Historical Socioeconomic Statistical Comparison Male/Female Life Expectancy - Assignment Example

Historical Socioeconomic Statistical Comparison – Male/Female Life Expectancy Executive Summary The following statistical analysis has a sample of 101 countries from six regions of the world. The socioeconomic data is of the year 1990. The purpose of this is paper is to conduct analysis on the historical socioeconomic data in for comparison with data to be collect early 2013. The study makes several conclusions in the first analysis. The first major conclusion is that there is a strong positive correlation between male life expectancy and female life expectancy for the sample countries. Secondly, the mean GNP per capita in the sampled countries from Africa is significantly different from the World Bank’s GNP per capital for all African countries which was $300. Thirdly, the difference between life expectancies of male and female in the 6 regions is not statistically significant. In the second analysis, GNP per capita” is identified as the explanatory variable while the “percentage of adult literacy” is the response variable. A regression model is also specified as y = 62.9748 + 0.0017x. A change in GNP per capita by one dollar causes a 0.0017% proportional change in adult literacy. The model explains 29.71% of the variance in adult literacy. Research Analysis Analysis 1 a) Summary Statistics GNP ID Mean N Std. Deviation Minimum Maximum Range 1 1536.67 21 957.895 360 3610 3250 2 15074.81 27 8693.220 1640 32370 30730 3 4988.57 7 5174.313 560 12400 11840 4 296.67 6 129.409 170 470 300 5 680.97 31 837.991 110 3750 3640 6 4843.33 9 6907.000 610 22370 21760 Total 5353.37 101 7897.926 110 32370 32260 Where: GNP = GNP per capita, 1990 ID = Regional identify (1=Latin America; 2 = OECD; 3 = East Asia; 4 = Other Asia; 5 = Africa; 6 = Gulf) From the above summary statistics, there are six regions the countries being studied are divided into. Africa has the largest number of countries under study with 31 countries followed by OECD, Latin America, Gulf, East Asia and Other Asian countries in that order. The total numbers of countries studied are 101. OECD countries have the highest level of GNP per capital with a mean of $15074.81 followed by East Asia with $4988.57 which is closely followed by the Gulf region which has a mean GNP per capita of $4843.33. Latin America has the fourth largest GNP per capital recording a mean $15367 followed by Africa with $681 and lastly the Other Asian countries which score last with a approximately $298GNP per capital. From the entire population, the mean GNP per capita is $5353. OECD countries have the largest dispersion of GNP recording a range of 30730 with the maximum being $32370 vis a vis the minimum which is 1640. Other Asia countries have a range of only $300 showing uniformity of the socioeconomic situation among the countries, b) Scatterplots The above diagram shows a scatterplot of the male life expectancy and female life expectancy for the sample of 101 countries. The scatter plots move from the bottom left to the top right. This shows that as the male life expectancy increases, the female life expectancy also increases. There is therefore a strong positive relationship between male life expectancy and female life expectancy for the sample. c) T-Test One-Sample Statistics N Mean Std. Deviation Std. Error Mean GNP 31 680.97 837.991 150.508 One-Sample Test Test Value = 300 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper GNP 2.531 30 .017 380.968 73.59 688.35 According to the World Bank, GNP per capital for all African countries was $300. To verify this claim, a One Sample T-test is necessary. From the t-test, the first table, the mean GNP per capita for the 31 African countries being studied was proximately 681. From the One-Sample