Task: · Your task is to analyze the results of tax compliance experiment. · Try to describe the behavior of participants (overall and session by session) during the experiment. The main variables of interest are as follows: · RealIncome - endowment (earnings) · ConIncome - income declare to tax authority · Control - if 1=> subject audited by tax authority · Catch - audit found subject "guilty." · rpref[1] -rpref[10] - risk aversion check Variables Treatment value 1 2 3 4 meaning baseline flat tax rate progressive tax rate regressive tax rate value 5 6 7 8 meaning flat t.r. + positive news headlines flat t.r. + negative news headlines baseline + positive news headlines baseline + negative news headlines Session value 1 or 2 meaning up to 2 sessions per treatment Subject value 1 to 24 meaning unique identification of an experimental subject in a session Group value 1 to 6 meaning subject in a session were divided into smaller groups who interact together RealIncome meaning in treatments 1, 7, 8 randomly given number other treatments from a real effort tasks ConIncome meaning reported income for taxation Compliance value 0 1 meaning RealIncome==ConIncome RealIncome>ConIncome Control value 0 1 meaning not audited audited Catch value 0 1 meaning not found guilty found guilty rpref[1-10] value 1 to 2 meaning risk preferences Description of data Table 1 - Number of Subjects (and their characteristics) per Treatment Treatment 1 2 3 4 5 Subjects 44 44 40 32 48 male 19 12 16 12 14 Czech 40 39 33 27 45 risk averse 2 6 3 2 4 risk neutral 41 35 36 30 43 risk loving 1 3 1 0 1 Treatment 6 7 8 total Subjects 44 44 40 332 male 19 12 16 121 Czech 40 39 33 298 risk averse 2 6 3 30 risk neutral 41 35 36 292 risk loving 1 3 1 10 Mann-Whitney U Test Mann-Whitney U test is the alternative test to the independent sample t-test. It is a non-parametric test that is used to compare two population means that come from the same population, it is also used to test whether two population means are equal or not. It is used for equal sample sizes, and is used to test the median of two populations. (see e.g. http://www.statisticssolutions.com/mann-whitney-u-test/) Test of session effect - Compare mean contribution (ConIncome) between two sessions of the same treatment In STATA: runksum by Treatment, sort : ranksum ConIncome, by(Session) --------------------------------------------------------------------------------------------------- ------------------------------------- -> Treatment = 1 Two-sample Wilcoxon rank-sum (Mann-Whitney) test Session | obs rank sum expected -------------+--------------------------------- 1 | 120 11921 13260 2 | 100 12389 11050 -------------+--------------------------------- combined | 220 24310 24310 unadjusted variance 221000.00 adjustment for ties -288.17 ---------- adjusted variance 220711.83 Ho: ConInc~e(Session==1) = ConInc~e(Session==2) z = -2.850 Prob > |z| = 0.0044 means differ at 99% significance level – Session effect --------------------------------------------------------------------------------------------------- ------------------------------------- -> Treatment = 2 Two-sample Wilcoxon rank-sum (Mann-Whitney) test Session | obs rank sum expected -------------+--------------------------------- 1 | 120 12902.5 13260 2 | 100 11407.5 11050 -------------+--------------------------------- combined | 220 24310 24310 unadjusted variance 221000.00 adjustment for ties -229.51 ---------- adjusted variance 220770.49 Ho: ConInc~e(Session==1) = ConInc~e(Session==2) z = -0.761 Prob > |z| = 0.4467 means do not differ at 99% significance level – No session effect Chi-square test The chi-square test is always testing what scientists call the null hypothesis, which states that there is no significant difference between the expected and observed result. Usually refers to frequency tables. The test measures (non)existence of differences between cells. Null hypothesis => no difference. In our example – to test whether there is a difference between compliance rate (Compliance) among treatments. STATA: . tabulate Compliance Treatment, chi2 column Compliance 1 2 3 4 5 6 7 8 Total 0 122 112 105 109 134 87 117 80 866 55.45 50.91 52.50 68.13 55.83 39.55 58.50 40.00 52.17 1 98 108 95 51 106 133 83 120 794 44.55 49.09 47.50 31.87 44.17 60.45 41.50 60.00 47.83 Total 220 220 200 160 240 220 200 200 1,66 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 Pearson chi2(7) = 47.8479 Pr = 0.000 Differences are significant at 99% level