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, The Percentage of Divorces Per 1000 Populations and The Percentage of Abortion Per 1000 Population?”

Appropriateness of a One-Way MANOVAAnalysis for the Research Question

The study will employ a One-Way 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 toolthat 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 studyare 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.

The Variables in the Research Study

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 variableis 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.

Appropriateness of the Variables for a One-Way MANOVA Analysis

The variables of the study fit the qualification for the selected statistical test. A MANOVA analysis requires that the dependent variables be continuous in nature, while the independent variables must be categorical variables(Laerd Statistics, 2014). For this study question, the response variables 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. They are continuous in nature and can take numerical values.The independent variable is the regions of the country which have been divided into four the West, the Mid-West, the Northeast and the South regions. They are categorical variables since they can only assume a figure that is one of several probable categories, and there is no intrinsic way of ordering them. Additionally,categorical variables have no numerical meaning.

Statistical Notation and Written Explanation for the Null and Alternative 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 tothe 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:

H₀: µ_w=µ_x=µ_y=µ_z

H₁: µ_w≠µ_x≠µ_y≠µ_z

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 supposes 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 vectorsof 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 has 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.

References

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

 
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