clusters. It is an inductive treatment and a purely empirical method of classification.
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Fisher’s Linear Discriminant Functions for differentiating Schools with Good and Poor Infrastructure -15.57 -26.27 Constant 2.03 2.58 Equal Opportunity 4.51 6.2 Reliability 3.76 4.93 Comfort -0.45 -1.27 Safety -0.46 5.05 Cleanliness Poor Infrastructure Good Infrastructure Attitudinal Dimensions 0 5 101.41 0.53 0.687 0.9 P-Value Df Chi-Square Wilk's Lambda Canonical Correlation Eigen Values
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Classification Matrix of Good and poor schools in terms of infrastructure availability Correct Classification Percentage= (75+60)/163 x 100=82.8 100 76.9 23.1 Poor 100 11.8 88.2 Percentage Good 163 70 93 Total 78 60 18 Poor 85 10 75 Count Good Total Predicted Group Poor Infrastructure Predicted Group Good Infrastructure Original Group
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Box-plot Analysis of Discriminant Scores between Good and Poor Infrastructure Schools.
Dutta Roy, D. (2007). Taxonomic approach in Job analysis. Psychological assessment in Personnel selection. In Dr. S. Subramony and S.B.Raj (Eds.), Psychological assessment in Personnel Selection. Delhi: Defense Institute of Psychological Research, p.25-39
Dutta Roy,D.(2006). Clusturing academic profiles of tribal and non-tribal school students of Manipur. Journal of Psychometry, 20,2, 1-12.
Dutta Roy,D.(2006). Clusturing academic profiles of tribal and non-tribal school students of Manipur. Journal of Psychometry, 20,2, 1-12.
Dutta Roy, D. (2002) Personality differences across four metropolitan cities of India , Indian Psychological Review , 58,2,71-78.
Dutta Roy.D. and Bannerjee,I.(1998) Correspondence analysis between stimulus length and amount of forgetting in assessment of short term memory span , Indian Journal of Psychometry and Education, 29,1,7-12
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