Fictitious Statistical Analysis: How to Make Data Work for You

This research is a quantitative research as it has its focus on numerical data. Qualitative research puts its emphasis on objective measurement and numerical analysis of the data collected through polls, questionnaires and surveys. Generally, qualitative research will focus on collecting numerical data across groups of people on particular issues. Other characteristics of quantitative data include a large sample size to represent the entire population, the research can be replicated, research questions and objectives are well elaborated, all aspects of the study are well elaborated before data is collected and research tools such as questionnaires are used to collect numerical data. In this research, the dean has already collected data on grade point average, graduate degree completion, GRE, and gender which are all quantitative data.

Analysis of variables

A variable in research is the item the research is trying to measure. In this study, they include gender, GPA, GRE score and the graduate completion frequency. In any research, there are two different types of variables that are the independent variable and the dependent variable. The independent variable is a variable that its changes are not affected by any other variable in the experiment. In this research gender, GPA and the GRE score are considered the independent variable as they cannot be affected by any other variable in the study. On the other hand, the dependent variable is the graduate completion frequency as it will be affected by all the three variables in the research. On the other hand, the dependent variable is what is being studied or measured in the experiment.

In this experiment, I will propose that regression analysis is used in the analysis of the relationship between variables. Regression is a set of processes of statistics that are used in estimating the relationship between variables in a study (Fox, 2015). These include many models that analyze several variables when focusing the relationship between dependent variables and independent variables. Additionally, this analysis will help us understand the typical value of the dependent variables changes when one independent variable is changed or varied while the other independent variables remain fixed (Fox, 2015).

In the measuring of the relationship between the different variables such as the relationship between the gender of the students and the GRE score or measuring the relationship between the GRE score and the gender of the student and the GPA of the students at the time of graduation will be the correlation analysis method. Additionally when there is more than one dependent variable to be measured against one dependent variable then I will use the coefficient of multiple correlation analysis. For example when measuring the relationship between the GRE score of the student at admission and the gender of the student to the GPA score at graduation. On the other hand when measuring the effect of the dependent variables to the independent variables such as the effect of the GRE score of the student at graduation and the gender of the student on the degree completion frequency of the students will be the Pearson regression correlation. Another type of analysis of effect especially when there are multiple variables in the study will be the multiple linear regressions.

In most cases, the regression analysis will estimate the conditional expectations of the dependent variable when presented with the independent variable. Furthermore, when regression is used in the analysis of variance in the research it is widely used for predictions and forecasting (Fox, 2015). Additionally, regression analysis is used to get an understanding on which among the independent variables are related to the dependent variable and illustrate the forms of the relationships. There are many models for carrying out the regression analysis. The most common methods include linear regression and ordinary least squares regression which is considered parametric (Fox, 2015).

Specifically, in this study, the type of regression to be used is the linear regression among other regression analysis methods. Linear regression basically is used to predict the relationship between the dependent variable denoted as Y and the independent variable X and also predicting the values of variables (Bates, 2014). When using this method to determine a relationship between two variables the variables are plotted randomly on a scatter plot of variable X and Y. in the case where the points randomly scattered it can be stated that the variables are not related (Bates, 2014). When drawing the regression line on the scatter plot some points will lie in the regression line and others will lie close to the line. This kind of plot will be due to the fact that the regression is probabilistic in nature and the predictions of the research are approximated (Bates, 2014). Therefore there will be an occurrence of errors, deviations and the observed values of Y. however when there is a linear relationship between independent and dependent variables on the scatter plot one can plot more than one line through the points (Bates, 2014).

Research question

1. What is the relationship between the GRE score of the student before admission and the GPA score at the time of graduation?

Null hypothesis

There is the relationship between the GRE score of the student during admission and the GPA score at the time of graduation.

Alternative Hypothesis.

There is no relationship between the GRE score of the student at the time of admission and the GPA score at the time of graduation.

Analysis proposal

The statistical analysis method that I will propose to measure the relationship between the GPA score and the GRE admission score will be the correlation analysis. This is the analysis that is used to study the strength and relationship between two numerical measures of variables that are continuous in nature. The variables, in this case, are the GPA and GRA score. This analysis is important as it establishes if there is any possible connection between variables. In the case where there is a correlation between the two variables, there will be a systematic change in one variable, in this case, the GPA score at graduation.

A correlation found depending with the values being measured in the research can either be positive or negative. A positive correlation will be present if one variable will increase simultaneously with the other variable. In this case, if the GPA at graduation increases when match with the high GRE score at admission then the two variables are related. On the other hand, a negative correlation will exist if one variable decreases when the other variable increases. In this case when the GPA score is high when compared to the GRE score during admission, therefore, no relationship between the two.

The coefficient value that measures the correlation between two continuous variables will range between +1 and -1. +1 indicates a strong positive correlation while -1 will indicate a strong negative correlation between variables (Cohen, 2014). Therefore the closer the coefficient number is to either of the numbers the stronger the correlation of the data present. When the correlation value is 0 then it represents a weak correlation. Therefore in this research, if the correlation value will be close to +1 then the null hypothesis will be significant and on the other hand, if the correlation value will be close to -1 then the alternative hypothesis will be significant (Cohen, 2014). However when the correlation figure will be zero then both the null and alternative hypothesis will not be significant.

