relationship between the anxiety of students towards an exam and the number of hours studied

In a study to assess the association between students’ exam anxiety and the number of hours studied. Data on this topic was gathered, and a statistical analysis was performed to determine the association. Statistical tests such as correlation can assist us in determining the type of link that exists between the two variables as well as the magnitude of the relationship. Other tests, such as the t-test and the ANOVA test, can be used to assess the variability of the two variables. We calculate the correlation between the two variables and analyze the results, as well as show how the t-test and ANOVA tests can be performed.Through the tests we can prove that anxiety decreases with the increase of hours studied.

Why is correlation the most appropriate statistics?

The study is aimed at identifying the relationship between the two variables, anxiety towards exams and the number of hours studied. The study aims to identify the relationship such as the effect of an increase in one variable on the other variable, this can be described as the correlation between the two variables. Correlation between variables can be measured both according to the direction and the magnitude of the correlation(Cohen, Cohen, West& Aiken, 2013). Direction can be either positive or negative, a positive correlation implies that as one variable increases, the other will increase too or as the as one decreases the other decreases too. Correlation coefficient is the statistic that enables us to measure the correlation between two variables. It indicates both the magnitude and the direction of the relationship. The magnitude ranges from zero to one with the strength increasing as the value approach one while the signs, positive and negative shows the direction of the relationship(Cohen et al.2013). Therefore, correlation is the most appropriate statistic for this study.

The null and alternative hypotheses.

Ho:There is no correlation between anxiety and the hours studied.

H1: The correlation between anxiety and the hours studied is not equal to zero.

Correlation.

Correlations

anxiety for exams

hours studied

anxiety for exams

Pearson Correlation

1

.565

Sig. (2-tailed)

.089

N

10

10

hours studied

Pearson Correlation

.565

1

Sig. (2-tailed)

.089

N

10

10

There exists a correlation of 0.565 between anxiety for exams and the number of hours taken to study for the exams. This is a positive correlation indicating the direction of the relationship which is anxiety increase with increase in time. The magnitude of the correlation indicates a moderate strengthof correlation.

Testing for the significance at a significance level of alpha =0.05, the test obtains a significance level of 0.089 which is greater than 0.05. Since 0.089 is greater than 0.05 it implies that the relationship between the anxiety score and the hours of study is statistically insignificant(Aron, Coups& Aron, 2013).

Interpretation

Since 0.089 > 0.05 we fail to reject the null hypothesis and conclude that the relationship between the anxiety score and the hours of study are statistically insignificant. This implies that in as much as the results shows the existence of correlation between the variables does not hold statistical significance. Thus a decrease or increase in one variable does not significantly relate to the decrease or increase in another variable.

Probability of a type 1 error

The probability of a type one error is the probability of rejecting the null hypothesis when it is right(Busk& Marascuilo, 2015). The probability is denoted by α(alpha). In this case the test is conducted at 95% confidence interval, implying that there is a 5% chance of rejecting the null hypothesis when it is right. Meaning that at every test of the hypothesis there exists a probability of 0.05 of wrongly rejecting the null hypothesis.

T-test and ANOVA test.

T-test and the ANOVA test are inferential statistics tests. Just like the correlation coefficient the t-tests and ANOVA tests are used to test and draw conclusions about the relationship between variables. T-test is used to compare the means of two variables to identify if there exists significant difference between the means of the variables(Brady et al. 2015). The ANOVA test compares means of two or more variables to test the significance of the mean differences. The data collected on the scores of anxiety and the hours used to study for exams can be used to conduct the tests. The data on the two variables can be used to compare the means of the variables using the t-test or ANOVA test to identify the significance of the mean difference.

Conclusion

The study was aimed at identifying the relationship between the anxiety and the hours of study. The correlation coefficient of the two variables indicated a positive correlation of moderate strength. However, on conducting a significance test we identify that the correlation between the two variables is statistically insignificant. This implies that the correlation coefficient may not necessarily indicate the significance of the relationship, therefore the significance test is very important for the correlation. From the results we identified that the correlation of the two variables is statistically insignificant. The data can also be used to conduct other inferential statistics test such as ANOVA test and t-test.

Reference

Aron, A., Coups, E., & Aron, E. N. (2013). Statistics for The Behavioral and Social Sciences: Pearson New International Edition: A Brief Course. Pearson Higher Ed.

Brady, S. M., Burow, M., Busch, W., Carlborg, Ö., Denby, K. J., Glazebrook, J., ... & Springer, N. M. (2015). Reassess the t test: interact with all your data via ANOVA. The Plant Cell, 27(8), 2088-2094.

Busk, P. L., & Marascuilo, L. A. (2015). Statistical Analysis in Single-Case Research. Single-Case Research Design and Analysis (Psychology Revivals): New Directions for Psychology and Education, 159.

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Applied multiple regression/correlation analysis for the behavioral sciences. Routledge.