Is there any difference in the number of students per teacher over years?

FACULTY OF MANAGEMENT AND TOURISM -o0o-STATISTICS FOR ECONOMICS Is there any difference in the number of students per teacher over years?. To be aware of this important issue, ourgroup d

FACULTY OF MANAGEMENT AND TOURISM

-o0o-STATISTICS FOR ECONOMICS

Is there any difference

in the number of students per teacher over years?

Tutor: Ms Lê Thị Ngọc Tú Tutorial: 4 – AC 09

Tutorial time: Tuesday – 12.30 – 14.00 Group members:

Nguyễn Huyền Trang

Trần Thu Hằng

Nguyễn Thị Tươi

0904010116 0904010030 0904010112

Nguyễn Thị Huệ Nguyễn Thị Hồng Nga Trần Thi Thanh Vân

0904010043 0904010077 0604040183

I Scenario 1

II Methodology 2

-1 Data collection 2

-2 Approach 3

III Analysis and discussion 3

-1 Check the required condition 3

-1.1 Normality 3

-1.2 Variances equality 3

-2 Hypothesis testing 5

2.1 Testing block means 5

2.2 Testing treatment means 6

-3 Discussion of finding 7

IV Limitation 8

V Recommendation and conclusion 9

-1 Recommendation 9

-2 Conclusion 9

-Reference i

Appendixes ii

A Calculating the sample variance ii

B Check the variances equality iii

C ANOVA (using Excel) iv

D Histograms v

E Data from GSO vii

I Scenario

In recent years, along with an increasing demand in human resources, a growingnumber of universities have plan to open new faculties as well as increase the number ofstudent admissions for these hot sectors However, it is undeniable that the mismatchbetween the number of students’ enrollment and teachers/lecturers’ quantity has largeeffect on the quality of education and training To be aware of this important issue, ourgroup decided to find out whether there are any differences in the number of students perteacher from 2005 to 2009 (particularly 2005, 2007 and 2009) by using statisticaltechnique (2-way ANOVA) The available data is blocked into six main regions inVietnam After conducting the test, the result show that during this 6-year period, despitethe 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 threeyears

II Methodology

1 Data collection

As the problem objective is to test whether there are changes in the amount ofstudents per teacher in recent years in Viet Nam, to be more detail we conduct the testover 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 VietnamGeneral Statistics Office website (shown in Appendix E)

However, we pointed out that many other factors may affect to the result of ourtest As a result, the variability within the samples might be large In order to reduce thevariation 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, Northernmidlands & 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 inthose areas over three years Nevertheless, because it was so difficult to conduct theexperiment on those areas, we continued using excel to select randomly one province ineach 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 arethe three years 2005, 2007, 2009

After doing the test, the following table was produced:

Red River delta 23.04452467 28.10416667 28.43558606Northern midlands & mountainous 21.81818182 31.32592593 10.34782609North Central and Central Coast 45.16666667 33.19047619 27.26348748Highlands 24.68253968 12.05464481 38.86703383South East 19.89583333 25.53491436 37.99269006Mekong River delta 14.95890411 8.356495468 11.10789474

2 Approach

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

III Analysis and discussion

3 Check the required condition

1.1 Normality

As you can see from the histogram in Appendix D, the three populations are nonnormal, in order to use 2 way ANOVA, we assume that all of them are normallydistributed

1.2 Variances equality

Since the best estimator of population variance is the sample variance, we appliedthe F - test to compare the variability of two populations (biggest versus smallest ones,shown in Appendix B) With α = 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 determinewhether differences exist among two or more population means It enables to measurehow much variation is attributable to difference among populations and how muchvariation is attributable to differences within populations By designing a randomizedblock design experiment, it reduces the within treatment variation so as to more easilydetect difference among the treatment means However, the technique only allowstesting for a difference rather than indicating which population means exceed others

After calculating the variance (shown in appendix A), the largest variance is thatone in 2009 while the smallest one is in 2007, so we use F-test to make inference aboutthose two population variances

1 Testing hypothesis:

2 1 2 2

O

 2 1 2 2

s F s

Since 0.0256 < F = 0.69 < 39, not reject Ho

Therefore, there is not enough evidence to conclude that the population variances differ

5 Value of test statistic:

As shown in the ANOVA table (Appendix C) F = 1.98995

6 Conclusion:

Since F = 1.98995 < 3.33, not reject Ho

Therefore, there is not enough evidence to conclude that block means differ,which indicate that we can use blocks to remove the variability and two-way ANOVAcan be conducted

