Summary of the results of the statistical tests regarding the distinct degrees of PaRA across genders
| Test | Test explanation | Test hypothesis | Task1 (PaRA) (Women = Men) | Task2 (PaRA) (Women = Men) | Task3 (PaRA) (Women = Men) | Women = Men (average of Pa-Tasks) | Overall conclusion |
|---|---|---|---|---|---|---|---|
| Wilcoxon-Mann-Whitney test | It tests whether the distributions in two groups are the same (non-parametric) | H0: Both distributions are the same | Reject H0 at 10% Prob>|z| = 0.0596 H1: Women≠Men Confirm H1 | Fail to Reject H0 Prob>|z| = 0.4128 H1: Women≠Men Cannot Confirm H1 | Reject H0 at 10% Prob>|z| = 0.0299 H1: Women≠Men Confirm H1 | Reject H0 at 10% Prob>|z| = 0.0687 H1: Women≠Men Confirm H1 | It shows that most designs as well as their average confirm that Women’s PaRA ≠ Men’s PaRA |
| Kolmogorov-Smirnov equality-of-distributions test | It tests the equality of distributions (non-parametric) | H0: Both distributions are the same | Fail to Reject H0 Co. P-value = 0.525 H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 P-value = 0.622 H1: Women≠Men Cannot Confirm H1 | Reject H0 at 10% P-value = 0.033 H1: Women≠Men Confirm H1 | Reject H0 at 10% P-value = 0.073 H1: Women≠Men Confirm H1 | It shows that the 3rd design as well as the average of the designs confirm that Women’s PaRA ≠ Men’s PaRA |
| Two-sample t-test for unpaired data (using mid-point CRRA’s) | It tests the equality of the means of a normally-distributed variable for two independent groups (parametric) | H0: The mean of the difference is zero | Reject H0 at 10% Prob(T > t) = 0.0249 H1: Women > Men Confirm H1 | Fail to Reject H0 Prob(T > t) = 0.2247 H1: Women > Men Cannot Confirm H1 | Reject H0 at 10% Prob(T > t) = 0.0139 H1: Women > Men Confirm H1 | Reject H0 at 10% Prob(T > t) = 0.0189 H1: Women > Men Confirm H1 | It shows that most designs as well as their average confirm that Women’s PaRA > Men’s PaRA |
| Regression analysis using ordered Probit model | It estimates relationships between an ordinal dependent variable and one or more independent variable(s) (An ordinal regression analysis) | H0: The difference between men’s degree of PaRA and that of women is zero | Reject H0 at 10% Prob>|z| = 0.035 Coef = −0.470 S.E. = 0.223 Z = −2.10 95% C.I. = [−0.908, −0.032] H1: Women > Men Confirm H1 | Fail to Reject H0 Prob>|z| = 0.527 Coef = −0.140 S.E. = 0.222 Z = −0.63 95% C.I. = [−0.574, 0.294] H1: Women > Men Cannot Confirm H1 | Reject H0 at 10% Prob>|z| = 0.044 Coef = −0.452 S.E. = 0.224 Z = −2.02 95% C.I. = [−0.891, −0.128] H1: Women > Men Confirm H1 | Reject H0 at 10% Prob>|z| = 0.096 Coef = −0.365 S.E. = 0.219 Z = −1.67 95% C.I. = [−0.796, 0.065] H1: Women > Men Confirm H1 | It shows that most designs as well as their average confirm that Women’s PaRA > Men’s PaRA |
| Test | Test explanation | Test hypothesis | Task1 (PaRA) | Task2 (PaRA) | Task3 (PaRA) | Women = Men (average of Pa-Tasks) | Overall conclusion |
|---|---|---|---|---|---|---|---|
| Wilcoxon-Mann-Whitney test | It tests whether the distributions in two groups are the same (non-parametric) | H0: Both distributions are the same | Reject H0 at 10% | Fail to Reject H0 | Reject H0 at 10% | Reject H0 at 10% | It shows that most designs as well as their average confirm that |
| Kolmogorov-Smirnov equality-of-distributions test | It tests the equality of distributions (non-parametric) | H0: Both distributions are the same | Fail to Reject H0 | Fail to Reject H0 | Reject H0 at 10% | Reject H0 at 10% | It shows that the 3rd design as well as the average of the designs confirm that |
| Two-sample t-test for unpaired data (using mid-point CRRA’s) | It tests the equality of the means of a normally-distributed variable for two independent groups (parametric) | H0: The mean of the difference is zero | Reject H0 at 10% | Fail to Reject H0 | Reject H0 at 10% | Reject H0 at 10% | It shows that most designs as well as their average confirm that |
