Application of Univariate, Bi-variate and Multivariate analysis Pooja k shetty

This is a brief summary about application of Uni variate, Bi-variate and Multivariate analysis

1. Business Research Methodology Topic:-Applications of univariate, Bi-variate and Multivariate analysis.

2. Statistical Analysis Analysis of data refers to the critical examination of the assembled and grouped data for studying the characteristics of the object under study and for determining the patterns of relationship among the variables relating to it. Statistical analysis summarizes data into understandable and meaningful forms and helps in the identification of the casual factors underlying complex phenomena. It also helps in making estimations or generalization from the results of sample surveys.

3. Univariate Analysis It is a method for analyzing data on a single variable at a time, where we’re observing only one aspect of phenomenon at a time time. With single-variable data, we can put all our observations into a list of numbers. Answers to statistical problems by collecting and analyzing data on one variable are known as Univariate analysis. Univariate analysis explores each variables in a data set separately.

4. For example, If a researcher records the income of all employed residents of a particular area and tabulates that data, it would depict just one variable, the income of employed people in that area. The statistics used to summarize Univariate data describe the data’s center and spread. There are many options for displaying such summaries. The most frequently used illustrations of univariate data are: Frequency distributions Histograms Stem and leaf plots Box and whisker plots Pie charts

5. Cont. Frequency distributions :- It shows you the number of times an event occurs within the topic being researched. For example, if one were to ask students about the mode of transport they take to come to college and the answers can be tabulated as follows

6. Cont. Student’s mode of transport to college Frequency Train 60 Bus 20 Bike 10 Walk 10 Total no. of students being surveyed 100

7. Cont. Histogram:- T he bars convey the relationship of one group or class of the variable to the other(s). For example, income earned (represented on the Y-axis in lakhs of rupees and types of grain sown(series) represented on the X-axis in four states in India.

8. Cont. Stem and Leaf plots:- A plot where each data value is split in to a “Leaf”(usually the last digit) and a “Stem”( the other digits). For example, “32” is split into “3”(stem) and “2”(leaf). The stem values are listed down, and the leaf values are listed next to them.

9. Cont. P ie chart:- In a Pie chart, each “slice” represents the proportion of the total phenomenon that is due to each of the classes or groups. For example, sales revenue in a year

10. Bivariate analysis Often researchers are interested in gathering information about more than one variable. For example, in study on the education levels of populations, researchers also obtain data on other variables such as age, sex, family income, distance of educational institutions etc. When we only two variables are under consideration, we are studying bivariate data.

11. Cont. In Bivariate data, two values are recorded for each observations. For example data on income and weight of individuals. Income of the respondents(in ‘000 rupees)(Y) Weight(in kgs.)(X) 1000 50 2000 55 3000 60 4000 62 5000 68

12. Cont. There are two important characteristics of the data revealed in this table: We can clearly observe that as the variable(income-Y) increases, the second variable (weight-X)also increases. If we graph the data we will see that the points cluster along a straight line. When this occurs, the relationship between two variables is called a linear relationship.

13. Types of variables Nominal variables: can be referred to as a set of categories that vary in quality but not quantity. There is no order, distance or origins between the attributes or variables. e.g., race, white, black, Asian. Ordinal variable: The distances between the values of the variables do not have precise numerical meaning, distance between the categories is unknown. The variables are ranked on certain characteristics or attributes of the objects.

14. Cont. Interval variables: include those variables whose attributes are separated by a uniform distance between them. The numbers associated with interval variables usually have real meaning. The interval measures has an arbitrary zero point and constant unit of measurement.e.g., age; city population; income. Ratio measures: are the same as interval measures except ratio measures are based on a true zero point(e.g., age). All statistical operations can be performed on ratio measures.

15. Association With bivariate analysis, we are testing the hypothesis of “association” and causality. Association is useful as it can be used to predict the value of the dependent variable once we know the value of the independent variable . A measures of association known as C orrelation coefficient. Regression analysis: Regression analysis is used to measure the degree of relationship between two or more ratio variables. In regression analysis, the dependent variable is generically denoted by Y, and the independent variable is denoted by X.

16. Multivariate analysis Multivariate analysis is a simultaneous study of several variables. It is more informative than univariate analysis. However, also more complex than univariate analysis. Multivariate stats test 3 or more variables together to check for all kinds of effects that occur together. Application areas Social science: (gender, age, Nationality)of an individual Climatology: (minimum temperature , maximum temperature. rainfall, humadity)on a day Econometrics : (input costs, production, profit) of a firm

17. Cont. Socio-Demographic: (GDP, Life expectancy, Literacy rate)of a country Medical: (systolic BP, diastolic BP, pulse rate)of persons Pathological: (blood sugar, uric acid, hemoglobin count) of patients Administrative: (admissions, operations, discharges, deaths) per day bin hospitals Pharmaceutical: (drug A, drug B,.. drug Z)sales per day in a pharmacy

18. conclusion Statistical analysis summarizes data into understandable and meaningful forms and helps in the making estimations or generalizations from the results of sample surveys. Answers to statistical problems by collecting and analyzing data on one variable are known as Univariate analysis. When we only two variables are under consideration, we are studying bivariate analysis or data. With bivariate analysis ,we are testing hypothesis of “association” and causality. Simultaneous study of several variables are known as multivariate analysis.