Correlation measures the degree of relationship between variables. The test is only important if all the variables are continuous in nature. In our case, student anxiety and study hours are all continuous variables and this necessitates the use of correlation test.
A hypothesis is an explanation relating facts which should be capable of being tested through further analysis. It gives an appropriate description of the research; supports reporting of results thereby proving whether or not the research under review offer correct explanation to the known fact. It can be null or alternative. The null hypothesis (
): Students’ anxiety for exams is not related to the number of study hours. Alternative hypothesis (
): Students’ anxiety for exams is related to the number of study hours.
Correlation coefficient=sum of ((X-mean of X)(Y-mean of Y)/(n-1*Standard deviation of X and of Y))= 47/(74.736*2.40*3.46)= 0.63
Under descriptive statistics, the mean number of students’ anxiety for an exam was estimated at 5.90 while the mean for study hours was 4.0. It is important to note that correlation coefficient measures only the relationship between one or more variables with its value ranging between -1, 0 to +1. For instance, a value close to 1 indicates a strong positive relationship while a value close to -1 shows a strong negative relationship with 0 indicating no relationship. The sign before the value here only serves to show the direction of the relationship. In our example above, for instance, there was a positive relationship between the students’ anxiety for an exam and the number of hours of studies (r = 0.62). This meant that the anxiety for exams shows a direct positive relationship to the study hours. In the example above, correlation is not significant at the alpha level of 0.05 (2-tailed). The P value was estimated at 0.089 which is greater than 0.05 and thus we can conclude that there is no existence of a relationship between the students level of exam anxiety and study hours.
Type I error: This error occurs due to a researcher decision to reject a true null hypothesis. It can also occur when the result from any analysis is consistent with known facts or reality but researchers reject this result as falls. The rate of the type I error denoted by alpha is known as the size of the test. In normal situation, the probability of this error equals to the significant level of the test and the probability of declining null hypothesis when it is false = 1. The probability of this error in our situation is 0.05. However, to decrease the probability of this error, a small the significance level is essential (Primer on type I and type II errors, 2001).
T- test: – This allows for testing of means of two groups of variables. It is important when one variable must be categorical and the other a continuous variable. In our case, students’ anxiety for the exam is a continuous variable while study hours can be mad to be categorical with more values. If that is possible, then a t-test can be run to test the means of these variables.
ANOVA (Analysis Of Variance): This test allows for the comparison of three or more group of variables. The test assumes that samples are drawn from two or more groups with a random population. However, care should be taken to ensure normal distribution of variables; and that samples should be independent of each other and an equal population variances. In our case, the data may be set in such a way that the students’ anxiety scores to have an effect on other different variables across the study but hours of study be only one of the factors (Silicon genetics, 2003). It is also necessary to consider the degree of freedom values, F test and an alpha usually estimated at 0.05. This is because ANOVA uses the effect size of F test to draw its conclusions (Vicky, 2009).
References
Primer on type I and type II errors. (2001). Web.
Silicon genetics. (2003).Statistical analysis, 1-way ANOVA. Web.
Vicky, R. N. (2009). T-tests and One-Way ANOVA. Web.