| Regression analysis using ordered Probit model | It estimates relationships between an ordinal dependent variable and one or more independent variable(s) | H0: The difference between men’s degree of PaRA and that of women is zero | Reject H0 at 10% | Fail to Reject H0 | Reject H0 at 10% | Reject H0 at 10% | It shows that most designs as well as their average confirm that |
Source(s): Author’s own work
Summary of the results of the statistical tests. Regarding the distinct degrees of PrRA across genders
| Test | Test explanation | Test hypothesis | Task4 (PrRA) (Women = Men) | Task5 (PrRA) (Women = Men) | Task6 (PrRA) (Women = Men) | Women = Men (average of Pr-Tasks) | Overall conclusion |
|---|---|---|---|---|---|---|---|
| Wilcoxon-Mann-Whitney test | It tests whether the distributions in two groups are the same (non-parametric) | H0: Both distributions are the same | Fail to Reject H0 Prob>|z| = 0.3597 H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 Prob>|z| = 0.2703 H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 Prob>|z| = 0.4776 H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 Prob>|z| = 0.1978 H1: Women≠Men Cannot Confirm H1 | It shows that under these three designs there is NOT strong evidence to suggest that Women’s PrRA ≠ Men’s PrRA |
| Kolmogorov-Smirnov equality-of-distributions test | It tests the equality of distributions (non-parametric) | H0: Both distributions are the same | Fail to Reject H0 P-value = 0.613 H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 P-value = 0.267 H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 P-value = 0.973 H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 P-value = 0.776 H1: Women≠Men Cannot Confirm H1 | It shows that under these three designs there is NOT much evidence to suggest that Women’s PrRA ≠ Men’s PrRA |
| Two-sample t-test for unpaired data (using mid-point CRRA’s) | It tests the equality of the means of a normally-distributed variable for two independent groups (parametric) | H0: The mean of the difference is zero | Fail to Reject H0 Prob(T < t) = 0.3098 H1: Women≠Men Cannot Confirm H1 | Reject H0 at 10% Prob(T < t) = 0.0932 H1: Women≠Men Confirm H1 | Fail to Reject H0 Prob(T < t) = 0.2039 H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 Prob(T < t) = 0.1315 H1: Women≠Men Cannot Confirm H1 | It shows that under these three designs (except for Task 5) there is NOT strong evidence to suggest that Women’s PrRA < Men’s PrRA |
| Regression analysis using ordered Probit model | It estimates relationships between an ordinal dependent variable and one or more independent variable(s) (An ordinal regression analysis) | H0: The difference between men’s degree of PrRA and that of women is zero | Fail to Reject H0 Prob>|z| = 0.319 Coef = 0.221 S.E. = 0.222 Z = 1.00 95% C.I. = [−0.214, 0.655] H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 Prob>|z| = 0.225 Coef = 0.267 S.E. = 0.221 Z = 1.21 95% C.I. = [−0.165, 0.700] H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 Prob>|z| = 0.326 Coef = 0.218 S.E. = 0.222 Z = 0.98 95% C.I. = [−0.218, 0.654] H1: Women≠Men Cannot Confirm H1 | Fail to Reject H0 Prob>|z| = 0.150 Coef = 0.313 S.E. = 0.218 Z = 1.44 95% C.I. = [−0.114, 0.739] H1: Women≠Men Cannot Confirm H1 | It shows that under these three designs, there is NOT strong evidence to suggest that Women’s PrRA < Men’s PrRA |
| Test | Test explanation | Test hypothesis | Task4 (PrRA) | Task5 (PrRA) | Task6 (PrRA) | Women = Men (average of Pr-Tasks) | Overall conclusion |
|---|---|---|---|---|---|---|---|
| Wilcoxon-Mann-Whitney test | It tests whether the distributions in two groups are the same (non-parametric) | H0: Both distributions are the same | Fail to Reject H0 | Fail to Reject H0 | Fail to Reject H0 | Fail to Reject H0 | It shows that under these three designs there is NOT strong evidence to suggest that |
