Research Tools and Techniques The Research Process: Step 7 (Data Analysis Part B) Lecture 29

Lecture Topics Covered Previously in the Last Lecture Introduction to Descriptive Statistics Measures of Central Tendency Measures of Dispersion

What we are going to Cover in this Lecture Methods of Bivariate Analysis Contingency tables X 2 Test Pearson’s Correlation

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

STATISTICAL DATA ANALYSIS BIVARIATE ANALYSIS: In this statistical analysis, the two variables are analyzed at a time in order to understand whether or not they are related. The hypotheses are tested applying this technique. MULTIVARIATE ANALYSIS: Statistical procedures that simultaneously analyze multiple measurements (Three or more variables) on each individual or object under study. It is the further extension of univariate and bivariate statistical procedures previously stated.

Methods of Bivariate Analysis NominalOrdinalInterval/RatioDichotomo us Nominal +Contingency Table +Chi Square +Cramer’s V +Contingency Table +Chi Square +Cramer’s V +Contingency Table +Chi Square +Cramer’s V If the interval/ratio variable is the dependent variable, Compare Means+Eta +Contingency Table +Chi Square +Cramer’s V Ordinal +Contingency Table +Chi Square +Cramer’s V Spearman’s rho Interval/Ratio +Contingency Table +Chi Square +Cramer’s V If the interval/ratio variable is the dependent variable, Compare Means+Eta Spearman’s rhoPearson’s rSpearman’s rho Dichotomous +Contingency Table +Chi Square+ Crm V Spearman’s rho Phi

Reasons for Visiting Gym Gender MaleFemale No.% % Relaxation Fitness Lose Weight Build Strength Total The cross tabulation / contingency table is like a frequency table but it allows two variables to be simultaneously analyzed so that patterns of association can be searched between them. Here in this example two category/nominal variables are analyzed simultaneously. Contingency Tables (A Bivariate Mode of Analysis)

X 2 Test Ho = The two criteria are independent Ha = The two criteria are associated with one another Level of significance α = 0.05 Test Statistics Used is x 2 = 3εi=1 2εj=1 (oij – eij) 2 / eij Degree of Freedom: (3-1)(2-1) 2x1 = 2 Do Watch Television Do Not Watch Television Total Morning Shift Evening Shift Night Shift Total Do Watch Television (B1) Do Not Watch Television (B2) Total Morning Shift (A1) 132x50/ 150 = Evening Shift (A2) Night Shift (A3) Total Table of Observed ValuesTable of Expected Values

X 2 - Statistical Table oijeijoij-eij(oij-eij) 2 (oij-eij) 2 /eij From the table critical region x ,(2) =5.99 X 2 Cal = 7.2 As x 2 Cal > x ,(2) 7.2>5.99 The Null hypothesis failed to get substantiated “The data provided statistical association between the variables of interest”

Pearson’s R Coefficient will lie between -1  0  +1 Y X Y X Y Perfect Positive Relationship +1 Perfect Negative Relationship -1 No Relationship 0 Age Use of Cardiovascular Equipment Age Use of Cardiovascular Equipment Correlation Coefficient: A quantitative description of the magnitude and direction of the linear relationship between two variables. Spearman’s Rho is just like Pearson’s R which is used for the data collected on Interval and Ratio Scales Variables whereas Rho is used for the Ordinal Scale Variables.

X Y (X-X) (Y-Y)(X-X)(Y-Y)  =25  30  =0  0  =18 X=5 Y=6

X Y (X-X) 2 (Y-Y)  =25  30  =28  30 (28x30=840) X=5 Y=6 Cor xy = 18 = 18 =.62 

Correlations between Employee’s Years in Service and Years with the Company, Senior Managers and Middle Managers, Bank Alfalah, 2010 Managerial Position Years With Company Senior Managers Years In Service Pearson Correlation.054 Sig. (2-tailed).725 N 45 Middle Managers Years In Service Pearson Correlation.540(**) Sig. (2-tailed).000 N 65 ** Correlation is significant at the 0.01 level (2-tailed). Phi and Cramer’s V: For dichotomous (phi) variables. Cramer’s V is for nominal variables but only in positive, indicates strength of relationship.

Summary Methods of Bivariate Analysis Contingency tables X 2 Test Pearson’s Correlation