Table of Contents
In this project report, discussions have been made regarding the different components described in Tasks 3 and 4 that focused on two significant variables i.e. driving course completion (took course or control) and driving test outcome (pass or fail). Initially, relevant data is collected about the number of participants who passed or failed their driving tests by course completion status. Therefore, based on the availability of these data, two hypotheses were designed to draw valid inferences. For instance, the Null hypothesis (H0) represented that there is no significant difference between driving test results and course completion and the alternative hypothesis (H1) signified that there is a significant difference between these two variables. Based on the results obtained, it can be observed that 60% of the people who took the course passed the test, which was greater than that of the people (35%) who had their own control and did not take the course. The statistical tool of chi-square test was considered in order to examine the association between driving course completion and driving test result. The obtained chi-square result was found to be insignificant, indicating that the participating people who took the course and who did not have any significant difference with the results of the driving test. Therefore, based on this notion, the null hypothesis is thereby accepted with rejecting the alternative hypothesis.
This discussion is based on the results obtained for the DE100 Project Report that comprised the components of online activities including Task 3 and Task 4. The study intended to investigate the relationship existing amid driving test completion (took course or control) and driving test outcome (pass or fail). Thus, it was hypothesised that the participants who partake in the training course would pass more than those who did not took part in the course. To be precise, prior to conducting this study, alternative hypothesis (H1) was considered, representing that people who took the driving training course were of higher proportion than those who did not and had their own control. Correspondingly, the null hypothesis (H0) signified that there was no major distinction between the two variables i.e. the pass rate and the training course. It is suggested that the people who are aged and have several years of experience usually develop cognitive skills for driving when evaluated based on their driving performances (Odenheimer et.al., 1994). From the data collected, it was observed that out of 20 participants, 12 people were involved in the course and passed the driving test, while the remaining 8 participants failed. Among the people who did not take the course and had their own control, it was found that only 7 of them passed and the remaining 13 failed the test. This implies the passing ratio to be 60% and 35% for those who had their own control. These obtained results therefore signified that the passing percentage of the people taking training course were higher than those who did not take the course and had their own control.
A statistical tool of chi-square test was considered in order to determine the affiliation existing amid driving course completion and driving test outcome. Chi-square test is a method, which is used to evaluate significant differences persisting between two variables considered in a given case. It is best suited for a quantitative research having sufficient sample size, which must be in a frequency form and the observed data should be included. In general, under chi-square test method, the disparity amid the expected frequency and the observed frequency is calculated. For this particular study, the null hypothesis would be particularly claiming the distribution pattern of the variables being identified. Correspondingly, in the case of alternative hypothesis, the expected frequency is likely to have major distinctions with the observed frequency, thereby rejecting the null hypothesis (University of Regina, 2004). The chi-square test result obtained for this particular study was insignificant in nature, implying that the null hypothesis must be retained. Therefore, the test result indicated that there was no major variation between the two variables i.e. driving course completion (took course or control) and driving test outcome (pass or fail).
According to the given data and the obtained results, it can be noted that the effect size of chi-square test was moderate in nature because it possessed certain drawbacks that might affected the test results. Even though it is best suited when deriving connection amid one nominal variable with two or more values, still it may not generate accurate results. This is possible if the expected observations are relatively smaller (McDonald, 2014). Another disadvantage of chi-square test is that the value of this test depends on the manner in which data to be used is segregated into different classes and thereby require adequate sample size for its validity (NIST, n.d.). In addition, discontinuity is another factor of concern that can create unreliable results wherein continuity must be required. In this context, continuous distribution implies that the value of the test can be negative or positive and the optimum results cannot be obtained with the use of chi-square test. It must be mentioned that chi-square test cannot be used for those data whose values are fewer than 5 or in excess of 20% of the total expected frequencies (Uebersax, 2016). Therefore, the test is not able to determine relationship strengths and the results are sensitive based on the sample size being considered. This implies that irrespective of the relationship, the chi-square test is directly comparative to the sample size (Boston University, n.d.).
Therefore, based on the above findings and the stated drawbacks of chi-square test, it can be inferred that if the limitations are not considered, then the test results will not be reliable, hence, selection of tests should be done carefully considering the limitations. If the available data comprises more than 20% expected frequencies, it is suggested to use certain other methods such as exact test or G-test. If the sample size is too large, the tests results may turn out to be statistically significant, thereby making the test quite reliable in nature. The case wherein the size of the sample does not surpass 1000, exact test or G-test can be recommended for usage where the expected frequency is more than 5.
- Boston University, No Date. Limitations of the Chi-Square Test. Boston University Metropolitan College. [Online] Available at: https://learn.bu.edu/bbcswebdav/pid-826908-dt-content-rid-2073693_1/courses/13sprgmetcj702_ol/week05/metcj702_W05S02T05_limitations.html [Accessed Aug 05, 2015].
- McDonald, J. H., 2014. Chi-Square Test of Goodness-of-Fit. Handbook of Biological Statistics. [Online] Available at: http://www.biostathandbook.com/chigof.html [Accessed Aug 05, 2015]
- NIST, No Date. Chi-Square Goodness-of-Fit Test. Engineering Statistics Handbook. [Online] Available at: http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm [Accessed Aug 05, 2015]
- Odenheimer, G. L. al., 1994. Performance-Based Driving Evaluation of the Elderly Driver: Safety, Reliability, and Validity. Journal of Gerontology, Vol. 49, No. 4, pp. M153–M159.
- Uebersax, J., 2016. Assumptions and Limitations of Chi-Squared Tests. Statistics 312, pp. 1-7.
- University of Regina, 2004. Chapter 10 Chi Square Tests. [Online] Available at: http://uregina.ca/~gingrich/ch10.pdf [Accessed Aug 05, 2015].