Categorical Data Analysis - Assignment Example

s College Quantitative Data Analysis SOC30060 Statistical methods are widely used in the analysis of survey data. The design, conduct and analysis of surveys should reflect sound statistical methodologies. This in turn ensures that the research question(s) of interest are adequately answered with reasonable power. Researchers may have different research questions which they seek to answer by conducting surveys. The aim of a survey is to have an adequate sample that is representative of the population for which the research question affects. As such, the sample should be drawn in such a way that heterogeneity in the population is adequately addressed. Concepts such as multi-stage sampling, stratification and weighting among others are used to achieve a representative sample (Agresti, 2000). The research questions should aim to explain a trend or trait in the population that is of interest to policy makers, the general population or any other interest groups. Depending on the end user of the information, different covariates may be collected either at baseline or at intervals to best describe the phenomenon under investigation ( Babbie, 2010). In this report, two research questions of interest were explored namely; 1) Should the government take strong action to look after the environment, even if this involves major limitations on people’s freedom to do as they wish (A3)? 2) Are the respondents satisfied with the way democracy works in Ireland (A7)? Regarding the first research question, there has been growing concern on the need to take care of the environment. Environmental degradation is on the rise and the impact of uncontrolled activities that negatively impacts on the environment are quite evident. Global warming has become a keyword in any talks, conferences, workshops or other forums where environmental matters are being discussed. Nations across the world are grappling with challenges resulting from environmental degradation. Issues such as air and water pollution, flooding, siltation of water bodies, deforestation, persistent droughts and a lot more have brought focus on the respective governments’ commitment towards preserving the environment. Being the major policy maker and regulatory authority, the government has the capability to implement policies that would preserve and protect the environment from further degradation. For instance, by the government licensing and subsidizing the adoption of green energy sources, offering carbon credits to industries that significantly cut down on their carbon emission and enforcing stringent laws against those found polluting the environment; this would go a long way towards protecting the environment. In so doing however, questions arise as to how far the government should go in its quest to preserve the environment especially if this would result in the government curtailing the citizen’s freedom to doing as they wish. Even though the government may be committed towards preserving the environment, this would call for goodwill from the general public. The first research question therefore, seeks the public’s opinion on the government’s role in preserving the environment, especially if in so doing, their freedom may be limited. Democracy in governance is viewed as having a government that is dully elected by the electorate and enjoys the support of the electorate. While a sitting government may be duly elected as per that country’s laws, if there is widespread resentment towards its existence, it would find it hard to implement policies or govern in peace. Coupe d’ ta results mainly from parties being dissatisfied with the current government. As a starting point towards having a popularly elected government, all citizens of voting age should ideally take part in deciding who should govern them. However, time and time again, whenever there are polls, voter turnout is far from perfect. It would be interesting to know whether people are satisfied with the democracy in Ireland. This is the goal of our second research question where we explore the people’s perception towards democracy and especially if they are equally satisfied on the whole with the way democracy works in Ireland. Statistical analysis to answer these questions requires formulation of appropriate hypothesis (Mendenhall & Sinchich, 2007). The hypothesis to test include 1) Null hypothesis: there is no association between the preferences of respondents in the government intervening in environmental control. Alternative hypothesis: there is an association between the preferences of respondents in the government intervening in environmental control 2) Null hypothesis: people are equally satisfied with the democracy in Ireland. Alternative hypothesis: People are not equally satisfied with the democracy in Ireland The covariates to use in answering each of these research questions are participants’ gender and marital status. The Irish Social and Political Attitudes Survey was carried out in late 2001/early 2002. The target population for the survey was all adults aged 18 years and over who were living in private households. This explicitly excluded the population in institutions such as long-term geriatric or psychiatric hospitals, old persons homes etc. Approximately 2.7 per cent of the total population of the Republic of Ireland are resident in institutions of this sort. A national random sample of the target population was selected as outlined below. All questionnaires were conducted on a personally administered papi basis Results Should the government take strong action to look after the environment, even if this involves major limitations on