## Introduction

The purpose of the research study was to determine whether students who do the extra credit project learn more and do better in the course (as observed by their total score in class) in spite of their individual score on the extra credit project. The study was controlled for the variable *student’s GPA*, since students who tend to have higher GPAs are likely to do well in classes overall.

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### Research Question

The research attempts to answer the following question: do those who do the extra credit project learn more and do better in the course (have significantly higher total score) than those who do not do the extra credit project, the student’s specific score on the extra credit project notwithstanding?

## Hypotheses

### Null Hypothesis

H_{0}: μ_{y} = μ_{n}, the mean student’s total score for those who do the extra credit project (μ_{y}) is the same as the mean student’s total score for those who do not do the extra credit project (μ_{n}).

### Alternative Hypothesis

H_{1}: μ_{y} ≠ μ_{n}, the mean student’s total score for those who do the extra credit project (μ_{y}) is the same as the mean student’s total score for those who do not do the extra credit project (μ_{n}).

## Variables

The following are the variables used in the study: student’s total score in the class, student’s GPA, and did extra credit project. The variable *student’s total score in the class (total score)* is a continuous, quantitative variable of the ratio scale of measurement. It is a dependent variable in this study. The variable *student’s GPA (GPA)* is also a continuous, quantitative variable of the ratio scale of measurement (Adèr, Mellenbergh & Hand, 2008). It is the control variable in this study. The variable *did extra credit project (extra credit)* is a discrete, categorical variable of the “nominal scale of measurement” (Creswell, 2012, p.17). It is the independent variable in this study.

## Descriptive Statistics

The mean and standard deviation for the overall total score in the class were 79.03 and 11.042, respectively. The students that did the extra credit project had a mean total score of 83.85 with a standard deviation of 9.167, while those who did not do the extra credit project had a mean total score of 74.20 with a standard deviation of 10.827. The median total score for those who did extra credit project was 81, while for those who did not was 73.5.

A mean value larger than the median suggests a positively skewed distribution (American Psychological Association, 2010; Huck, 2012). Therefore, the distributions of the total scores of the students that did extra credit project and those who did not, as well as the distribution of the overall total scores are positively skewed. The mean for the overall GPA was 2.6158, and the standard deviation was 0.65613. The students that did the extra credit project had a mean GPA of 2.7150 with a standard deviation of 0.62818. Their median GPA was 2.635. Those who did not do the extra credit project had a mean GPA of 2.5165 with a standard deviation of 0.68434.

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Their median GPA was 2.455. The means and medians also suggest that the distributions for the GPA of both the students that did extra credit project and those who did not as well as the distribution of the overall GPA are also positively skewed. Forty individuals participated in the research study, of which half of them did the extra credit project while the other half did not do the extra credit project. The mean and median are not meaningful for a nominal variable, such as *did extra credit project* as well as ordinal variables.

## ANOVA and ANCOVA

A one-way ANOVA was conducted for this study because only one factor was involved. There is an interaction between the independent variable and the covariate (P<0.05). This result is significant because it highlights that the differences observed between the condition mean may be due to the manipulation of the independent variable as opposed to chance. It is not important to report the significant results for GPA because the variable is a control variable. The variable of interest was the students’ total score.

The results of the ANCOVA (P < 0.05) lead us to reject the null hypothesis (the mean student’s total score for those who do the extra credit project is the same as the mean student’s total score for those who do not do the extra credit project) in favor of the alternative hypothesis (the mean student’s total score for those who do the extra credit project is significantly different to the mean student’s total score for those who do not do the extra credit project).

In other words, there is a significant difference between the means for the total scores of students that did the extra credit project and those that did not need when adjusted for the covariate – Student’s GPA (P < 0.0005). It can be concluded that students that do extra credit projects learn more and do better in the course than those who do not do the extra credit project. However, it cannot be concluded that doing the extra credit project is the cause of the students’ better performance.

### Issues related to Data Collection

A number of issues concerning how the data was gathered should be considered in the interpretation of data. In regards to ethics, subjects should not be forced or tricked to provide responses. The need to inform the subjects of the purpose of the research may lead to bias of results. An appropriate research design should be used with various data collection methods. For instance, a research design that is suitable for data collected through random sampling may not be suitable for data collected through non-random samples. Correlation should not be interpreted to mean causation. Causation can be viewed as probabilistically or deterministically.

## Conclusion

The results of the ANOVA showed that an interaction existed between the covariate and the independent variable. This means that the difference in the condition means could be due to independence variable manipulation as opposed to chance. The results of the ANCOVA led to the rejection of the null hypothesis and the conclusion that there is a significant difference between the means for the total scores of students that did the extra credit project and those that did not do the extra credit project when adjusted for the covariate – Student’s GPA. Therefore, students who do extra credit projects learn more and do better in the course than those who do not.

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## References

Adèr, H. J., Mellenbergh, G. J., & Hand, D. J. (2008). *Advising on research methods: A consultant’s companion*. Huizen: Johannes van Kessel Publishing.

American Psychological Association (2010). *Publication manual of the American Psychological Association *(6^{th} ed.). Washington, D.C.: American Psychological Association.

Creswell, J.W. (2012). *Educational research: Planning, conducting, and evaluating quantitative and qualitative research*. Upper Saddle River, NJ: Prentice Hall.

Huck, S. W. (2012). *Reading statistics and research* (6^{th} ed.). Boston, MA: Pearson.