Inferential Statistical Techniques - Math Problem Example

?Assignment Question In your opinion, which of the inferential statistical techniques that you learned would be test the idea of a quantitative model and why? Use specific examples from the field of public affairs. There are various inferential statistical techniques available to test an idea of quantitative model such as correlation, regression analysis, ANOVA, independent samples t (or z) tests and many more. The inferential statistics helps a researcher to conclude beyond the descriptive conclusions of data. There are various quantitative data analysis methods that help in testing the quantitative model. The inferential statistical techniques correlation or bivariate regression analysis are used for examining relationship between two continuous variables (one independent variable and one dependent variable). The multiple regression analysis helps in examining relationship between one continuous dependent variable with one or more continuous independent variables. The regression analysis uses numeric data for analysis. In the field of public affairs, a researcher usually has to study various variables to quantify effect of one variable to other. In the case researcher does not include other factors affecting a particular variable it would lead to a particular bias known as ‘omitted variable biases. Multiple regression analysis helps in removing this bias by dealing with large number of explanatory variables. The study of these variables helps in asserting hypothesis wrong or vice-versa. This helps in identifying and generalizing the research findings for a larger population. The sample size needs to be sufficient for the analysis. The t-test or ANOVA is used with the data where variables are categorical and continuous. The mean scores of the groups are compared in order to understand the difference between the groups. In the case of public affair, this analysis helps to test the probability differing two means. The correlation studies help in conducting rigorous research that can be done in order to understanding the nature of relationship between the variables. The correlation study helps in testing the validity of the research. The paired variables are linked with each other. The scatter plot produced to graphically present the correlation of a variable with the help of a linear line. The more is the gap between points from the straight line, the higher will be the weakness of relationship between those two variables. The direction refers to the slope of the scatter point. The variables can be in positive or negative relationship. The difference in one variable will have corresponding changes in the other variable. The positive correlation provides us information about the nature of change towards one another. The negative correlation shows that the change is opposite direction. The correlation method is an appropriate method to examine the relationship of meaningful data. The data should be quantifiable. The correlation cannot be examined using categorical data. The correlation and regression studies are used for testing hypothesis and determining cause-and-effect relationships. The associated variables are studied for the association and the nature of association. There are various benefits of correlation test. This can help in predicting and helps in validating. This is a reliable method and helps in verifying theory. The Pearson coefficient is used when the variables are continuous. This requires one independent and one dependent variable. For example if there is a need to study the level of awareness of a social-environmental sustainability programs among different genders and its relation with success of program in particular geographic region. The level of awareness and the difference of awareness among the population can be understood by the correlation study. The regression analysis will help in identifying if the level of awareness was linked to the level of success of program. The t-test can help in accepting or rejecting the hypothesis that success of program is dependent on the level of awareness of program in different gender groups. Question 2: Why would the field of public administration and affairs concern itself with populations and how could the use of hypothesis testing, and correlation and regression analysis help with the study of problems facing populations. Use a specific example to illustrate your answer. The Correlation and regression analysis helps in hypothesis testing. These analyses are run on the large number of sample. In the correlation the relation between two variables are quantified. The sums of squares of each variable are calculated and sum of cross production is calculated in order to identify the correlation coefficient. The correlation strength of the data is also studied with the help of scatter diagram. In the correlation analysis scatter plot can be created for positive or negative correlation. The Pearson correlation usually provides the strength of correlation for the studied variables. This can be weak correlation, moderate correlation and strong correlation. The correlation coefficient helps in understanding if the variables have any kind of correlation or not and based on that a null hypothesis is accepted or rejected. There are certain assumptions made for the correlation studies that can be validity assumption and distributional assumption. The public affair usually includes large pool of data and study of many variables in order to develop new policy or procedure for the benefit of the nation. The public information is available in various forms like demographic detail of people that include age, gender, income level, geographic region and many more. This information can be used for understanding effectiveness of any particular governmental programs. This can also help in understanding the perception of people at large regarding any policy or program. This can help in determining the best options and designing the policy or program for the target group accordingly. The null hypothesis is tested by the absence of any relationship between the studied variables. If there is no relationship between the variables the hypothesis will be rejected. Correlation analysis provides us the strength between different variables, whereas the regression analysis provides the relationship of the variables. For example the correlation study can help in identifying the relationship between the variables like income and happiness among the subject. The income and happiness is related to each other in positive way. If income increases, happiness increases. However the regression analysis is done to determine whether a prediction can be made with the help of one variable i.e. determining if from the level of income can be used to predict level of happiness among the target population. Therefore, it can be concluded that these two methods offer the great tool for hypothesis testing for any research with large number of variables. References Izenman, Alan J. Modern multivariate statistical techniques: regression, classification, and manifold learning. Springer, 2008. McMillan, James H., and Sally Schumacher. Research in education. Pearson Education, 2009. Cooper, Donald R., and Pamela S. Schindler. "Business research methods." (2003). Weiss, Neil A., and Carol A. Weiss. Introductory statistics. Pearson Education, 2012. Read More