Analysis of Cross- Sectional Data Exercise WS 2017/18

Transcription

1 Analysis of Cross- Sectional Data Exercise WS 2017/18 Exercise III: Variables October 25 / 26, 2017 czymara@wiso.uni-koeln.de

2 Remember So far: types of data Experimental vs. observational Cross-section, panel, time series, pooled cross-section Today Types of variables Their description & analysis

3 Quantitative data Non-metric (distance between scale values can t be measured) vs. metric nominal ordinal discrete: can only take particular (but possibly many) values continuous (dt. stetig): can occupy any value over a continuous range. Practically, an underlying continuous construct is sufficient

4 Levels of measurement Categorical Continuous Level of measurement Nominal Characteristics Identification No intrinsic order Examples Gender, country of origin Ordinal Order (<, =, >) Level of education, Likert scales Interval Ratio Order Difference Arbitrary zero point Like interval but absolute zero points Temperature in Celsius, year dates Temperature in Kelvin, income, age Absolute Like ratio but fixed units Rooms in a house, inhabitants in a country

5 Odds & odds ratios Group 1 Group 2 Category 1 a b N(cat. 1) Category 2 c d N(cat. 2) N(group 1) N(group 2) Odds: Relations, e. g. from cat. 1 to cat. 2: N(cat. 1) / N(cat. 2) Odds ratios: Relations of relations, e. g. from cat. 1 to cat. 2 for group 1 to group 2: (a/c) / (b/d)

6 Reading odds ratios! Group 1 Group 2 Category 1 a b Category 2 c d Formula Odds ratios OR >1: odds are higher in first group (compared to second); <1: odds are smaller in first group (compared to second) But NOT The probability!! The odds (chances) of being in category 1 rather than in category 2 are [OR] times larger (smaller) for group 1 than for group 2. Alternatively: The odds (chances) of being in category 1 rather than in category 2 are [(OR-1)*100] percent larger (smaller) for group 1 than for group 2.

7 Odds vs. probability Simple example: flipping a coin Odds of heads (vs. tails): 1:1 Probability of heads: 50% But both mathematically related: probability heads = odds(heads) 1 + odds(heads) Cf.

8 Odds & odds ratios in a nutshell Gender (x) Passanger survivied (Y) Yes (b1) No (b2) Total Female (a1) 344(h11) 126 (h12) 470 (h1.) Male (a2) 367 (h21) 1364 (h22) 1731 (h2.) Total 711 (h.1) 1490 (h.2) 2201 (n) O surv., no surv. female = survival female no survival female O b1, b2 X = a 1 = h 11 h 12 O surv., no surv. male = survival male no survival male O b1, b2 X = a 2 = h 21 h 22 OR = Odds survival, no survival female Odds survival, no survival male OR = O b1, b2 X = a 1 O b1, b2 X = a 2 = h 11/h 12 h 21 /h 22

9 Exercise III: Variables (p. 75 f.)

10 Help for exercise 3: No 2 (p. 75 f.) a) Variable Type Description Scale age Continuous?? sex? 1=male, 2=female nominal degree??? papres80??? b) Use tab command e) Use options:,by & discrete & percent i) Tab degree fpresqu

11 2a solution Variable Type Description Scale age continuous Age (in years) ratio sex categorical 1=male, 2=female nominal degree categorical 5 categories ordinal papres80 continuous Prestige scale ordinal / interval

12 Multiple choice questions

13 + = + =

14 Percentage men: 50/632= Percentage women: 31/876= Difference: =0.0437

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17 Happy holiday (so next week no lecture & no exercises)

18 In addition: Stata commands

19 DESCRIPTION Frequency table Calculator (odds) Cross-table COMMAND tab varname dis a/b tab varname1 varname2 (rows) (columns) Histogram hist varname1, by(varname2) discrete percent Quantiles (creates equal sized groups out of a continuous variable) xtile newvar = oldvar, n(#) # = Number of quantiles Universität zu Köln Folie: 8

20 DESCRIPTION Summarize with extra details Cross-table Histogram Box-plot Box-plots for different groups COMMAND sum varname, detail tab varname1 varname2 (rows) (columns) hist varname graph box varlist graph box varlist, over(varname) (group) Universität zu Köln Folie: 10