If the null hypothesis in this study is significant then the recommendation will be that the GRE score test before admission should be scrapped as it will not be an accurate predictor of the student’s performance in graduate school. On the other hand, if the alternative hypothesis is significant then the GRE score test will stay put as it is a good predictor of the performance and GPA of the student at the time of graduation, therefore, an important indicator tool. However, if they are both neither significant then more research should be conducted while including other variables in the study to be able to measure the two variables more appropriately.

Research questions

1. Is there the relationship between gender of the student and the GRE score at admission and GPA score at graduation?

Null Hypothesis

There is the relationship between the gender of the students to the GRE score at admission and the GPA score at graduation.

Alternate hypothesis

There is no relationship between the gender of the students and the GRE score at admission and the GPA score at graduation.

Analysis method

In this category, I will use the coefficient of multiple correlation analysis in measuring the relationship between the gender of the student, the GRE score at admission and the GPA score at graduation. The coefficient of multiple correlations measures how well a variable can be predicted using the linear function of a set of other variables. The coefficient of multiple correlations will have the values between zero and one. In case the results show a higher value it indicates that there exists a better prediction of the dependent variables and the independent variables. A value of one will indicate that the predictions are exactly correct and the assumptions are right while the value of zero indicates that there no linear combination and relationship of the independent variables is a better predictor as compared to the fixed mean of the dependent variable. In this analysis, the coefficient of multiple correlations will be computed by use of the square root of the coefficient of determinants. However, this is done with the assumption that the intercept will include the best possible linear predictor is used.

In this case, the coefficient of multiple correlations will be computed using the vector of correlation between Gender as a predictor variable and the GRE score before joining the school and the GPA score at the time of graduation as the target variables. Additionally, a correlation matrix will be required to establish the correlation between the predictor variables. In the case where the predictor variable is uncorrelated to the target variables, the identity matrix will simply equal to the sum of the squared correlations with the dependent variables. Additionally, if the predictor variable in this case gender is correlated to the target variables that is the GRE score and the GPA score then the inverse of the correlation matrix will account for it.

On the other hand, the coefficient of multiple correlations can also be computed by use of the fraction of variance of the dependent variable that will be examined by the independent variables. This is computed by buy subtracting the unexplained fraction from 1. The unexplained variable will be calculated as the sum of squares of the prediction errors then divided by the squared deviations of the values of the predictor variable.

If the regression of the predictor variable gender to the target variable GPA and GRE is zero then there is no significant relationship between gender and the GRE and GPA score of the students. In this case, the null hypothesis will be rejected and an alternate hypothesis accepted. On the other hand, if the correlation of the predictor variable to the target variable is one then there is the significant relationship between the gender of the student and the GRE and GPA score of the students. Therefore, the null hypothesis is accepted and the alternate hypothesis rejected in this research. In the null hypothesis is accepted in this research then it will show that there is the relationship between the gender of the student and the GRE score before admission and the GPA at the time of graduation. On the other hand, if the regression value is one then there will be no relationship between the gender of the student and the GRE score at admission and the GPA at the time of graduation.

If the null hypothesis is significant then the GRE test before admission should be scrapped as gender as a variable has the ability to affect the GPA of the student at the time of graduation. Additionally if the alternate hypothesis is significant then it shows that the GPA of the student will not be affected at the time of graduation by their gender, therefore, the GRE test should not be scrapped as it has proven as an important determinant of the GPA of the student at the time of graduation other than other variables such as gender.

Research question

1. Does the gender of the student have any effect on the GRE score at admission of the student?

Null hypothesis

The gender of the student affects the GRE score of the students at admission.

Alternative hypothesis

The gender of the students has no effect on the GRE score of the students at admission.

Effect Analysis

The main goal of this research question is to the causal relationship between the dependent variable gender and the independent variable which is the GRE score of the student at admission. In this case, the dependent variable is the cause and the independent variable is the effect. It's additionally important to note that establishing the cause and effect in research is one of the most challenging aspects of data analysis.

The first step in the establishing of the cause-effect relationship in a research analysis is to demonstrate the association between the dependent and independent variables. Since both the gender and GRE score of the student are numerical data, therefore, will use correlation analysis to determine if there is the appearance of conveying between the variables. Once the association has been determined the next step is to determine the time order of the variable of interest. This, in a nutshell, means that for an independent variable to cause the effect on the dependent variable then the independent variable must occur first in time so as to cause the effect. This time ordering allows the researcher to control the research and then measure the outcome of interest.

In the analysis of the effect research questions and hypothesis, I will use the Pearson regression correlation (Zhou, 2016). This is because this analysis method has the ability to measure the degree of the relationship between two variables. In this case, the Pearson regression correlation will be used to measure the relationship between the gender of the student and the GRE score (Zhou, 2016). The assumption of this type of data analysis is that both variables are normally distributed. Additionally, this analysis method will assume that the variables are in a straight line in terms of the relationship between the two variables and that the data is equally distributed on the regression line (Zhou, 2016).

