Research Question: “Does The Region Of The Country Have Any Significant Impact On The Percentage Of People Who Adhere To The Christians Faith, The Percentage Of Divorces Per 1000 Populations And The Percentage Of Abortion Per 1000 Population?”
The research question for the study is “Does the Region of the Country Have Any Significant Impact on The Percentage of People Who Adhere to The Christians Faith, The Percentage Of Divorces Per 1000 Populations And The Percentage Of Abortion Per 1000 Population?” The objective of the study is to assess the differences between the groups on all the dependent variables. That is, to compare the different regions, the West, the Mid West, the Northeast and the South regions. These regions would be compared based on the percentage of people who adhere tothe Christian faith, the percentage of divorces per 1000 population and the percentage of abortions per 1000 population. The study employed a one-way MANOVA analysis to conduct the investigation.
The research question is “Does the region of the country have any significant impact on the percentage of people who adhere to the Christians faith, on the percentage of divorces per 1000 populations and on the percentage of abortion per 1000 population?”
The study will employ a MANOVA analysis. A MANOVA analysis is employed when modelling two or more response variables which are continuous in nature with one or more explanatory variables which are categorical. A MANOVA is a statistical analysis tool that tests a hypothesis that presumes that one or more explanatory factors, or variables, have an effect on a series of two or more response variables (Institute for Digital Research and Education, 2014). That is, the dependent variables should be should be more than one and should also be conceptually related ( (Laerd Statistics, 2014)). It is useful as it avoids the necessity of conducting a series of one-at-a-time ANOVAs.
The research question has the objective of establishing whether the region of the country, in this case the West, the Mid-West, the Northeast and the South has any significant effect on the percentage of people who practice the Christian faith, percentage of divorces per 1000 populations and percentage of abortions per 1000 population. The study’s independent variables are the regions of the country, which are in the context of the research study are the West, the Mid-West, the Northeast and the South regions. The response variables for the research question are the percentage of people who adhere to the Christians faith, on the percentage of divorces per 1000 populations and on the percentage of abortion per 1000 population.
This research question is appropriate for the use of a MANOVA because the dependent variable has more than two dependent variables all of which are conceptually related. That is, religion plays a big role in influencing the moral decisions of people, in this case, their decision to divorce, or their decision to commit an abortion. Additionally, the dependent variables are continuous, while the independent variable is categorical.
StatisticalNotation and Explanations for the Hypotheses
The study wishes to assess the differences between the groups on all the dependent variables. That is, to compare the different regions, the West, the Mid West, the Northeast and the South regions. These regions would be compared based on the percentage of people who adhere to the Christian faith, the percentage of divorces per 1000 population and the percentage of abortions per 1000 population.
The statistical notation for the null hypothesis and alternate hypothesis is:
Where: W, X, Y, and Z stand for differences between regions in terms of their score on at least one of the dependent variables
The null hypothesis presupposes that there is no significant difference among the different regions in terms of their score on at least one of the dependent variables. This is to say, the vectors of means for the three dependent variables are not different among regions of the country. That is, there is no significant difference between the West, the Mid West, the Northeast and the South regions in terms of their scores on the percentage of people who adhere to the Christian faith, the percentage of divorces per 1000 population and the percentage of abortions per 1000 population.The alternative hypothesis presumes that there is a significant difference among the different regions in terms of their score on at least one of the dependent variables. That is, the vectorsof means for the three dependent variables are different among regions of the country.
Types of Errors that Can Occur
Errors that can be associated with the use of MANOVA stream from its assumptions. First, MANOVA assumes that there is multivariate normality. That is, all dependent variables are distributed normally, and all subsets of the variables have a multivariate normal distribution. Second, MANOVA assumes homogeneity of the covariance matrices. Finally, it assumes independence of observations. These assumptions are hard to meet therefore, its likely that a research study is violating something when it conducts a MANOVA (Grimm & Yarnold, 1995).
MANOVA analyses have the weakness that due to their complexity and inclusion of many variables, they have a tendency to produce incorrect or ambiguous results. Additionally, the results are harder to interpret because there are more things going at the same time.
These errors associated with MANOVA notwithstanding, it have a key strength. A common error that is usually associated with any study that employs the use of a form of an analysis of variance is Type I error. However, with MANOVA it reduces the experimental-wise level of this type of error. That is, it reduces the probability of a research study rejecting the null hypothesis when in fact it is true, thereby making the findings more valid and reliable.
The total number of participants would be 4000 people. The regions included in the independent variable, the West, the Mid-West, the Northeast and the South regions, will each provide a sample of 1000 participants. These participants will not be discriminated based on any demographic characteristics; they will simply have to be Christians and must have been married at one point in their lives or are still married. The participants will be selected conveniently based on whether they meet the characteristics targeted by the research study. That is to say, the participants will be chosen from among Christians who have been married before or are still married.