2.2 Testing treatment means

5 Value of test statistic:

As shown in the ANOVA table (Appendix C): F = 0.11241

6 Conclusion:

Since F = 0.11241 < 4.10, we do not reject Ho

Hence, there is not sufficient evidence to conclude that differences exist among the three years

f(F)

0 0.11241 4.10

Rejection Region

5 Discussion of finding

It is obvious from the hypothesis tests that there is not enough evidence to rejectthe null hypothesis, which assumes that there is no difference between the ratios ofstudents/teacher in Vietnam over five year period From the result extracted from the dataanalysis section, there is also no difference among the block means representing thepopulation of six main regions in Vietnam Therefore, it is quite easy to recognize thebalance state through these six areas

If the test were not conducted, people may think that the ratio of students perteacher increases over the years because of the student growth in Vietnam The factshows that due to high demand in high quality human resource to meet challenges ofeconomic growth, many universities/colleges have increased the number of admissionyear by year To be aware of that fact, education units have had plan to recruit moreteachers to keep up with the increase in number of students and remain/improve teachingquality This fact somehow explains the reason for unchanged number of students per

teacher over the years However, compared with the world’s standard (15-20

students/teacher) and the goal of Ministry of Education and Training (20 students/teacher), the current ratio in Vietnam is still much higher with 28 students/teacher Therefore, we need to increase the number of teachers to improve the

quality of our country‘s education Besides, teachers’ quality (degree, teaching skills, etc)which directly affects education quality should be concerned about From the resultextracted from the data analysis section, there is also no difference among the blockmeans representing the population of six main regions in Vietnam So, it is quite easy torecognize the balance state through these six areas

 Rejection regions: we chose α = 0.05, which might lead to type II error.However, we believed that it is not affecting our result so much.

 Time consuming: because checking consumptions are necessary for testing so

we spend lots of time to check the normality of populations and the equality ofits variance Fortunately, histograms drawn resulting normally distributedpopulations as we expected Moreover, we also check SSB to ensure that there

is no difference between blocks

 Normality: In order to follow the 2 way ANOVA test above, we have assumedthat the three populations are normally distributed

V Recommendation and conclusion

6 Recommendation

In the recent years, the number of student increases continuously in universities

As we expected, the ratio of the professors and their students does not change from year

to next year, which means that it does not have strong influences on the quality ofteaching and studying However, we still have some recommendation in order to improvethose qualities.

+ Reinforcing high qualified professors: since the number of students increases inuniversities, it creates a lot of pressure on education The lack of high qualified teachers

is inevasible Therefore, reinforcing high qualified professors are the first principles

+ Motivating teachers: the teachers should be facilitated studies with suitablecompensations Beside, creating good relationships between teachers and their studentsare respected also Thus, that reduce a large number of teachers quit their jobs

+ Changing from traditional classes to new model ones: let Hanoi University be

an example, the students and teachers attend at five lectures and five tutorials each week.Consequently, the professors and their students have extra time for self-study

+ Flexible time: both teachers and student as well can involve in the socialactivities, voluntary event, and part-time jobs in order to gain practical experiences, softskills like communication skills In addition, universities can provide enough facilitiesand equipments for teaching

7 Conclusion

In conclusion, the report carried out on the purpose of dealing with a statisticsquestion: whether there exist any differences in the number of students per teacherthrough 5-years period of time from 2005 to 2009 in six main regions in Vietnam

year in regions which we indicate above It also means that Vietnamese universityeducation can provide enough teachers to meet the need of social in general and theincrease in enrolment target through years However, we still need some recommendation

in order to improve the education system as shown in our report

During the time we were conducting the research, some limitation occurredwhich lead to inaccuracy result In addition, because of the characteristic of ANOVA testand time consuming, we can not show the whole picture of the issue for example, thetrend of enrolment target, change in method and model class, etc If by any chance ourreport has aroused interest in other researchers about the same topic, we hope that futurestudies would be conducted on a larger time scale, with more detailed data, and withfurther knowledge of statistic

A Calculating the sample variance

Northern midlands and mountains areas 3 63.4919 21.164 110.341

Northern Central area and Central coastal area 3 105.621 35.2069 83.1804

F-Test Two-Sample for Variances

Since 0.198 < F = 0.689 < 5, we do not reject Ho

There is enough evidence to conclude that the two population variances are the same

C ANOVA (using Excel)

2007 2008 2009Teacher Student S/T Teacher Student S/T Teacher Student S/T