The Level of Distress - Assignment Example

Quantitative Analysis in Social Science Research ID Question Interest was in testing whether the mean level of distress differs across the different levels of financial strain with regards to difficulties in paying bills. The hypothesis being tested is as follows Null hypothesis: the mean level of distress is the same across the levels of financial strain Alternative hypothesis: there is a difference in the mean level of distress in at least one of the levels of financial strain. The distribution of respondents based on their financial strain revealed that those who were very often financially strained had the highest distress levels while those who never were financially strained had the lowest distress level. An ANOVA test for whether there was a significant difference in the groups is shown in table 1. Table 1: Levels of Distress and Financial Strain—Difficulty Paying Bills financial | Summary of Distress strain | Mean Std. Dev. Freq. ------------+------------------------------------ never | 7.1135909 4.6651367 3002 rarely | 8.0343511 4.401147 1310 sometimes | 9.6756198 5.1753277 968 often | 10.764706 5.1637426 340 very often | 11.045455 5.7949559 330 ------------+------------------------------------ Total | 8.1598319 4.9749921 5950 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 10585.6409 4 2646.41022 115.13 0.0000 Within groups 136655.359 5945 22.9866037 ------------------------------------------------------------------------ Total 147241 5949 24.7505463 The between groups mean sum of squares is larger than the within groups sum of squares, resulting in a large F statistic. The p-value of the test is 0.0000, which at 5% significance level is highly significant. Therefore, there is a significant difference between the levels of financial strain with regards to distress. To evaluate whether the mean level of sleep problems varies with the level of financial strain, the hypothesis was formulated as follows. Null hypothesis: the mean level of sleep problems is the same across the levels of financial strain Alternative hypothesis: there is a difference in the mean level of sleep problems in at least one of the levels of financial strain. Respondents who were often financially strained had the highest mean level of sleep problems while those who were never financially strained had the least mean level of sleep problems. Results of an ANOVA test are presented in table 2. Table 2: Levels of Sleep Problems and Financial Strain—Difficulty Paying Bills Financial | Summary of Sleep Problems Strain | Mean Std. Dev. Freq. ------------+------------------------------------ never | 4.8709784 2.8872193 3015 rarely | 5.3860322 2.7949408 1303 sometimes | 5.8136842 2.9698205 950 often | 6.5216049 2.9667136 324 very often | 6.8125 3.0514878 272 ------------+------------------------------------ Total | 5.3194065 2.9479177 5864 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 1918.80676 4 479.701691 57.32 0.0000 Within groups 49031.9448 5859 8.36865417 ------------------------------------------------------------------------ Total 50950.7515 5863 8.69021858 As before, the mean sum of squares between the financial strain levels was much larger than that within the financial strain levels. This resulted in a large F statistic with a highly significant p-value (0.000) at 5% alpha level. The level of distress was hypothesized to vary with the education level of respondents. The corresponding hypothesis can be stated as follows; Null hypothesis: the mean distress level is the same across the levels of respondent’s education Alternative hypothesis: there is a difference in the mean distress levels in at least one of the respondents’ education levels. From the summary statistics (table 3 ), the respondents who had an 8th grade or less education level had the highest mean level of distress while graduates or those with advanced degree (MA/PHD) had the lowest mean distress levels. Results of an ANOVA test are presented in table 3. The P-value of 0.1573 is indicative of a non-significant difference in the mean distress across the respondents’ education level Table 3: Levels of distress and education | Summary of Distress Education | Mean Std. Dev. Freq. ---------------------------------+------------------------------------- 8th grade or less | 9.3269231 5.5367618 52 some high school but no degree | 8.5361111 5.6295902 360 high school graduate or GED | 8.014245 5.2263214 1053 specialized vocational training | 8.0605653 5.0459178 743 some college/univ, but no degree | 8.4041184 5.0854942 777 college graduate (BA/BS