| Kolmogorov-Smirnov equality-of-distributions test | It tests the equality of distributions (non-parametric) | H0: Both distributions are the same | Fail to Reject H0 | Fail to Reject H0 | Fail to Reject H0 | Fail to Reject H0 | It shows that under these three designs there is NOT much evidence to suggest that |
| Two-sample t-test for unpaired data (using mid-point CRRA’s) | It tests the equality of the means of a normally-distributed variable for two independent groups (parametric) | H0: The mean of the difference is zero | Fail to Reject H0 | Reject H0 at 10% | Fail to Reject H0 | Fail to Reject H0 | It shows that under these three designs (except for Task 5) there is NOT strong evidence to suggest that |
| Regression analysis using ordered Probit model | It estimates relationships between an ordinal dependent variable and one or more independent variable(s) | H0: The difference between men’s degree of PrRA and that of women is zero | Fail to Reject H0 | Fail to Reject H0 | Fail to Reject H0 | Fail to Reject H0 | It shows that under these three designs, there is NOT strong evidence to suggest that |
Comparative analysis of PaRA and PrRA across contexts: key findings from three statistical tests for Men
| Test | Test explanation | Test hypothesis | Men Task1 = Task6 (PaRA=PrRA) | Men Task2 = Task5 (PaRA=PrRA) | Men Task3 = Task4 (PaRA=PrRA) | Men PaRA=PrRA (average of Pa- and Pr-Tasks) | Overall conclusion |
|---|---|---|---|---|---|---|---|
| Wilcoxon matched-pairs signed-ranks test | It tests the equality of matched pairs of observations (non-parametric) | H0: Both distributions are the same | Reject H0 at 10% Prob>|z| = 0.0056 H1: PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob>|z| = 0.0020 H1: PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob>|z| = 0.0355 H1: PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob>|z| = 0.0005 H1: PaRAM≠PrRAM Confirm H1 | It shows that all of the designs as well as their average confirm that PaRAM≠PrRAM |
| Arbuthnott- Snedecor- Cochran sign test | It tests the equality of matched pairs of observations (non-parametric) | H0: The median of the differences is zero (the true proportion of positive (negative) signs is one-half) | Reject H0 at 10% Prob(.) = 0.0243 H1: PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob(.) = 0.0336 H1: PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob(.) = 0.0652 H1: PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob(.) = 0.0008 H1: PaRAM≠PrRAM Confirm H1 | It shows that all of the designs as well as their average confirm that PaRAM≠PrRAM |
| Two-sample t-test for paired data (using mid-point CRRA’s) | It tests if two variables have the same mean, assuming paired data (parametric) | H0: The mean of the difference is zero | Reject H0 at 10% Prob(|T|>|t|) = 0.0027 PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob(|T|>|t|) = 0.0005 PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob(|T|>|t|) = 0.0460 PaRAM≠PrRAM Confirm H1 | Reject H0 at 10% Prob(|T|>|t|) = 0.0005 PaRAM≠PrRAM Confirm H1 | It shows that all of the designs as well as their average confirm that PaRAM≠PrRAM |
| Test | Test explanation | Test hypothesis | Men | Men | Men | Men | Overall conclusion |
|---|---|---|---|---|---|---|---|
| Wilcoxon matched-pairs signed-ranks test | It tests the equality of matched pairs of observations (non-parametric) | H0: Both distributions are the same | Reject H0 at 10% | Reject H0 at 10% | Reject H0 at 10% | Reject H0 at 10% | It shows that all of the designs as well as their average confirm that |
