Report of Sta2

I. Scenario

In recent years, along with an increasing demand in human resources, a growing number of universities have plan to open new faculties as well as increase the number of student admissions for these hot sectors. However, it is undeniable that the mismatch between the number of students' enrollment and teachers/lecturers' quantity has large effect on the quality of education and training. To be aware of this important issue, our group decided to find out whether there are any differences in the number of students per teacher from 2005 to 2009 (particularly 2005, 2007 and 2009) by using statistical technique (2-way ANOVA). The available data is blocked into six main regions in Vietnam. After conducting the test, the result show that during this 6-year period, despite the changes in both number of students and teachers, the number of students per teacher is nearly the same, which lead to our conclusion that there is no difference among three years.

II. Methodology

1. Data collection

As the problem objective is to test whether there are changes in the amount of students per teacher in recent years in Viet Nam, to be more detail we conduct the test over three years including 2005, 2007, and 2009. Moreover, the data type is quantitative; we decided to use the analysis of variance. The data was collected from the Vietnam General Statistics Office website (shown in Appendix E).

However, we pointed out that many other factors may affect to the result of our test. As a result, the variability within the samples might be large. In order to reduce the variation in each year, we made the survey according to blocks and then did the test. Therefore, we took a random sample of six regions containing Red River delta, Northern midlands & mountainous, Northern Central and Central Coastal, Highlands, South East, and Mekong River delta to test the changes in the rate of student over one teacher in those areas over three years. Nevertheless, because it was so difficult to conduct the experiment on those areas, we continued using excel to select randomly one province in each area to be on behalf of that region. And thereafter, we got the result of six provinces: Hai Phong, Son La, Da Nang, Kon Tum, Dong Nai, and the last one is Kien Giang. Thus, there are six blocks containing six regions and three treatments are three years in this test. The experimental design used here is a randomized block design, which treatments are the three years 2005, 2007, 2009.

After doing the test, the following table was produced:

2005 2007 2009

Red River delta 23.04452467 28.10416667 28.43558606

Northern midlands & mountainous 21.81818182 31.32592593 10.34782609

North Central and Central Coast 45.16666667 33.19047619 27.26348748

Highlands 24.68253968 12.05464481 38.86703383

South East 19.89583333 25.53491436 37.99269006

Mekong River delta 14.95890411 8.356495468 11.10789474

2. Approach

In order to indicate whether differences exist among the number of students over the quantity of teachers over three years, it is necessary to check the required conditions for using F-test of two-way ANOVA, which are the random variable is normally distributes and the population variances are equal. We will check each condition one by one.

III. Analysis and discussion

1. Check the required condition

1.1. Normality

As you can see from the histogram in Appendix D, the three populations are non normal, in order to use 2 way ANOVA, we assume that all of them are normally distributed.

1.2. Variances equality

Since the best estimator of population variance is the sample variance, we applied the F - test to compare the variability of two populations (biggest versus smallest ones, shown in Appendix B). With ? = 5%, the F-values of the three tests are higher than 0.05. Therefore, it can be inferred that the variances are equal.

For its applicability, two-way ANOVA is a procedure that testes to determine whether differences exist among two or more population means. It enables to measure how much variation is attributable to difference among populations and how much variation is attributable to differences within populations. By designing a randomized block design experiment, it reduces the