degree) | 8.1724138 4.7858766 2088 graduate/advanced degree (MA/PHD)| 7.9662005 4.5994799 858 ---------------------------------+------------------------------------- Total | 8.1630416 4.9754768 5931 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 230.247309 6 38.3745515 1.55 0.1573 Within groups 146569.091 5924 24.7415752 ------------------------------------------------------------------------ Total 146799.339 5930 24.7553691 Further statistical analysis using ANOVA may be done to evaluate whether the respondents’ level of distress varies with their gender. The hypothesis to test is as follows; Null hypothesis: there is no significant difference in the mean distress levels between males and females Alternative hypothesis: there is a significant difference between the levels of distress in males and females We expect a significant difference and therefore reject the null hypothesis. This is because males and females react do distress situations differently. QUESTION 2 A chi square test for the existence of an association between the respondents’ gender and financial strain levels was conducted and results presented in table 4. The hypothesis being tested is as follows; Null hypothesis: there is no significant association between the respondents’ gender and financial strain. Alternative hypothesis: there is a significant association between the respondents’ gender and financial strain. From the resulting output, there was no evidence of a significant association between gender and financial strain Table 4: Gender and Financial Strain--Difficulty Paying Bills Note: Low financial strain = “never, rarely, sometimes” responses to the question in Table 3.1A; High financial strain = “often, very often” responses to this same question. FIN Strain | Men Women | Total -----------+----------------------+---------- LOW | 2,187 3,135 | 5,322 | 2,167.9 3,154.1 | 5,322.0 | 89.56 88.24 | 88.77 -----------+----------------------+---------- HIGH | 255 418 | 673 | 274.1 398.9 | 673.0 | 10.44 11.76 | 11.23 -----------+----------------------+---------- Total | 2,442 3,553 | 5,995 | 2,442.0 3,553.0 | 5,995.0 | 100.00 100.00 | 100.00 Pearson chi2(1) = 2.5398 Pr = 0.111 This chi square test was for whether there was a significant association between males and females regarding job pressure. The corresponding hypotheis was; Null hypothesis: there is no significqnt association between the respondents’ gender and the feeling of being overwhelmed (Job pressure). Alternative hypothesis: there is a significant association between the respondents’ gender and job pressure From table 5 however, there was a significant association between gender and job pressure on the respondents. Table 5: Gender and Job Pressure—Felt Overwhelmed Note: Low job pressure = “never, rarely, sometimes” responses to the question in Table 3.2A; High job pressure = “often, very often” responses to this same question. JobPressure| Men Women | Total -----------+----------------------+---------- Low | 1,761 2,339 | 4,100 | 1,672.1 2,427.9 | 4,100.0 | 72.50 66.32 | 68.84 -----------+----------------------+---------- High | 668 1,188 | 1,856 | 756.9 1,099.1 | 1,856.0 | 27.50 33.68 | 31.16 -----------+----------------------+---------- Total | 2,429 3,527 | 5,956 | 2,429.0 3,527.0 | 5,956.0 | 100.00 100.00 | 100.00 Pearson chi2(1) = 25.6261 Pr = 0.000 Of interest also was the significance of the association between education and financial strain on the respondents. Null hypothesis: there is no significant association between respondents’ education and financial strain. Alternative hypothesis: there is a significant association between respondents’ education and financial strain. Results of the chi square test are presented in table 6, from which we conclude that there is a significant association between the respondents’ education level and their financial strain. Table 6: Education and Financial Strain--Difficulty Paying Bills Notes: Low financial strain = “never, rarely, sometimes” responses to the question in Table 3.1A; High financial strain = “often, very often” responses to this same question. Low education = less than college graduate (BA/BS degree) versus “high education” = college graduate (BA/BS degree) or more (from the original Table 1.4 in Part 1). Education Financial Strain | LOW HIGH | Total -----------+----------------------+---------- Low | 2,595 2,717 | 5,312 | 2,674.2 2,637.8 | 5,312.0 | 86.38 91.70 | 89.02 -----------+----------------------+---------- High | 409 246 | 655 | 329.8 325.2 | 655.0 | 13.62 8.30 | 10.98 -----------+----------------------+---------- Total | 3,004 2,963 | 5,967 | 3,004.0 2,963.0 | 5,967.0 | 100.00 100.00 | 100.00 Pearson chi2(1) = 43.0856 Pr = 0.000 Further analysis may be done on the observations on the employees perception on their job security and whether they feel the supervisor in unfair. The appropriate hypothesis to test in this case would be; Null hypothesis: there is no significant association between job security and employees’ perception on the supervisor’s fairness. Alternative hypothesis: there is a significant association between job security and employees’ perception on the supervisor’s fairness. There might be an association between these two variables in that employees who feel insecure about their jobs may more often than not find the supervisor to be unfair to them. QUESTION 3 Regression analysis to test the existence of a significant linear relationship between the psychological distress and economic hardship index was conducted. The null hypothesis presumed that there was no significant linear relationship. This assumption was however rejected based on the p-value of the covariate (table 7). There is therefore a significant positive linear relationship between the psychological distress and the economic hardship index. Therefore the mean psychological distress increases with the increase in the economic hardship index. Table 7: Psychological Distress Regressed on Economic Hardship Index Source | SS df MS Number of obs = 5889 -------------+------------------------------ Model | 13157.5418 1 13157.5418 Residual | 132515.136 5887 22.5097904 R-squared = 0.0903 -------------+------------------------------ Total | 145672.678 5888 24.7406043 ------------------------------------------------------------------------------ Distress | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- Econ Hardship| .6063892 .0250813 24.18 0.000 .5572206 .6555577 _cons | 4.702025 .1563131 30.08 0.000 4.395594 5.008456 ------------------------------------------------------------------------------ In testing whether there is a significant linear relationship between the psychological distress levels and the job pressure index, regression analysis was conducted. Table 8 reveals that there is a significant linear relationship between these variables. Moreover, being a positive coefficient, an increase in job pressure index by one unit results in an increase in a mean psychological distress of 0. 4931643 Table 8: Psychological Distress Regressed on Job Pressure Index Source | SS df MS Number of obs = 5888 -------------+------------------------------ Model | 15887.9279 1 15887.9279 Residual | 128355.789 5886 21.8069639 R-squared = 0.1101 -------------+------------------------------ Total | 144243.717 5887 24.5020753 ------------------------------------------------------------------------------ Distress | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- Job Pressure | .4931643 .0182707 26.99 0.000 .457347 .5289817 _cons | 5.133067 .1269768 40.43 0.000 4.884145 5.381988 ------------------------------------------------------------------------------ Another interesting research question was evaluating the association between sleep problems index and age. Regression analysis results for the existence of a linear relationship between the sleep problems index and age are presented in table 9. From the table, there was no evidence if a significant linear relationship between sleep problems index and age based on an alpha level of 5% (P-value 0.993) Table 9: Sleep Problems Index Regressed on Age Source | SS df MS Number of obs = 5818 -------------+------------------------------ Model | .000728839 1 .000728839 Residual | 50675.7726 5816 8.71316585 R-squared = 0.0000 -------------+------------------------------ Total | 50675.7733 5817 8.71166809 ------------------------------------------------------------------------------ Sleep Probs | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | .0000293 .0032053 0.01 0.993 -.0062542 .0063128 _cons | 5.324398 .1489566 35.74 0.000 5.032387 5.616408 ------------------------------------------------------------------------------ Further statistical analysis using regression analysis may be done to evaluate whether the respondents’ sleep problems index varies with their gender. The hypothesis to test is as follows; Null hypothesis: there is no significant linear relationship between the mean respondents’ sleep problems index and gender. Alternative hypothesis: there is a significant linear relationship between the mean respondents’ sleep problems index and gender. We may not expect a significant difference and therefore won’t reject the null hypothesis. Read More