| Arbuthnott- Snedecor- Cochran sign test | It tests the equality of matched pairs of observations (non-parametric) | H0: The median of the differences is zero (the true proportion of positive (negative) signs is one-half) | Reject H0 at 10% | Reject H0 at 10% | Reject H0 at 10% | Reject H0 at 10% | It shows that all of the designs as well as their average confirm that |
| Two-sample t-test for paired data (using mid-point CRRA’s) | It tests if two variables have the same mean, assuming paired data (parametric) | H0: The mean of the difference is zero | Reject H0 at 10% | Reject H0 at 10% | Reject H0 at 10% | Reject H0 at 10% | It shows that all of the designs as well as their average confirm that |
Source(s): Author’s own work
Comparative analysis of PaRA and PrRA across contexts: key findings from three statistical tests for Women
| Test | Test explanation | Test hypothesis | Women Task1 = Task6 (PaRA=PrRA) | Women Task2 = Task5 (PaRA=PrRA) | Women Task3 = Task4 (PaRA=PrRA) | Women PaRA=PrRA (average of Pa- and Pr-Tasks) | Overall conclusion |
|---|---|---|---|---|---|---|---|
| Wilcoxon matched-pairs signed-ranks test | It tests the equality of matched pairs of observations (non-parametric) | H0: Both distributions are the same | Fail to Reject H0 Prob>|z| = 0.9818 H1: PaRAW≠PrRAW Cannot Confirm H1 | Fail to Reject H0 Prob>|z| = 0.3828 H1: PaRAW≠PrRAW Cannot Confirm H1 | Reject H0 at 10% Prob>|z| = 0.0796 H1: PaRAW≠PrRAW Confirm H1 | Fail to Reject H0 Prob>|z| = 0.4669 H1: PaRAW≠PrRAW Cannot Confirm H1 | Most designs as well as their average confirms that PaRAW and PrRAW are NOT statistically significantly different |
| Arbuthnott- Snedecor- Cochran sign test | It tests the equality of matched pairs of observations (non-parametric) | H0: The median of the differences is zero (the true proportion of positive (negative) signs is one-half) | Fail to Reject H0 Prob(.) = 1.0000 H1: PaRAW≠PrRAW Cannot Confirm H1 | Fail to Reject H0 Prob(.) = 0.5716 H1: PaRAW≠PrRAW Cannot Confirm H1 | Fail to Reject H0 Prob(.) = 0.1516 H1: PaRAW≠PrRAW Cannot Confirm H1 | Fail to Reject H0 Prob(.) = 0.8601 H1: PaRAW≠PrRAW Cannot Confirm H1 | All designs as well as their average confirms that PaRAW and PrRAW are NOT statistically significantly different |
| Two-sample t-test for paired data (using mid-point CRRA’s) | It tests if two variables have the same mean, assuming paired data (parametric) | H0: The mean of the difference is zero | Fail to Reject H0 Prob(|T|>|t|) = 0.7724 H1: PaRAW≠PrRAW Cannot Confirm H1 | Fail to Reject H0 Prob(|T|>|t|) = 0.5466 H1: PaRAW≠PrRAW Cannot Confirm H1 | Reject H0 at 10% Prob(|T|>|t|) = 0.0652 H1: PaRAW≠PrRAW Confirm H1 | Fail to Reject H0 Prob(|T|>|t|) = 0.3736 H1: PaRAW≠PrRAW Cannot Confirm H1 | Most designs as well as their average confirm that PaRAW and PrRAW are NOT statistically significantly different |
| Test | Test explanation | Test hypothesis | Women | Women | Women | Women | Overall conclusion |
|---|---|---|---|---|---|---|---|
| Wilcoxon matched-pairs signed-ranks test | It tests the equality of matched pairs of observations (non-parametric) | H0: Both distributions are the same | Fail to Reject H0 | Fail to Reject H0 | Reject H0 at 10% | Fail to Reject H0 | Most designs as well as their average confirms that |
| Arbuthnott- Snedecor- Cochran sign test | It tests the equality of matched pairs of observations (non-parametric) | H0: The median of the differences is zero (the true proportion of positive (negative) signs is one-half) | Fail to Reject H0 | Fail to Reject H0 | Fail to Reject H0 | Fail to Reject H0 | All designs as well as their average confirms that |
| Two-sample t-test for paired data (using mid-point CRRA’s) | It tests if two variables have the same mean, assuming paired data (parametric) | H0: The mean of the difference is zero | Fail to Reject H0 | Fail to Reject H0 | Reject H0 at 10% | Fail to Reject H0 | Most designs as well as their average confirm that |