people’s freedom to do as they wish? As a starting point towards answering this research question, the distribution of the respondents’ responses regarding the government’s involvement in environmental conservation was obtained. Figure 1: Bar graph of the respondents’ perception towards government’s involvement in environment Approximately 900 respondents were in agreement with the government’s interventions in environmental control even if this interfered with their freedom. Roughly 100 respondents strongly disagreed with the government’s intervention while approximately 180 respondents neither agreed nor disagreed. Overall, there were more participants who either slightly agreed, agreed or strongly agreed to the government’s involvement as compared to those that strongly disagreed, disagreed or slightly disagreed with the government’s involvement. To further answer the research question, baseline differences in the sampled respondents was taken into consideration. The respondents’ gender and marital status were used as covariates. A cross tabulation of the responses by gender is presented in table 1. Table 1: Cross tabulation of respondents by perception towards government’s involvement Perception towards Government’s involvement in environment Total strongly disagree disagree slightly disagree neither agree/disagree slightly agree agree strongly agree strongly disagree sex of respondent male 67 270 127 87 147 429 96 1223 female 56 242 134 87 148 507 91 1265 Total 123 512 261 174 295 936 187 2488 There were an approximately equal number of males and females in the study. Moreover, the number if males giving a particular response was approximately equal to that of females. For instance, 67 males and 56 females strongly disagreed with the government’s involvement in environmental control especially if it would curtail their freedom. A clearer representation of the distribution of responses by gender is given by the bar chart in figure 2. Figure 2: Distribution of responses by gender The bar chart suggests a difference in the number of respondents who were either in agreement or disagreement with the government’s involvement in environmental control. A statistical test however is needed to confirm whether this difference in responses is statistically significant especially taking into consideration the respondents’ gender. A chi square test for whether there is an association between the respondent’s gender and their perception towards the government’s involvement in looking after the environment, even if this involves major limitations on people’s freedom to do as they wish was conducted (Agresti, 2000). The results are as shown in table 2. Table 2: Chi square test for the association between gender and perception towards the government’s involvement Value df 2 sided P-value Pearson Chi-Square 8.633 6 .195 Results of the test indicate that there is no significant association between the respondent’s gender and their perception towards the government’s involvement in looking after the environment, even if this involves major limitations on people’s freedom to do as they wish. This is at a significance level of 5%. Similarly the marital status of the respondents was explored with regards to their perception on the government’s involvement in looking after the environment, even if this involves major limitations on people’s freedom to do as they wish. Table 3: Cross tabulation of respondents marital status and their Perception towards Government’s involvement in environment Perception towards Government’s involvement in environment Total current marital status strongly disagree disagree slightly disagree neither agree/disagree slightly agree agree strongly agree strongly disagree married 62 240 128 89 113 497 99 1228 separated 3 8 5 6 6 35 3 66 divorced 1 5 1 1 1 7 1 17 widowed 3 30 9 9 15 72 23 161 never married 54 229 119 70 160 325 60 1017 Total 123 512 262 175 295 936 186 2489 There was evidence of a difference in distribution of respondents with regards to their marital status with the sample comprising mostly of married respondents (1228) and only 17 divorced respondents. Moreover, the distribution of responses by marital status was better visualized in the bar chart shown in figure 3. It is evident that responses were quite comparable in the married and never married group but differennt from those that were separated,divorced or widowed. A chi square test for the associaton between respondents’ marital status and their perception on the government’s involvement in looking after the environment, even if this involves major limitations on people’s freedom to do as they wish was conducted and results displayed in table 4. Table 4: chi square test for the association between the marital status and perception towards the government’s involvement Value df 2-sided P-value Pearson Chi-Square 70.638 24 .000 A test conducted at 5% significance level revealed that there was a significant association between the respondents’ marital status and their perception on the government’s involvement in looking after the environment, even if this involves major limitations on people’s freedom to do as they wish. People are equally satisfied with the democracy in Ireland As a starting point towards answering this research question, the distribution of the respondents’ responses regarding their satisfaction with the way democracy works in Ireland was obtained. Table 5: Summary statistics for satisfied with way democracy works-Ireland Frequency Percent Valid Percent Cumulative Percent Valid very satisfied 204 8.2 8.8 8.8 fairly satisfied 1497 60 64.3 73 not very satisfied 449 18 19.3 92.3 not at all satisfied 179 