Quantitative Analysis. ESP178 Research Methods Professor Susan Handy 2/23/16

Transcription

1 Quantitative Analysis ESP178 Research Methods Professor Susan Handy 2/23/16

2 You ve done your survey. You ve got your data. Now what?

3 Back to the cul-de-sac example Living on a cul-de-sac Outdoor play

4 8 Neighborhoods Survey 4 matched-pairs of neighborhoods By location: metro area, small city By design: traditional, suburban Random sample in each neighborhood: Recent movers All residents Mail-out, mail-back survey Two mailings of survey Two post-card reminders 1672 respondents (24.7%) About $10 per completed survey Manual data entry twice!

5 Data preparation not trivial! Data entry: for mail surveys and in-person surveys; check for accuracy (e.g. enter data twice) Data coding: create codebook that defines each variable, its response scale, how it was coded Missing values: delete surveys with too many missing values or impute missing values based on data you do have Data transformation: e.g. convert positive to negative responses; convert ratio variables to nominal

6 Each row is a survey response one person or household Each column is a variable one question on the survey

7 Codebook shows important information for each variable

8 Measure of living on a cul-de-sac

9 Measure of outdoor play

10 What do the variables look like? Use descriptive statistics.

11 Review: Levels of measurement Level Nominal Ordinal Ratio Definition Categorical, no order Categorical, with order Continuous variable Level of measurement determines what kind of analysis Note: We ll ignoring interval variables here

12 What kind of variables to we have here? Ordinal but could be converted to nominal Ratio but could be converted to nominal

13 What descriptive statistic(s) do we look at for outdoor play? ratio version Statistics - Number of days children played outside in last 7 days N Valid 389 Missing 10 Mean 2.81 Median 2.00 Mode 0 Std. Deviation Variance Percentiles Measures of Central Tendency Measures of Variation

14 What descriptive statistic(s) do we look at for outdoor play? ratio version Frequencies - Number of days children played outside in last 7 days Frequency Percent Valid Percent Cumulative Percent Valid Total Missing System Total

15 What descriptive statistic(s) do we look at for outdoor play? ratio version Histogram - Number of days children played outside in last 7 days Frequency Q II. #6d - Times Playing Mean = 2.81 Std. Dev. = N = 389

16 What descriptive statistic(s) do we look at for outdoor play? nominal version Statistics - Children Played Outside at least once in Last 7 Days N Valid 389 Missing 10 Mean.7147 Median Mode 1.00 Std. Deviation Variance.204 Percentiles

17 What descriptive statistic(s) do we look at for outdoor play? nominal version Frequencies - Children Played Outside at least once in Last 7 Days Frequenc y Percent Valid Percent Cumulative Percent Valid Total Missing System Total

18 What descriptive statistic(s) do we look at for outdoor play? nominal version Histogram - Children played outside at least once in Last 7 Days Frequency outside_play Mean = Std. Dev. = N = 389

19 What descriptive statistic(s) do we look at for living on cul-de-sac? ordinal version Not at all true Entirely true

20 What descriptive statistic(s) do we look at for living on cul-de-sac? nominal version Not on cul-de-sac On cul-de-sac

21 Is there an association? Use bivariate analysis.

22 Statistics by variable types Independent Variable Nominal or Ordinal Dependent Variable Nominal or ordinal Crosstabulation with Chi-square test Ratio Difference of means with t- test (if 2 categories) Analysis of Variance (ANOVA) with F-test (if multiple categories) Ratio Logistic regression Correlation coefficient Other forms of modeling Linear regression Other forms of modeling

23 Association? Days playing outside in last 7 days Difference = 0.99 days 0.0 Not cul-de-sac Cul-de-sac Is this a big enough difference that we can say they are different?

24 Review: hypotheses Null hypothesis: means are not different H 0 : µ 1 = µ 2 Alternative hypothesis: means are different H 1 : µ 1 µ 2 Is the difference in means big enough that we can reject the null hypothesis? Remember sampling error: we don t know for sure that sample mean = population mean

25 Review: p-values Probability of obtaining an effect at least as extreme as the one in the sample data if the null hypothesis is true. Could it be chance? How to use it Choose a significance level, e.g. α = 0.10, 0.05, or 0.01 If p-value is less than α, then reject null hypothesis. If p-value is greater than α, then do not reject null hypothesis. Helpful video by KahnAcademy

26 Nominal vs. ratio association Number of times children played outside in last 7 days vs. living on cul-de-sac 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Total Reflects difference between each case and the mean SD/N 0.5 Mean +/- 2 SE Whoops!

27 Not on cul-de-sac On cul-de-sac

28 Nominal vs. ratio association Number of times children played outside in last 7 days vs. living on cul-de-sac 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Total Student s t-test* = p < *t = ( mean 1 mean 0 )/square root (sd 12 /N 1 + sd 02 /N 0 )

29 Nominal vs. ratio association Analysis of Variance (ANOVA) Sum of Squares df Mean Square F Sig. Between Groups Within Groups Total F is a measure of difference between the groups vs. differences within group F = btwn groups mean sqquare = btwn groups sum of squares/df w/in groups mean square w/in groups sum of squares/df Where: Between group sum of squares = (mean for group overall mean) 2 Within group sum of squares = (individual observation group mean) 2

30 Nominal vs. nominal association Crosstabulation - Children played outside at least once in last 7 days vs. living on cul-de-sac culdesac Total outside_play.00 Count % within culdesac 32.5% 23.7% 29.8% 1.00 Count % within culdesac 67.5% 76.3% 70.2% Total Count % within culdesac 100.0% 100.0% 100.0% Chi-square statistic = p = 0.083

31 Is there a non-spurious association? Use multivariable analysis that takes into account control variables.

32 Regression models e.g. general linear model (GLM) Y = β 0 + β 1 X 1 + ε Y = days playing outside X = living on a cul-de-sac β 0 = constant or intercept, i.e. baseline days playing outside β 1 = coefficient or slope, i.e. effect of living on a cul-de-sac ε = error term Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 + ε

33 Regression model - # days playing Unstandardized Standardized P-value Coefficients Coefficients t Sig. B Std. Error Beta H 0 : B=0 H 1 : B 0 (Constant) Culdesac (1,0) Work or not current (1,0) Current Total Income Presence of related kids <=5 (1,0) Presence of related kids <=12 (1,0) Safe for Kids (1-4) Low Traffic (1-4) Low Crime(1-4) Nbr Interaction (1-4) Nbrs Active Outside (1-4) Adjusted R-square = Diff in play for 1 std dev diff in var Difference in play for a 1 unit difference in variable

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35 Looking at regression models Is the coefficient positive or negative? How big is the coefficient how much impact does the independent variable have on the dependent variable? What is the p-value can we reject the null hypothesis that the coefficient is 0? What is the adjusted R-square for the model how much of the variation in the dependent variable do the independent variables explain?

36 To do Bring 3 copies of your draft survey to class on Thursday! Meet in 1034 PES for section on Friday!!! Assignment 4 due next Tuesday!