Introduction
This paper seeks to critique a statistical study by Sue B. Schou titled “A study of Student Attitudes and Performance in an Online Introductory Business Statistics Class.” This article was selected because it used t-test in data analysis. This paper will discuss t-test, summarize the study and critique the use of t-test for the study.
T-test
T-tests are often used to compare the mean of a given group with a given value or compare the mean of two groups. On that vein, there are two broad categories of t-test; independent t-tests and dependent t-tests. Independent t tests are intended to compare the group mean of a variable of interest with a predetermined level of the variable. The null hypothesis assumes that the group mean is the same as the predetermined level of the variable whereas the alternate hypothesis assumes that the group mean is not the same as the predetermined level of the variable . On the other hand, dependent t tests are intended to compare a given variable in two groups using their mean. The null hypothesis assumes that the group mean in the two groups is the equal while the alternate hypothesis the group mean in the two groups is not equal. There are two types of dependent t-test; two sample t-test and paired sample t-test. Two sample t-tests are used when the researcher is comparing two distinct groups. Paired sample t-test is used when the researcher uses one group but compares pre-test and post-test mean of the variable of interest. In the selected study, the researcher used dependent sample t-test because she was interested in comparing two groups. Two sample t-tests were used to test the first hypothesis while paired sample t-test was used to test the second hypothesis.
Summary of the Article
How T-test was used in the study
The researcher sought to find out whether distance learning via online courses is effective by comparing the learning outcomes and attitude toward statistics of students in a conventional business statistics course with the learning outcomes and attitude towards statistics of online students undertaking the same course at Idaho State University. To examine the learning outcomes, the null and alternate hypothesis were as follows;
Ho: Utraditional = Uonline There is no difference in the final examination mean score between students in the traditional course and students in the conventional class.
H1: Utraditional ≠ Uonline There is a difference in the final examination mean score between students in the traditional course and students in the conventional class.
Ho: Upretest ≤ Uposttest The pre-test mean of the Survey of Attitude toward Statistic (S.A.T) is lower than the mean post-test S.A.T score.
The researcher used a sample of 31 participants; one group of 16 participants who were enrolled in a conventional class and 15 participants who undertook the same course via online learning. Both groups had competent and experienced statistics tutors. The same topics were taught to both groups. The instructors gave similar notes and similar regular homework assignments were given to students in both groups. Both classes took eight weeks before they were assigned a common final examination that was supervised. The scores of students in the final examination were recorded. To evaluate the first hypothesis, a two sample t-test was used. The results revealed that the p-value was 0.15. Therefore, the researcher concluded that there is no significant difference in the learning outcomes of students in a traditional course and students in an online course. The research findings concurred with previous studies done by other researchers on the same subject. To analyse the second hypothesis, the researcher used a paired sample t-test. The results revealed that the p-value for online students was 0.016. Therefore, students in the online class had improved attitude towards statistics after instructions. On the contrary, the results revealed that students in the traditional class did not have improved attitudes towards statistics after instruction.
Appropriateness of T-test for the study
T-test was appropriate for this study because the researcher was interested in comparing learning outcomes of two groups. Therefore, two sample t-tests were most appropriate since there were two groups involved; traditional class group and online class group. Secondly, the researcher was interested in evaluating students’ attitudes towards statistics before and after instructions. Paired sample t-test was the most appropriate test when comparing pre-test and post-test groups. In this case, the pre-test group mean was the average Survey of Attitude Toward Statistic (S.A.T) score before attending classes and the post-test group mean was the average Survey of Attitude Toward Statistic (S.A.T) score after attending classes.
Assumptions of T-test
The accuracy of any statistical test depends on whether appropriate measures were taken to ensure that the assumptions relating to the test were met. The study under examination took measures to ensure the assumptions were met. However, the researcher overlooked other assumptions as discussed below.
The first assumption relates to instrumentation. T-test assumes that the collected data for the variable of interest is based on a scale or instrument that is ordinal or continuous. Learning outcomes was measured using final examination scores which are ordinal data. The researcher was also interested in students’ attitudes towards statistics which was measured using a scale using Survey of Attitude toward Statistic (S.A.T). Therefore, the research met this assumption.
Secondly, t-test assumes that random sampling was used. Random sampling is used to eliminate researcher’s bias. Although the researcher indicated that a sample of 31 participants was selected, she did not indicate whether the sample was selected randomly. The researcher ignores this assumption hence reducing the accuracy of her research findings. Lastly, t-test assumes that the data collected from the sample assumes a normal distribution. The researcher did not make any attempts to test whether the data assumes a normal distribution. Besides, the fact that the sample was not randomly selected casts doubt as to whether the data was normally distributed. This is because the sample may contain the researchers’ bias hence it may be skewed.
Levels of measurement
The researcher sought to find out whether distance learning via online courses is effective by comparing the learning outcomes and attitude toward statistics of students in a conventional business statistics course with the learning outcomes and attitude towards statistics of online students undertaking the same course. Therefore the researcher was interested in two variables; learning outcomes and attitude towards statistics. Learning outcomes was measured using final examination scores which are ordinal data. Students’ attitudes towards statistics were measured using a scale using Survey of Attitude toward Statistic (S.A.T) which is also ordinal data.
Appropriateness of the level of measurement
The levels of measurement were appropriate. The most practical way to measure learning outcome is examination scores. Use of ordinal data in measuring learning outcomes and students’ attitudes towards statistics made it possible to use various t-tests.
Display of data
The researcher used table to display descriptive statistics of both the traditional class group and the online class group. In addition, the researcher used a table to display descriptive statistics for the pre-test and post-test scores obtained using S.A.T for both groups.
Appropriateness of the data display
References
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Klugh, H. E. (2009). Statistics: the essentials for research (6, illustrated ed.). New York: Wiley.
LeBlanc, D. C. (2004). Statistics: Concepts and Applications for Science (illustrated ed.). New York: Jones & Bartlett Learning.
Peck, R., & Devore, J. L. (2011). Statistics: The Exploration and Analysis of Data (7 ed.). New York: Cengage Learning.
Schou , S. B. (2011, May 10). A study of Student Attitudes and Performance in an Online Introductory Business Statistics Class. Retrieved June 19, 2013, from http://ejite.isu.edu: http://ejite.isu.edu/Volume6/Schou.pdf