The study’s independent variables are the regions of the country, which in the context of the research study are the West, the Mid-West, the Northeast and the South regions. The independent variable is a categorical variable. This is for the reason that it is not quantitative and has more than two categories all of which have no intrinsic ordering. That is, the West, the Mid-West, the Northeast and the South regions.Conversely, the response variables for the study are the percentage of people who are practice the Christian faith, percentage of divorces per 1000 populations and percentage of abortions per 1000 populations. The dependent variables are continuous variables measured at the interval or ratio level. This is because they take numeric values and are on a real scale.
In the context of this study, a region of the country refers to the geographical location of an area recognized and defined by official records. In this research study, the South Region refers to States located in the southern part of the United States such as Maryland, Missouri, Texas and Florida. Region is a categorical variable, which takes a figure with no numerical meaning.
A Christian refers to a person who believes in the tenets of the Christian faith and on a regular basis attends a congregation of people who hold the similar faith. In the context of this study, divorce refers to the dissolution of a marriage legally through court or through any other competent body or through mutual agreement to separate and annul the marriage. Abortion refers to the premeditated and intentional termination of a pregnancy for any other reason rather than medical reasons. These are the response variables continuous variables and are measurable through counting.
In order to make correct inferences about the findings of a MANOVA analysis, a multivariate test statistics would have to be carried out. An overall F test will have to be conducted over all the dependent variable. This will assist in computing the f value and Wilks’ Lambda (λ). The lambda is a measure of the percent of variance in the response variables which is not explained by differences in the level of the independent variable. Ideally it is supposed to be zero to denote that there is no variance that is not explained by the explanatory variable. In the occasion that Wilks’ lambda is not available; Roy’s Greatest Characteristic root, or Hotelling’s trace or Pillai’s criterion can be used.
In a MANOVA analysis, post hoc tests are carried out when there are more than two levels of the independent variable. These tests are necessary to examine the nature of the findings. If a MANOVA analysis reveals that it is statistically significant, a number of follow up analyses can be conducted. These include; multivariate contrasts, step down analysis, dependent variable contribution, multiple univariate ANOVAs and discriminant analysis (Stevens, 2002)(Tatsuoka, 1971).If from the research study it is found that the f value is significant, there will be a need to assess the tests of between-subjects effects for each of the response variables. To control for Type I error, a Bonferroni adjustment can be employed to divide the original alpha level by the number of tests. In the context of this study, if there are patterns in the data, one of the post hoc tests will have to be conducted to ascertain the correctness of the findings.
For this study to reach any conclusion, the Wilks’ lambda, the f value and the partial eta squared would have to be computed in order to determine the multivariate main effect for the regions. With regards to the dependent variables the f test has to be computed, if it is found to be significant, the study will have to look at the individual dependent variables with separate ANOVA tests.
The MANOVA is generally a very powerful statistical tool as opposed to stand alone univariate tests(Stevens, 2002). However, they have the weakness that due to their complexity and inclusion of many variables, they have a tendency to produce incorrect or ambiguous results. Additionally, they presume a lot of sensitive assumptions with regards to the normality of distribution of the dependent and independent variables. Furthermore, the results are difficult to interpret because there are manyvariables going at the same time.Another key shortcoming of the MANOVA model is that it requires complete data. Subjects with incomplete data must be removed from the analysis, leading to potential bias, or have their missing values imputed in some way. These weaknesses have the overall effect of making the study reveal incorrect results.
Although MANOVA is used as an initial test in cases where there is a set of dependent variables, it does not provide information about how the independent and dependent variables are associated. MANOVA models focus more on comparison of group means and provide no information regarding subject- specific relationships. For instance, a significant multivariate F test in a MANOVA analysis means that there is some pattern of differences across the groups on the dependent variables, but it does not provide any information about what these differences are(Stangor, 2014). This limits the conclusions that can and cannot be obtained from the study.
The results of this research study would be invaluable to behavioral social scientists. The findings will help in explaining the role of religion in influencing the decisions of people with regards to a particular moral or ethical issue.
Grimm, L. G., & Yarnold, P. R. (1995). Reading and Understanding Multivariate Statistics. Washington, D.C: American Psychological Association.
Institute for Digital Research and Education. (2014, September 24). One-way MANOVA. Retrieved September 28, 2014, from Institute for Digital Research and Education-University of California, Los Angeles: http://www.ats.ucla.edu/stat/sas/dae/manova1.htm
Laerd Statistics. (2014, September). One-way MANOVA in SPSS. Retrieved September 28, 2014, from Laerd Statistics: https://statistics.laerd.com/spss-tutorials/one-way-manova-using-spss-statistics.php
Stangor, C. (2014). Research Methods for the Behavioral Sciences (5 ed.). : Cengage Learning.
StatSoft. (2014, September 27). Introduction to ANOVA / MANOVA. Retrieved September 28, 2014, from StatSoft-Dell: http://www.statsoft.com/Textbook/ANOVA-MANOVA
Stevens, J. P. (2002). Applied Multivariate Statistics for the Social Sciences (Fourth Edition ed.). New Jersey: Lawrence Erlbaum Associates, Inc.
Tatsuoka, M. M. (1971). Multivariate Analysis: Techniques for Educational and Psychological Research. New York: John Wiley and Sons.
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