The analysis and interpretation of data represent the application of deductive and inductive logic to the research process. The data are often classified by division into, subgroups, and are then analyzed and synthesized in such a way that hypothesis may be verified or rejected. The final result may be a new principle or generalization. Data are examined in terms of comparison between the more homogeneous segments within the group any by comparison with some outside criteria.
NEED FOR ANALYSIS OF DATA OR TREATMENT OF DATA After administering and scoring research tools scripts, data collected and organized. The collected data are known as „raw data.‟ The raw data are meaningless unless certain statistical treatment is given to them. Analysis of data means to make the raw data meaningful or to draw some results from the data after the proper treatment.
Thus, the analysis of data serves the following main functions: 1. To make the raw data meaningful, 2. To test null hypothesis, 3. To obtain the significant results, 4. To draw some inferences or make generalization, and 5. To estimate parameters.
Analysis means “computation of certain measures along with searching for pattern of relationships that exist among data groups” Depending on the measurement and sampling procedures, the analysis of data are of two types. Statistical analysis (inferential) Non-statistical (Descriptive)
Descriptive analysis is largely the study of distributions of one variable. This study provides us with profiles of companies, work groups, persons and other subjects on any of a multiple of characteristics such as size. Composition, efficiency, preferences, etc.” Statistical analysis is always more precise and objective. Selection and choice of statistical tool depends on three factors.
1) DEPENDING ON TYPE OF MEASUREMENT a) Nominal measurement b) Ordinal measurement c) Interval measurement d) Ratio measurementFor nominal and ordinary measurement, we commonly use nonparametric tests.For interval and ratio measurement, we commonly use parametric tests. Parametric statistics are commonly used tests.
For application of parametric test the data should fulfil two conditions: A) Homogeneity of variance B) variables involved must be true numerical Nonparametric tests are also called “distribution- free tests”. so these can be used in statistics involved in nominal measurements and ordinal measurements.
2) DEPENDING ON NUMBER OF VARIABLES TO BE ANALYZED:- a) One variable - unidimensional analysis b) Two variable – bivariate analysis c) More than two variables – multivariate analysisIf investigator is interested in describing a single population, he should use “unidimensional analysis”.If investigator wants to study interrelationship between two variables he should use “bivariate analysis”.
If the investigator wants to study interrelationship between more than two variables, he should use Regression analysis and multiple discriminant analysis. It should be remembered that regression technique is useful only if both variables (independent variable and dependent variable) are interval variables.
3) DEPENDING ON TYPE OF ANALYSIS TO BE DONE:- a) Requires estimating a parameter 1. Point estimate (measures of central tendency) 2. Interval estimate (measures of dispersion) b) Testing of hypothesis 1.„t‟ test. 2. ANOVA test 3. chi-square test
Choice of statistical technique depends on the type of “statistical inference” the researcher wants. Point estimate:- A single statistic is used as an estimate of a parameter ( mean, median, mode ) Interval estimate:- An interval within which the true value of a parameter of a population is stated to lie with a predetermined probability on the basis of sampling statistics. (also called range)
STATISTICAL ANALYSIS:- It includes various ”tests of significance” and “testing of hypothesis” It is also useful in the estimation of population values. Ex. Z test, „t‟ test, chi-square test etc.Now there are two type of analysis.1. Correlation analysis2. Causal analysis
Correlation analysis:- It is useful to study the correlation between two or more variables and determining the amount of correlation between two or more variables. It is relatively more important in most social and business researches. Causal analysis:- It is concerned with the study of how one or more variables(independent variable) affect the changes in another variable(dependent variable). This analysis can be termed as “Regression analysis” It is considered relatively more important in experimental researches.
MULTIVARIATE ANALYSIS:- A) Multiple regression analysis: In this type of analysis we measure the changes in dependent variable, with changes in two or more than two independent variables. This is done by finding a constant called “regression coefficient”. So the main objective of multiple regression analysis is to make a prediction about the dependent variable based on its “covariance” with two or more independent variables.
B) Multiple discriminant analysis: This analysis is used when there is a single dependent variable, which needs to be classified into two or more than two groups. This analysis is used when we want to predict an entity‟s possibility of belonging to a particular group based on several predictor variables. C) Multivariate analysis of variance (Multi ANOVA): ANOVA is the ratio of “variance among the groups” to “variance within the groups”
Multi ANOVA is an extension of “ two-way ANOVA”, wherein the ratio of among group variance to within group variance is worked out on set of variables. When we want to use ANOVA or Multi ANOVA, the data should meet three assumptions. These are: 1) Selection of subjects on the basis of random sampling. 2) Existence of homogeneity of variance between groups. 3) Variables under study should follow normal distribution.
D) Canonical analysis: This analysis is useful in case of both measurable and non-measurable variables. for the purpose of simultaneously predicting a set of dependent variables from their joint covariance with a set of independent variables.