Test, the test value was $300. The significance level is 0.017 which is less than 0.05. The mean GNP per capita in the sampled countries from Africa is therefore significantly different from the World Bank’s GNP per capital for all African countries which was $300. There is therefore no statistical evidence for the World Banks claim. The assumption taken in this statistical analysis is that the data used from the sampled African countries is normally distributed. The One-Sample Test is however reasonably robust to vary from normality. d) Oneway Anova Descriptives N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound lexpf 1 21 69.52 6.282 1.371 66.66 72.38 56 78 2 27 78.59 2.925 .563 77.44 79.75 69 82 3 7 71.43 5.827 2.202 66.04 76.82 64 80 4 6 56.00 9.121 3.724 46.43 65.57 47 73 5 31 53.26 7.057 1.267 50.67 55.85 43 73 6 9 67.11 3.516 1.172 64.41 69.81 62 74 Total 101 66.07 11.669 1.161 63.77 68.37 43 82 lexpm 1 21 64.62 5.408 1.180 62.16 67.08 53 73 2 27 72.33 2.882 .555 71.19 73.47 64 76 3 7 66.57 5.318 2.010 61.65 71.49 60 75 4 6 56.17 7.468 3.049 48.33 64.00 49 69 5 31 49.84 6.277 1.127 47.54 52.14 40 67 6 9 63.89 2.934 .978 61.63 66.14 59 69 Total 101 61.71 10.240 1.019 59.69 63.73 40 76 Test of Homogeneity of Variances Levene Statistic df1 df2 Sig. lexpf 3.715 5 95 .004 lexpm 3.343 5 95 .008 The table above displays Levene’s test for homogeneity of variance. Since the significance level for both life expectancy for males and female is less than 0.05, the assumption of homogeneity of variance is violated. We will therefore use the Robust Tests of Equality of Means rather than the Anova table. ANOVA Sum of Squares df Mean Square F Sig. lexpf Between Groups 10392.220 5 2078.444 61.239 .000 Within Groups 3224.295 95 33.940 Total 13616.515 100 lexpm Between Groups 7986.091 5 1597.218 60.680 .000 Within Groups 2500.582 95 26.322 Total 10486.673 100 Robust Tests of Equality of Means Statistica df1 df2 Sig. lexpf Brown-Forsythe 53.802 5 24.920 .000 lexpm Brown-Forsythe 55.774 5 28.217 .000 a. Asymptotically F distributed. From the Robust Tests of Equality of Means, the significance column has figures less than 0.05. This means that life expectancy of women is different to that of men in at least one region across the world. We will therefore use the Post Hoc Tests to determine in which specific regions the significant difference occurs. Since the test for homogeneity of variance was violated, we will use the Game-Howell test (instead of) to determine the specify region with significant differences in male and female life expectancies. From the multiple comparisons table below, the mean difference column has asterisks is some but not all of the figures. This shows that in some regions, the difference between life expectancies of male and female is not statistically significant. This statistical evidence sufficiently rejects the claim that life expectancy of women across the world is different to that of men. Multiple Comparisons Dependent Variable (I) ID (J) ID Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound LEXPF Games-Howell 1 2 -9.069* 1.482 .000 -13.61 -4.53 3 -1.905 2.594 .973 -10.74 6.93 4 13.524 3.968 .087 -1.92 28.97 5 16.266* 1.867 .000 10.72 21.82 6 2.413 1.803 .762 -3.13 7.96 2 1 9.069* 1.482 .000 4.53 13.61 3 7.164 2.273 .111 -1.52 15.85 4 22.593* 3.766 .011 6.82 38.36 5 25.335* 1.387 .000 21.19 29.48 6 11.481* 1.300 .000 7.11 15.85 3 1 1.905 2.594 .973 -6.93 10.74 2 -7.164 2.273 .111 -15.85 1.52 4 15.429 4.326 .054 -.25 31.11 5 18.171* 2.541 .000 9.41 26.93 6 4.317 2.495 .545 -4.48 13.11 4 1 -13.524 3.968 .087 -28.97 1.92 2 -22.593* 3.766 .011 -38.36 -6.82 3 -15.429 4.326 .054 -31.11 .25 5 2.742 3.934 .976 -12.73 18.21 6 -11.111 3.904 .174 -26.65 4.42 5 1 -16.266* 1.867 .000 -21.82 -10.72 2 -25.335* 1.387 .000 -29.48 -21.19 3 -18.171* 2.541 .000 -26.93 -9.41 4 -2.742 3.934 .976 -18.21 12.73 6 -13.853* 1.726 .000 -19.13 -8.57 6 1 -2.413 1.803 .762 -7.96 3.13 2 -11.481* 1.300 .000 -15.85 -7.11 3 -4.317 2.495 .545 -13.11 4.48 4 11.111 3.904 .174 -4.42 26.65 5 13.853* 1.726 .000 8.57 19.13 LEXPM Games-Howell 1 2 -7.714* 1.304 .000 -11.69 -3.74 3 -1.952 2.331 .953 -9.98 6.07 4 8.452 3.269 .224 -4.17 21.08 5 14.780* 1.632 .000 9.93 19.63 6 .730 1.533 .997 -3.98 5.44 2 1 7.714* 1.304 .000 3.74 11.69 3 5.762 2.085 .176 -2.16 13.68 4 16.167* 3.099 .019 3.29 29.04 5 22.495* 1.257 .000 18.75 26.24 6 8.444* 1.124 .000 4.74 12.15 3 1 1.952 2.331 .953 -6.07 9.98 2 -5.762 2.085 .176 -13.68 2.16 4 10.405 3.652 .137 -2.60 23.41 5 16.733* 2.305 .000 8.75 24.71 6 2.683 2.236 .827 -5.30 10.66 4 1 -8.452 3.269 .224 -21.08 4.17 2 -16.167* 3.099 .019 -29.04 -3.29 3 -10.405 3.652 .137 -23.41 2.60 5 6.328 3.250 .453 -6.31 18.96 6 -7.722 3.202 .281 -20.43 4.99 5 1 -14.780* 1.632 .000 -19.63 -9.93 2 -22.495* 1.257 .000 -26.24 -18.75 3 -16.733* 2.305 .000 -24.71 -8.75 4 -6.328 3.250 .453 -18.96 6.31 6 -14.050* 1.493 .000 -18.60 -9.51 6 1 -.730 1.533 .997 -5.44 3.98 2 -8.444* 1.124 .000 -12.15 -4.74 3 -2.683 2.236 .827 -10.66 5.30 4 7.722 3.202 .281 -4.99 20.43 5 14.050* 1.493 .000 9.51 18.60 *. The mean difference is significant at the 0.05 level. Analysis 2 a) “GNP per capita” is the explanatory variable while the “percentage of adult literacy” is the response variable. An explanatory variable acts as an input while the response variable acts as the output. A high GNP per capital leads to a higher percentage of adult literacy since wealthy individuals can afford a good education system compared to poor ones. A high GNP per capital is therefore the cause while a high percentage of adult literacy is the effect. b)   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 62.9748 2.5486 24.7100 0.0000 57.9173 68.0323 57.9173 68.0323 X Variable 1 0.0017 0.0003 6.4355 0.0000 0.0012 0.0022 0.0012 0.0022 From the regression coefficients above, our model can be specified as: y = 62.9748 + 0.0017x Where: y = adult literacy and x = GNP per capita From the p-values column, the figures on both the intercept and the x variable rows are less than 0.05. This means that both the intercept (constant) and the GNP per capita are significant predictors of adult literacy. An increase in GNP per capita by one dollar causes a 0.0017% increase in adult literacy. c) d) The line does not provide an adequate fit to the data considering the fit from the diagram. This is because the actual adult literacy levels are not in tandem with the predicted adult literacy level. Regression Statistics Multiple R 0.5450 R Square 0.2971 Adjusted R Square 0.2899 Standard Error 21.0264 Observations 100.0000 From the R square, the regression model derived has a prediction power of approximately 29.71%. The model explains 29.71% of the variance in adult literacy. This prediction power is low. e) There is a significant relationship between adult literacy and GNP per capita. This is because the gradient of the line is different from zero. Specifically, the gradient of the line is 0.0017 showing that a change in GNP per capita by one dollar causes a 0.0017% proportional change in adult literacy. f) The diagram above represents plots of the regression residuals. There are no remaining patterns in the residuals, which might suggest ways to improve the model. The residuals are not normally distributed. g) The gradient of the line is 0.0017 showing that a change in GNP per capita by one dollar causes a 0.0017% proportional change in adult literacy. Using the regression line, y = 62.9748 + 0.0017x, 1) If GNP per capital is $100, percentage adult literacy = 62.9748 + 0.0017(100) = 63.1448. 2) If GNP per capital is $20,000, percentage adult literacy = 62.9748 + 0.0017(20,000) = 96.9748. Read More