Research Tools and Techniques The Research Process: Step 7 (Data Analysis Part C) Lecture 30

Lecture Topics Covered Previously in the Last Lecture Methods of Bivariate Analysis Contingency tables X 2 Test Pearson’s Correlation

What we are going to Cover in this Lecture Regression Analysis Paired Sample t-tests Independent Sample t-tests Contents of Research Proposal and Report

THE RESEARCH PROCESS (1). Observation The Broad Problem Area (2). Preliminary Data Gathering Interviews and Library Search (3). Problem Definition (4). Theoretical Framework Variables Identification (5) Generation of Hypothesis (6). Scientific Research Design (7). Data Collection and Analysis (8) Deduction (9). Report Writing (10). Report Presentation (11). Managerial Decision Making

Data Analysis Process Data Collection Data Analysis Getting Data Ready for Analysis Editing Data 1.Incompleteness /omissions 2.Inconsistencies 3.Legibility 4.Coding Data 5.Categorizing 6.Creating a Data File Feel for Data 1.Mean 2.Median 3.Mode 4.Variance 5.Frequency Distribution Goodness of Data 1.Reliability 2.Validity Hypotheses Testing Appropriate Statistical Manipulation (Inferential Statistics) Interpretation of Results Discussion Recommendations Introduction to Data Analysis Process

Tests of Statistical Significance Do our tests apply to general population or not (Confidence in the Generalizability of findings) The mode of calculation of statistical significance hence prove Ho or Ha  Only for samples drawn from probability sampling.  Determine level of statistical significance.  P < 0.05  Find the test result using SPSS or any other software.  If resulting value > table value (incase of chi square) you accept alternate hypothesis.  For Pearson’s r, Spearman’s Rho, Phi and Cramer’s V, SPSS automatically generates statistical significance as shown in table.

Regression Analysis Used to understand the nature of the relationship between two or more variables A dependent or response variable (Y) is related to one or more independent or predictor variables (Xs) Object is to build a regression model relating dependent variable to one or more independent variables Model can be used to describe, predict, and control variable of interest on the basis of independent variables

Simple Linear Regression Yi = βo + β1 xi + εi Where Y Dependent variable X Independent variable βo Intercept Mean value of dependent variable (Y) when the independent variable (X) is zero β 1 Model parameter Slope that measures change in mean value of dependent variable associated with a one-unit increase in the independent variable ε i Error term that describes the effects on Y i of all factors other than value of X i Model Summary with R Square and ANOVA table with F value and Significance. More than one independent variable is included in a multiple linear regression model.

ANOVA – Analysis of Variance between Groups The reason for doing an ANOVA is to see if there is any difference between groups on some variable. Example of Groups: You might guess that the size of maple leaves depends on the location of the trees. For example, that maple leaves under the shade of tall oaks are smaller than the maple leaves from trees in the prairie and that maple leaves from trees in median strips of parking lots are smaller still. To test this hypothesis you collect several (say 7) groups of 10 maple leaves from different locations. F=(Found variation of the group averages)/(Expected variation of the group averages).

Significant Mean Differences Between Two Groups – t-tests Paired Sample t-tests An independent testing agency is comparing the daily rental cost for renting a compact car from Hertz and Avis. A random sample of eight cities is taken and the following rental information obtained. At the.05 significance level can the testing agency conclude that there is a difference in the rental charged? Step 1: Ho μ d =0; Ha μd ≠0 Step 2: The significance level is.05. Step 3: H 0 is rejected if t Step 4: t=avg. of dif/[sd/√n] t=(1.00)/[3.162/√8]=0.89 Step 5: H 0 is not rejected. There is no significant difference in the rental charged.

Independent Sample t-test: Comparing Two Population Means A recent EPA study compared the highway fuel economy of domestic and imported passenger cars. A sample of 15 domestic cars revealed a mean of 33.7 mpg with a standard deviation of 2.4 mpg. A sample of 12 imported cars revealed a mean of 35.7 mpg with a standard deviation of 3.9. At the.05 significance level can the EPA conclude that the mpg is higher on the imported cars? (Let subscript 1 be associated with domestic cars.) Step 1: Ho μ 2 μ 1 Step 2: The significance level is.05 Step 3: H0 is rejected if t<-1.708, df=25 Step 4: t= Step 5: H0 is not rejected. There is insufficient sample evidence to claim a higher mpg on the imported cars.

Contents of the Research Proposal & Report 1.A. Research Proposal 1.A.1. Problem Statement: Background of the problem 1.A.2. Research Objective: What the research is actually going to do How it solves the problem 1.A.3. Importance/Benefits: Mention in points 1.A.4. Research Design 1.A.4.1. Elements of research design in brief 1.A.4.2. Research Instrument: Approximate number of questions, sample size, mail/hand delivered, geographical premises 1.A.4.3. Pilot test if any

1.A.5. Data Analysis 1.A.6. Result & Deliverables 1.A.7. Budget 1.A.7.1. Time 1.A.7.2. Money

Writing Research Report 1.B. Abstract 1.B.1. Research Topic 1.B.2. Data and methods utilized 1.B.3. Summary 1.B.4 Conclusion

2. Research Topic and Introduction 3. Literature Review 4. Theoretical Framework 5. Hypotheses 6. Methodology 7. Data Findings and Analysis 8. Conclusion 9. Limitations 10. Discussion & Recommendations 11. References 12. Appendix Research Correspondence if any Research Instrument: The Questionnaire

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Summary Regression Analysis Paired Sample t-tests Independent Sample t-tests Contents of Research Proposal and Report