BUSI 820 Liberty University Interpreting Correlations Statistics Response

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Review one students response to D6.1 and D6.2 Summarize their findings and indicate areas of agreement, disagreement and improvement. Support your views with citations and include a reference section.

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Discussion Forum Six

D6.1 Interpreting Correlations

D6.1a From Output 9.2 What do Correlations Coefficients tell us?

In a review of output 9.2, the Spearman’s rho correlation coefficients tell the researcher the linear relationship between variables based on ranking scores and ordinal data. The request in the problem was to investigate statistical significance in the association between mother’s education and math achievement. Due to mother’s education being skewed, the Spearman’s rho was calculated. When looking at correlation coefficients, the researcher is investigating positive or negative relationships. In this instance, the correlation was positive at 0.32, meaning that students who have highly educated mothers tend to have higher math achievement test scores, the reverse is also indicated.

D6.1b Determine the r^2 for the Pearson Correlation and Explain the Meaning

Morgan et al. (2013) elaborate, the r^2 is used as an indication of variance for the requested variables, in this case the variance between math achievement test scores is based on the Pearson Correlation. As the r value is equal to 0.34, the r^2 value is 0.58, meaning that approximately 58% of the variance in math achievement test scores can be predicted from mother’s education. In this case, however, the mother’s education variable is skewed, so the Pearson Correlation matrix test is violated. The Correlations should thus be run on the Spearman’s rho.

D6.1c Compare the Pearson and Spearman Correlations, Explain Comparison and Type

Morgan et al. (2013) define the Pearson correlation as a bivariate parametric statistic that is used when variables are scale or normally distributed. Moreover, Morgan et al. (2013) argue the Spearman rho is used to compute both parametric and nonparametric correlations to complete comparisons of variables and associations between them. Spearman rho is used for ordinal statistics, as the Pearson correlation is used for scale statistics.

D6.2 Interpreting Regressions

D6.2a Using Output 9.4, Find the Regression Coefficient and Standardized Regression

In Problem 9.4, the author ran linear bivariate regressions to establish the r value between different variables of grades in high school and math achievement. In this instance, the r value, or the regression coefficient was 0.50, meaning this relationship is positive. Moreover, in looking at the r^2 of this model, it is seen that the value is 0.25, explaining in this model that 25% of the time those students who had high math achievement test scores also had high grades in high school, and vice versa.

D6.2b How do these Values Compare to the Same Variables in Output 9.3?

In this case, the variables structures are of the same in type, the calculation is just completed differently as a simple regression. For Output 9.4, math achievement test variables are scale, while grades in high school are ordinal. For Output 9.3, math achievement test score was a scale variable, while mother’s education is an ordinal variable. From a comparative perspective, the correlation coefficient for the Spearman’s rho in output 9.3 was 0.34, while the simple regression coefficient was 0.50, since a perfect positive or negative relationship would be +1.00, or -1.00, this tells us that the strength of the positive relationship is higher between the variables of math achievement test scores and grades in high school, rather than mother’s education and math achievement test scores.

D6.2c What does the Regression Coefficient tell you?

A regression coefficient tells the researcher the slope of the best fit line, or in this case the regression line. While this slope is not equal to the correlation coefficient, in looking at the model for grades in high school, the regression coefficient is equal to 2.142. In a review of the coefficients table, the slope line affixes as a best fit regression line for the variety of data on a scatterplot, showing the association between the two requested variables. While the standardized coefficient is equal to the correlation between the two variables. The main difference between bivariate regression and bivariate correlation is that in the bivariate regression model, the researcher is predicting one variable from another variable; however, in bivariate correlation simple relationships are requested.

D6.2d Problem 9.4 Design a Research Question so the Pearson Correlation is Appropriate

The first question for consideration is: will student’s grades in high school be associated with their overall math achievement, and if so, what is the strength of the association? Since grades in high school is an ordinal variables and math achievement is a scale variable, the Pearson Correlation will tell us the intercorrelations of the variables. This does assume, however, that the variables are normally distributed and not skewed, and assumptions of linearity are not markedly violated.

D6.2e Problem 9.4 Design a Research Question so the Bivariate Regression is Appropriate

The second question for consideration is: will student’s grades in high school be predicted by their overall math achievement, and if so, what is the strength of the association? By using a simple bivariate regression, the researcher can determine a simple analysis of the effect size between the two variables. In looking at the effect size for multiple variables, the researcher can determine the strengths of multiple relationships which may support the variety of hypotheses established before the research project began.

References

Morgan, G., Leech, N., Gloeckner, G., & Barrett, K. (2013). IBM SPSS for Introductory Statistics (5th Ed.). New York, NY.