To measure the effect the Cohen's standard will be used to evaluate the coefficient of correlation and determine the effect size. The correlation coefficient will show the small effect or associated with gender and its effect on the GRE score at admission if they are between 0.1 to 0.29 (Zhou, 2016). if there is a small effect on them the null hypothesis will be rejected and the alternate hypothesis accepted. On the other hand if the coefficient value of between 0.3 to 0.49 it will show that gender has a medium effect on the GRE score on admission and that means we accept the null hypothesis and reject the alternative hypothesis (Zhou, 2016). Finally, if the coefficient correlation values are 0.5 and above then there is a large effect of gender on the GRE score of the student at the time of admission. In this case, the null hypothesis is significant and is accepted and the alternate hypothesis will not be significant and therefore rejected.

If the null hypothesis is significant and the null hypothesis is insignificant then it shows that the gender of the student does not affect the GRE score of the student. This, therefore, means that the GRE score is a perfect predictor of the GPA of the students at the time of graduation and it is not affected by the gender of the student and other variables. Therefore there will be no need of scrapping the GRE exam as it will be important. On the other hand, if the gender of the student affects the GRE score at admission then it is not a good predictor of the GPA score at graduation. Therefore we will reject the alternate hypothesis and reject the null hypothesis. In this case, the GRE score test can be scraped as it is not an accurate predictor of the GPA of the student at the time of graduation and the GPA of the student can be affected by other variables.

Research question

1. Does the gender of the student affect their degree completion frequency?

2. Does the GRE score of the student affect the degree completion frequency of the student

Null hypothesis

The gender and GRE score of the student affects the degree completion frequency of the students

Alternate hypothesis

The gender and GRE score of the student has no effect on the degree completion frequency of the students.

Analysis

In the analysis of the effect of gender and the GRE score of the students on the degree, completion frequency will use the multiple linear regressions. This analysis method is a predictor analysis and is used to explain the effects of two dependent variables to one independent variable (Cohen, 2014). In this case, the independent variable can be continuous or categorical. The assumptions of this analysis method are that the regression residual should be normally distributed (Cohen, 2014). The effect of the dependent variables on the independent variable takes the assumption that the linear relationship exists between the dependent variables and the independent variables (Cohen, 2014). Finally, this analysis method assumes that in the absence of the multicollinearity then the independent variables are not highly correlated therefore have no much effect on the dependent variables, in this case, the degree completion frequency of students (Cohen, 2014).

When conducting a linear regression analysis of data the first activity is to fit a single line on the scatter plot. To be more specific in a multilinear regression a line is fit through a variety of dimensions and data points. In this case, GRE score and the gender of the students will be the predictor variables also referred to as the regressand and the degree completion frequency among students will be the outcome variable also referred to as the regressors (Cohen, 2014).

In interpreting the effects of the dependent variables on the independent variable the p-value will be used and also to test the null hypothesis (Cohen, 2014). The p-value of zero will mean gender and the GRE score have no effect on the degree completion frequency of the students and therefore making the null hypothesis not significant and the alternate hypothesis significant (Cohen, 2014). A p value of less than o.o5 also is an indicator of no significant effect by the dependent variables to the independent variable, therefore, making the null hypothesis not significant and the alternate hypothesis significant. Additionally, a predictor variable either gender or GRE score with a p-value that is low is likely to be meaningful as it can have an effect on the response variable (Cohen, 2014). Furthermore, a large p-value indicates that the predictor variables have an effect on the response variables, therefore, leading to the null hypothesis being significant and the alternate hypothesis not being significant (Cohen, 2014).

When using a regression coefficient that represents the changes in the variables and keeping the other variables constants and unchanged. This is important as it isolates the roles of one variable from the other in the study. This makes it possible to be able to measure the effect of a single variable on the constants variable. The example you can independently measure the effect of gender of the student on the degree completion frequency and do the same for the GRE score.

If in this case it is found that the gender of the student and the GRE score has no effect on the degree completion of students then we accept the alternate hypothesis and reject the null hypothesis. In this case, I will recommend that the GRE exam should be scrapped as it has no effect on whether the student will complete their degree or not. On the other hand, if the null hypothesis is accepted and the alternate hypothesis is rejected then it means that the GRE score and the gender of the students affect their degree completion frequency. Therefore there is no need of scrapping the GRE test done before admission as it is an important predictor of whether the student will graduate or not.

References

Bates, D., Maechler, M., Bolker, B., & Walker, S. (2014). lme4: Linear mixed-effects models using Eigen and S4. R package version , 1 (7), 1-23.

Cohen, P., West, S. G., & Aiken, L. S. (2014). Applied multiple regression/correlation analysis for the behavioral sciences . Psychology Press.

Fox, J. (2015). Applied regression analysis and generalized linear models . Sage Publications.

Hox, J. J., Moerbeek, M., & Van de Schoot, R. (2017). Multilevel analysis: Techniques and applications . Routledge.

Zhou, H., Deng, Z., Xia, Y., & Fu, M. (2016). A new sampling method in particle filter based on Pearson correlation coefficient. Neurocomputing , 216 , 208-215.