Introduction to Data Analysis

1. Introduction to Data Analysis • Why do we analyze data? • Make sense of data we have collected • Basic steps in preliminary data analysis • Editing • Coding • Tabulating

2. Introduction to Data Analysis • Editing of data • Impose minimal quality standards on the raw data • Field Edit -- preliminary edit, used to detect glaring omissions and inaccuracies (often involves respondent follow up) • Completeness • Legibility • Comprehensibility • Consistency • Uniformity

3. Introduction to Data Analysis • Central office edit • More complete and exacting edit • Best performed by a number of editors, each looking at one part of the data • Decisions on how to handle item non-response and other omissions need to be made • List-wise deletion (drop for all analyses) vs. case-wise deletion (drop only for present analysis)

4. Introduction to Data Analysis • Coding -- transforming raw data into symbols (usually numbers) for tabulating, counting, and analyzing • Must determine categories • Completely exhaustive • Mutually exclusive • Assign numbers to categories • Make sure to code an ID number for each completed instrument

5. Introduction to Data Analysis • Tabulation -- counting the number of cases that fall into each category • Initial tabulations should be preformed for each item • One-way tabulations • Determines degree of item non-response • Locates errors • Locates outliers • Determines the data distribution

6. Preliminary Data Analysis • Tabulation • Simple Counts • For example • 74 families in the study own 1 car • 2 families own 3 • Missing data (9) • 1 Family did not report • Not useful for further analysis

7. Preliminary Data Analysis • Tabulation • Compute Percentages • Eliminate non-responses • Note – Report without missing data

8. Preliminary Data Analysis • Cross Tabulation • Simultaneous count of two or more items • Note marginal totals are equal to frequency totals • Allows researcher to determine if a relationship exists between two variables • Used a final analysis step in majority of real-world applications • Investigates the relationship between two ordinal-scaled variables

9. Preliminary Data Analysis • Cross Tabulation • To analyze the data • Calculate percentages in the direction of the “causal variable” • Does number of cars “cause” income level?

10. Preliminary Data Analysis • Cross Tabulation • To analyze the data • Does income level “cause” number of cars?

11. Preliminary Data Analysis • Cross Tabulation allows the development of hypotheses • Develop by comparing percentages across • Lower income more likely to have one car (89%) than the higher income group (59%) • Higher income more likely to have multiple cars (41%) than the lower income group (11%) • Are results statistically significant? • To test must employ chi-square analysis

12. Preliminary Data Analysis • Chi-square analysis • Allows the statistical testing of the independence of two or more nominally-scaled variables • Null hypothesis (HO) is that the variables are independent (i.e., no relationship exists) • Alternative hypothesis (HA) is that a statistical relationship exists among the variables • Present example • HO: Income level will have no affect on the number of cars that a family owns • HA: Income level will affect the number of cars that a family owns

13. Preliminary Data Analysis • Chi-square analysis • General Approach • Based on “marginal totals” compute the expected values per cell • Compare expected values to actual values to compute chi-square value (C2) • Compare computed C2 to critical C2 • Table 4 on p. 442 in text

14. Preliminary Data Analysis • Chi-square analysis • Compute Expected Values • E1 = (75 * 54)/100 • E1 = 40.5 • E2 = (75 * 46)/100 • E2 = 34.5 • Note E1 + E2 = 75 • E3 = ? • E4 = ?

15. Preliminary Data Analysis • Compute C2 value • C2 = S (Oi – Ei)2/Ei • C2 = • df = (rows - 1) + (cols. - 1) = 1 + 1 =2 • a = .05 • Critical C2 = 5.99 • 12.08 > 5.99: Reject the Null Hypothesis

16. Preliminary Data Analysis • Conclusion • Income has an influence on number of cars in a family • BUT: • Does family size matter?? • Do a 3-way Cross-Tabulation • Is Income more important than Family Size?

17. Preliminary Data Analysis • Total Data

18. Preliminary Data Analysis • Families with 4 Members or Less

19. Preliminary Data Analysis • Families with 5 Members or More

20. Preliminary Data Analysis Families with 4 Members or Less Families with 5 Members or More

21. Preliminary Data Analysis Create New Table – Look at those families with 2 or more cars by family size Families with 2 or More Cars by Income and Size Certainly Both family size and income level contribute to the number of cars that a family owns – But family size seems to be the driver