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 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 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) 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 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 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 1 Number of Families 75 2 23 3 9 2 1 Total 101 Preliminary Data Analysis Tabulation Compute Percentages Eliminate non-responses Note – Report without missing data Number of Cars 1 Number of Families 75% 2 23% 3 Total 2% 100 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 1 48 27 75 2 or More 6 19 25 Total 54 46 Total 100 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? Lower Income Higher Income Total 1 64% 36% 100% 2 or More 24% 76% 100% Total 54% 46% 100% Num ber of Cars 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% Lower Income Higher Income 1 89% 59% 75% 2 or More 11% 41% 25% Num ber of Cars Total Total 100% 100% 100% 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 Preliminary Data Analysis Chi-square analysis Tests the hypothesis that two or more nominallyscaled variables are NOT independent 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 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 Num ber of Cars Lower Income Higher Income Total 1 75 2 or More 25 Total 54 46 100 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 = ? Lower Income Higher Income 1 E1 E2 75 2 or More E3 E4 25 Total 54 46 100 Num ber of Cars Total Preliminary Data Analysis Compute C2 value Cell Oi C2 = S (Oi – Ei)2/Ei Computed C2 = 12.08 E1 df = (rows - 1) x (cols. - 1) = 1 x 1 =1 a = .05 Critical C2 = 3.84 12.08 > 3.84: Reject the Null Hypothesis (reject if Computed > Critical) Ei Oi - Ei (Oi – Ei)2 (Oi – Ei)2/Ei 48 40.5 7.5 56.25 1.39 E2 27 34.5 -7.5 56.25 1.63 E3 6 13.5 -7.5 56.25 4.17 E4 19 11.5 7.5 56.25 4.89 C2 12.08 S Preliminary Data Analysis Conclusion Income has an influence on number of cars in a family