# Statistics: Academic Performance Correlation Study

## Research design

In this project, I was interested in determining whether there is a relationship between academic performance in reading and academic performance in science courses. The study sought to test the following hypothesis:

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• H0: There is a significant correlation between reading performance and performance in science courses.
• H1: There is no correlation between reading performance and performance in science courses.

To test this hypothesis, I used a correlation research design in this project. Correlation refers to a measure of the degree of association between independent variables and dependent variables (Cresswell, 2003). Coefficients of correlation can range from a negative one to a positive one, and it is a dimensionless quantity (Cresswell, 2003). Besides indicating a possible causal relationship, correlation can be used to demonstrate a predictive relationship in this project.

When considering a linear relationship between variables, one must have a dependent and independent variable. The data should be continuous because if it is categorical then the best-suited measure of the association will be a chi-square. I found this type of design relevant since the study seeks to determine the relationship between two quantitative variables to predict or explain the results. The independent variable in this study included proficiency in reading while the dependent variable was comprised of scores in science courses. I collected data from a selected school from the Department of Education database.

## Sample size

The sample size for this project included 54 students who took both reading and science courses during the 2013-2014 academic year. The participants were on average between the ages of ten and thirteen. The scores were for the same students and the same grade reading and science achievement scores.

## Data analysis

I utilized the statistical package SPSS for window application to perform all the data analysis. The SPSS program avails the capabilities for the data to be analyzed fully and flexible (Saunders, Lewis, & Thornhill, 2003). The tools provided by SPSS include the Shapiro-Wilk test, Pearson correlation, and linear regression test.

Once I obtained the data, I checked to confirm whether it was normal using the Shapiro-Wilk test. The Shapiro-Wilk test analyzes whether the sample population is normally distributed. The null hypothesis for this sample is that the population is normally distributed. When the p-value is less than the chosen alpha value (0.05), then the null hypothesis that the population is normally distributed is rejected. If the p-value is equal or greater than the chosen alpha value, the null hypothesis is accepted. From the following table, I did not reject the null hypothesis since all sig values (P- Values) were greater than 0.05 hence the data is normal at a 95% confidence interval (Cresswell, 2003).

 Tests of Normality Kolmogorov-Smirnova Shapiro-Wilk Statistic df Sig. Statistic df Sig. Science .140 54 .010 .959 54 .062 Reading .098 54 .200* .983 54 .631

I used Pearson correlation to assess the relationship between performance in reading and performance in science courses.

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 Correlations Reading Science Reading Pearson Correlation 1 .662** Sig. (2-tailed) .000 N 54 54 Science Pearson Correlation .662** 1 Sig. (2-tailed) .000 N 54 54

From the table above there is a positive linear correlation of 0.662. Therefore, there is a positive relationship between the ability of the student to read and their ability to pass science courses. The higher the pupil’s ability to read the higher their test scores in science and vice versa.

To get a model relationship, I performed a regression analysis. Regression analysis is a statistical tool for evaluating the relationship of one or more independent variable {x1, x2, …, xn} to a single continuous dependent variable y. It attempts to establish the nature of a relationship between variables thus provide a mechanism for predicting or forecasting. In this case, I performed simple regression since the regression study, in this case, is confined to a study of only two variables. I utilized a linear regression test to determine whether performance in reading can predict proficiency in science courses.

 Model R R Square Adjusted R Square Std. The error of the Estimate Durbin-Watson 1 .662a .439 .428 7.18031 2.051 a. Predictors: (Constant), Reading b. Dependent Variable: Science

The model can explain 43.9% of the variation in the dependent variable (Science). The remainder is due to chance or other factors. The value of Durbin-Watson of 2.051 indicates that the data is independent.

 ANOVA Model Sum of Squares df Mean Square F Sig. 1 Regression 2097.135 1 2097.135 40.676 .000b Residual 2680.958 52 51.557 Total 4778.093 53 a. Dependent Variable: Science b. Predictors: (Constant), Reading

The table above reports a significant F-statistics [F (1, 52) =40.676,

P – Value>0.0001] indicating a significant and valid model.

 Coefficients Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 21.160 4.913 4.307 .000 Reading .589 .092 .662 6.378 .000 a. Dependent Variable: Science
 From the model, all the parameters are significant since they have p-values greater than 0.05. Therefore, all parameters contribute to the model.

The model is given by Science = bo + b1Reading.

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A unit increase in reading leads to an increase in science score by 0.589.

Cresswell, J. W. (2003). Research Design: qualitative, quantitative and mixed method approach. London: Sage Publications.

Saunders, M., Lewis, P., & Thornhill, A. (2003). Research Methods for Business Students. London: Prentice Hall.

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