ESP 178 Applied Research Methods 2/26: Quantitative Analysis Key Concepts from Chapter 14 (Chapter 12 in Red Book): Descriptive Statistics Frequency distributions and graphs to show central tendency, variation, and skewness Purpose Measure Variable Type Definition Measures of Mode Best for nominal Most frequent value central Median Ordinal, interval, ratio Position average the midpoint Mean Interval, ratio Arithmetic average tendency (sometimes ordinal) Measures of Range Interval, ratio Highest value lowest value + 1 variation (sometimes ordinal) Variance Interval, ratio Average squared deviation of each case from the (sometimes ordinal) mean Standard deviation Interval, ratio (sometimes ordinal) Square root of the variance Associations Between One or More Variables p-value: Probability that the association is due to chance; goal is p-values less than 0.05 (5% significance level) or 0.01 (1% significance level). Independent Variable Nominal or Ordinal Ratio or interval Dependent Variable Nominal or ordinal Crosstabulation with Chi-square test Logistic regression Other forms of modeling Ratio or interval Difference of means with t-test (if 2 categories) Analysis of Variance (ANOVA) with F-test (if multiple categories Correlation coefficient Linear regression Other forms of modeling Chi-square: Compares expected frequencies in cells to observed frequencies in cells F-statistic: Compares variation between groups to variation within groups Multivariate analysis: Allows us to test causal hypothesis with non-experimental data by testing for relationship between independent and dependent variables while controlling for other variables that might cause a spurious relationship. Ethical issues: guidelines for graphs (pg. 377) Readings for 2/27: See if you can understand tables on the following pages of the reader: pg. 56 (Tables 2 through 4) from Gaterslaben; pg. 101 (Table 3) from Grob; pg. 27 (Table 2) and pg. 28 (Table 4) from Staats. Bring 3 copies of your draft survey to section on Thursday! Remember to meet in 1137 PES on Thursday!
Frequencies - Number of Times Children Played Outside in Last 7 Days Statistics N Valid 389 Missing 10 Mean 2.81 Median 2.00 Mode 0 Std. Deviation 2.703 Variance 7.307 Percentiles 25.00 50 2.00 75 5.00 Frequency Percent Valid Percent Cumulative Percent Valid 0 111 27.8 28.5 28.5 1 47 11.8 12.1 40.6 2 56 14.0 14.4 55.0 3 39 9.8 10.0 65.0 4 28 7.0 7.2 72.2 5 32 8.0 8.2 80.5 6 11 2.8 2.8 83.3 7 57 14.3 14.7 97.9 8 2.5.5 98.5 10 5 1.3 1.3 99.7 15 1.3.3 100.0 Total 389 97.5 100.0 Missing System 10 2.5 Total 399 100.0 Histogram 120 100 80 Frequency 60 40 20 0-2 0 2 4 6 8 10 12 14 16 Mean = 2.81 Std. Dev. = 2.703 N = 389 2
Frequencies - Whether or Not Children Played Outside in Last 7 Days Statistics N Valid 389 Missing 10 Mean.7147 Median 1.0000 Mode 1.00 Std. Deviation.45216 Variance.204 Percentiles 25.0000 50 1.0000 75 1.0000 Frequency Percent Valid Percent Cumulative Percent Valid.00 111 27.8 28.5 28.5 1.00 278 69.7 71.5 100.0 Total 389 97.5 100.0 Missing System 10 2.5 Total 399 100.0 Histogram 400 300 Frequency 200 100 Mean = 0.7147 Std. Dev. = 0.45216 0 N = 389-0.50 0.00 0.50 1.00 1.50 3
Crosstabs - Cul-de-sac or Not vs. Played Outside or Not Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent * 373 93.5% 26 6.5% 399 100.0% * Crosstabulation Total.00 1.00.00 1.00 Total Count 83 28 111 % within 32.5% 23.7% 29.8% Count 172 90 262 % within 67.5% 76.3% 70.2% Count 255 118 373 % within 100.0% 100.0% 100.0% Chi-Square Tests Value df Asymp. Sig. (2-sided) Exact Sig. (2-sided) Exact Sig. (1-sided) Pearson Chi-Square 3.002(b) 1.083 Continuity Correction(a) 2.595 1.107 Likelihood Ratio 3.078 1.079 Fisher's Exact Test.089.052 Linear-by-Linear Association 2.994 1.084 N of Valid Cases 373 a Computed only for a 2x2 table b 0 cells (.0%) have expected count less than 5. The minimum expected count is 35.12. 4
Oneway ANOVA - Times Playing Outside by Cul-de-Sac or Not Descriptives 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum.00 255 2.48 2.492.156 2.17 2.79 0 10 1.00 118 3.47 3.063.282 2.92 4.03 0 15 Total 373 2.80 2.721.141 2.52 3.07 0 15 ANOVA Sum of Squares df Mean Square F Sig. Between Groups 79.420 1 79.420 11.015.001 Within Groups 2675.094 371 7.210 Total 2754.515 372 Oneway ANOVA - Times Playing Outside vs. Cul-de-sac score (1 to 4 scale) Descriptives 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum 1 229 2.50 2.533.167 2.17 2.83 0 10 2 26 2.31 2.131.418 1.45 3.17 0 7 3 38 3.34 3.034.492 2.34 4.34 0 10 4 80 3.54 3.093.346 2.85 4.23 0 15 Total 373 2.80 2.721.141 2.52 3.07 0 15 ANOVA Sum of Squares df Mean Square F Sig. Between Groups 81.287 3 27.096 3.740.011 Within Groups 2673.228 369 7.245 Total 2754.515 372 5
Regression - Times Playing Outside as Dependent Variable Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.361(a).130.104 2.604 a Predictors: (Constant), Q I. #9 - Nbrs Active Outside, #8 - Current Total Income,, presence of related kids <=5 current, Work or not current, Q I. #9 - Low Traffic, Q I. #9 - Low Crime, Q I. #9 - Nbr Interaction, presence of related kids <=12 current, Q I. #9 - Safe for Kids ANOVA(b) Model 1 Sum of Squares df Mean Square F Sig. Regressio n 343.683 10 34.368 5.070.000(a) Residual 2297.986 339 6.779 Total 2641.669 349 a Predictors: (Constant), Q I. #9 - Nbrs Active Outside, #8 - Current Total Income,, presence of related kids <=5 current, Work or not current, Q I. #9 - Low Traffic, Q I. #9 - Low Crime, Q I. #9 - Nbr Interaction, presence of related kids <=12 current, Q I. #9 - Safe for Kids b Dependent Variable: Coefficients(a) Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -.876.896 -.977.329.932.312.158 2.986.003 Work or not current.821.403.106 2.035.043 #8 - Current Total Income.000.000 -.045 -.860.391 presence of related kids <=5 -.265.346 -.048 -.766.444 current presence of related kids <=12 1.519.376.252 4.038.000 current Q I. #9 - Safe for Kids.762.269.203 2.827.005 Q I. #9 - Low Traffic -.161.165 -.057 -.974.331 Q I. #9 - Low Crime.042.246.012.169.866 Q I. #9 - Nbr Interaction.312.187.104 1.669.096 Q I. #9 - Nbrs Active Outside -.321.202 -.099-1.591.113 a Dependent Variable: 6