7.2 7.7 100 Total 2328 93.4 100 From table 5, most people (60%) are fairly satisfied with the way democracy works in Ireland. Only 8.2% of the respondents are very satisfied with the way democracy works in Ireland. Both the histogram and summary statistics show that the least people are not satisfied with democracy at all. Figure 4: Bar graph of the respondents’ level of satisfaction with the way democracy works Table 6: Cross tabulation of sex and level of satisfaction with way democracy works satisfied with way democracy works-IRL Total   very satisfied fairly satisfied not very satisfied not at all satisfied sex of respondent male Count 113 762 198 97 1170 % within satisfied 55.40% 51.00% 44.00% 54.20% 50.30% female Count 91 733 252 82 1158 % within satisfied 44.60% 49.00% 56.00% 45.80% 49.70% Total Count 204 1495 450 179 2328 % within satisfied 100.00% 100.00% 100.00% 100.00% 100.00% Democracy satisfaction was crossed with gender to get an idea of how males and females are distributed within levels of satisfaction. Results in table 6 indicate that there are more males than females who are very satisfied as well as not satisfied at all with the way democracy works in Ireland. It can be noted that there are approximately equal number of males and female in the study irrespective of the satisfaction status. Figure 4: Bar graph of the respondents’ level of satisfaction with the way democracy works by gender A chi square test was done to check whether the level of satisfaction is different for males and females. Table 7: Chi square test for the association between gender and level of satisfaction with the way democracy works   Value df Asymp. Sig. (2-sided) Pearson Chi-Square 10.611(a) 3 0.014 Likelihood Ratio 10.632 3 0.014 Linear-by-Linear Association 1.987 1 0.159 N of Valid Cases 2328 a :0 cells (.0%) have expected count less than 5. The minimum expected count is 89.04. From table 7, the two sided test is significant at 5% level of significance implying that there is a difference between males and females with regards to level of satisfaction with the way democracy works in Ireland. From table 8, there are more married people in the different levels of satisfaction than other marital status levels. This difference can also been seen for never married people compared to separated, divorced and widowed. This suggests that there is a possible difference between levels of satisfaction with the way democracy works in Ireland depending on the marital status of the person. Fig 5 gives a clear pictorial view of the distribution of respondents with regards to satisfaction with the way democracy works according to marital status. Table 8: Cross tabulation of respondents’ level of satisfaction with the way democracy works by marital status       very satisfied fairly satisfied not very satisfied not at all satisfied Total current marital status married Count 106 770 218 88 1182     % within satisfied 52.20% 51.50% 48.40% 48.90% 50.80%   separated Count 4 38 13 4 59     % within satisfied 2.00% 2.50% 2.90% 2.20% 2.50%   divorced Count 0 12 3 1 16     % within satisfied 0.00% 0.80% 0.70% 0.60% 0.70%   widowed Count 27 92 21 9 149     % within satisfied 13.30% 6.20% 4.70% 5.00% 6.40%   never married Count 66 582 195 78 921     % within satisfied 32.50% 39.00% 43.30% 43.30% 39.60% Total   Count 203 1494 450 180 2327     % within satisfied 100.00% 100.00% 100.00% 100.00% 100.00% Figure 5: Bar graph of the respondents’ level of satisfaction with the way democracy works by marital status A chi square test was conducted to test this difference and the results in table 9 shows a statistically significant difference between level of satisfaction with the way democracy works among married, separated, divorced, widowed and never married at 5% level of significance. Table 9: Chi square test for the association between marital status and level of satisfaction with the way democracy works Value df Asymp. Sig. (2-sided) Pearson Chi-Square 25.991(a) 12 0.011 Discussion and conclusion There is no significant association between the respondent’s gender and their perception towards the government’s involvement in looking after the environment, even if this involves major limitations on people’s freedom to do as they wish. This is at a significance level of 5%. On the other hand, a test conducted at 5% significance level revealed that there was a significant association between the respondents’ marital status and their perception on the government’s involvement in looking after the environment, even if this involves major limitations on people’s freedom to do as they wish In testing the second hypothesis, a two sided test is significant at 5% level of significance. This implies that there is a difference between males and females with regards to level of satisfaction with the way democracy works in Ireland. A chi square test was conducted to test if there is a statistically significant association between the levels of satisfaction with the way democracy works among married, separated, divorced, widowed and never married at 5% level of significance. There was a significant association between the levels of satisfaction with the way democracy works among married, separated, divorced, widowed and never married. References Babbie, E. R., 2010. The Practice of Social Research. s.l.:Cengage Learning. Agresti, A., 2000. Categorical Data Analysis. Second Edition ed. Florida: John Wiley & Sons, Inc. Kutner, M. H., Nachtsheim, C. J., Neter, J. & Li, W., 2005. Applied Linear Statistical Models. Singapore: Mc Graw Hill. Mendenhall, W. & Sinchich, T., 2007. Statistics for engineering and the sciences. New Jersey: Prentice Hall. Read More