Source(s): Author’s own work
Summary of statistical tests on payoff-risk premiums and price-risk premiums for Men
| Test | Test explanation | Test hypothesis | For men: RPTask2 = RPTask5 (PaRPM = PrRPM) | Overall conclusion |
|---|---|---|---|---|
| Wilcoxon matched-pairs signed-ranks test | It tests the equality of matched pairs of observations (non-parametric) | H0: Both distributions are the same | Reject H0 Prob>|z| = 0.0013 H1: PaRPM≠PrRPM Confirm H1 | It shows that PaRPM ≠ PrRPM |
| Arbuthnott- Snedecor- Cochran sign test | It tests the equality of matched pairs of observations (non-parametric) | H0: The median of the differences is zero (the true proportion of positive (negative) signs is one-half) | Reject H0 Prob(.) = 0.0168 H1: PaRPM < PrRPM Confirm H1 | It shows that PaRPM < PrRPM |
| Two-sample t-test for paired data | It tests if two variables have the same mean, assuming paired data (parametric) | H0: The mean of the difference is zero | Reject H0 Prob(T < t) = 0.0002 H1: PaRPM < PrRPM Confirm H1 | It shows that PaRPM < PrRPM |
| Test | Test explanation | Test hypothesis | For men: RPTask2 = RPTask5 (PaRPM = PrRPM) | Overall conclusion |
|---|---|---|---|---|
| Wilcoxon matched-pairs signed-ranks test | It tests the equality of matched pairs of observations (non-parametric) | H0: Both distributions are the same | Reject H0 | It shows that |
| Arbuthnott- Snedecor- Cochran sign test | It tests the equality of matched pairs of observations (non-parametric) | H0: The median of the differences is zero (the true proportion of positive (negative) signs is one-half) | Reject H0 | It shows that |
| Two-sample | It tests if two variables have the same mean, assuming paired data (parametric) | H0: The mean of the difference is zero | Reject H0 | It shows that |
Source(s): Author’s own work
Summary of statistical tests on payoff-risk premiums and price-risk premiums for Women
| Test | Test explanation | Test hypothesis | For women: RPTask2 = RPTask5 (PaRPW = PrRPW) | Overall conclusion |
|---|---|---|---|---|
| Wilcoxon matched-pairs signed-ranks test | It tests the equality of matched pairs of observations (non-parametric) | H0: Both distributions are the same | Fail to reject H0 Prob>|z| = 0.2588 H1: PaRPW≠PrRPW Cannot Confirm H1 | It shows that PaRPW and PrRPW are NOT statistically significantly different |
| Arbuthnott- Snedecor- Cochran sign test | It tests the equality of matched pairs of observations (non-parametric) | H0: The median of the differences is zero (the true proportion of positive (negative) signs is one-half) | Fail to reject H0 Prob(.) = 0.5716 H1: PaRPW≠PrRPW Cannot Confirm H1 | It shows that PaRPW and PrRPW are NOT statistically significantly different |
| Two-sample t-test for paired data | It tests if two variables have the same mean, assuming paired data (parametric) | H0: The mean of the difference is zero | Fail to reject H0 Prob(T < t) = 0.3627 H1: PaRPW≠PrRPW Cannot Confirm H1 | It shows that PaRPW and PrRPW are NOT statistically significantly different |
| Test | Test explanation | Test hypothesis | For women: RPTask2 = RPTask5 (PaRPW = PrRPW) | Overall conclusion |
|---|---|---|---|---|
| Wilcoxon matched-pairs signed-ranks test | It tests the equality of matched pairs of observations (non-parametric) | H0: Both distributions are the same | Fail to reject H0 | It shows that |
| Arbuthnott- Snedecor- Cochran sign test | It tests the equality of matched pairs of observations (non-parametric) | H0: The median of the differences is zero (the true proportion of positive (negative) signs is one-half) | Fail to reject H0 | It shows that |
| Two-sample | It tests if two variables have the same mean, assuming paired data (parametric) | H0: The mean of the difference is zero | Fail to reject H0 | It shows that |
Source(s): Author’s own work