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 Number of Cars Number of Families 175 223 32 91 Total101

7. Preliminary Data Analysis Tabulation  Compute Percentages  Eliminate non-responses  Note – Report without missing data Number of Cars Number of Families 175% 223% 32% Total100

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 Number of Cars Lower Income Higher Income Total 14827 75 2 or More 619 25 Total 5446100

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? Num ber of Cars Lower Income Higher Income Total 164%36%100% 2 or More 24%76%100% Total 54%46%100%

10. Preliminary Data Analysis Cross Tabulation  To analyze the data Does income level “cause” number of cars? Seem like this is the case. In the direction of income – thus, income marginal totals should be 100% Num ber of Cars Lower Income Higher Income Total 189%59%75% 2 or More 11%41%25% Total 100%

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  Tests the hypothesis that two or more nominally- scaled variables are NOT independent Null hypothesis (H O ) is that the variables are independent (i.e., no relationship exists) Alternative hypothesis (H A ) is that a statistical relationship exists among the variables  Present example H O : Income level will have no affect on the number of cars that a family owns H A : 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 (C 2 )  Compare computed C 2 to critical C 2  Table 4 on p. 442 in text Num ber of Cars Lower Income Higher Income Total 1 75 2 or More 25 Total 5446100

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 = ? Num ber of Cars Lower Income Higher Income Total 1E1E2 75 2 or More E3E4 25 Total 5446100

15. Preliminary Data Analysis Compute C 2 value C 2 =  (O i – E i ) 2 /E i Computed C 2 = 12.08 df = (rows - 1) x (cols. - 1) = 1 x 1 =1  =.05 Critical C 2 = 3.84 12.08 > 3.84: Reject the Null Hypothesis (reject if Computed > Critical) CellOiOi EiEi O i - E i (O i – E i ) 2 (O i – E i ) 2 /E i E1 4840.57.5 56.25 1.39 E2 2734.5-7.5 56.25 1.63 E3 613.5-7.5 56.25 4.17 E4 1911.57.5 56.25 4.89  C2C2 12.08

16. Preliminary Data Analysis Conclusion  Income has an influence on number of cars in a family