STATISTICAL HYPOTHESIS TESTING IN EXCEL HÍC Pavel, (SK), POKORNÝ Milan, (SK) Abstract. The paper deals with statistical hypothesis testing in Excel. At the Faculty of Education at Trnava University a huge amount of students needs the basic knowledge of mathematical statistics to test hypothesis in their seminar or bachelor works and dissertations. The authors describe easily operated excel sheets which enable students to test their hypothesis. An e-learning course which the authors designed to integrate the sheets and videos presenting how to operate them is characterized, too. Key words. Statistical hypothesis testing, Excel, ICT, e-learning. Mathematics Subject Classification: 97U50

1 Introduction The importance of modern information and communication technologies has rapidly grown in recent years. These technologies have penetrated into all spheres of human activities. Nowadays, it is quite easy to operate a huge amount of data using modern technologies, for example Excel which contains a lot of functions from different categories. Some calculations in mathematical statistics, which lasted for a long time in past because of complicated formulas, can be made in few seconds using modern spreadsheets. That is why the methods of teaching statistical hypothesis testing have changed significantly. It is not necessary to spend hours by routine calculations. On the other hand, it is necessary to obtain special abilities to operate the spreadsheets. The faculty of Education, Trnava University, prepares students who will work as teachers at nursery, primary and secondary schools or as educators in social institutions. These students not only have to learn how to teach, but they also have to learn how to design experiments, how to collect data from these experiments, operate and analyse them in an efficient way. In many cases these experiments are part of seminar or bachelor works and dissertations. For the students it is not important to understand the statistical methods in details, neither do the students need to master all statistical functions in Excel. The students just need to know how to choose the most appropriate method to operate their data from experiment and to test their hypothesis. That is why we have prepared Excel sheets for statistical tests that are operated easily and we teach our students how to use them at the subject Basics of statistics. It is important to notice that our students are not

Aplimat – Journal of Applied Mathematics specialists neither at the field of ICT nor operating computers. They are ordinary users. However, they are taught how to work effectively with ICT in the subject ICT in education. 2 Statistical hypothesis testing in Excel As we mentioned above, there is a lot of students in our faculty who have to test hypothesis of their experiments. These students are not specialists in mathematical statistics, they just need to choose an appropriate statistical test and implement it in Excel as simply as possible. That is why it is sufficient to teach them how to operate the excel sheets which we created for them and how to choose the appropriate sheet to solve their problem. The majority of problems that our students solve when they need to test their hypothesis can be sorted into the following groups. 1. The students make an experiment on a sample of people and they need to compare the selected sample with the whole population or a part of population. 2. The students make an experiment on a sample of two groups. The first group, which serves as a control group, is taught by a classical method. The second group, which serves as an experimental group, is taught by an experimental method. The students need to compare the knowledge or abilities of selected groups before the experiment and after the experiment. 3. The students make an experiment on a sample of people and they need to compare the knowledge or abilities of these people before and after the experiment. 4. The students make an experiment on a sample of people under two different conditions and they need to compare the results. 5. The students make an experiment on a sample of people and they need to formulate conclusions for the whole population or a part of population. 6. The students make a questionaire on a sample of people and they need to formulate conclusions for the whole population or a part of population. 7. The students make a questionaire on a sample of people and they need to compare the answers of two different groups, for example to compare the answers of men with the answers of women. 8. The students make a questionaire on a sample of people and they need to know whether there is some correlation between answers on two different questions. 9. The students explore a correlation between two variables and they need to determine a confidence interval for correlation coefficient. For each group we designed excel sheets that help students to test their hypothesis. We tried to prepare the sheets as simply as possible, so in majority of cases students need just to choose the appropriate sheet, put their own values and add or remove some cells. The students usually do not have to master the excel functions that are necessary to solve the problem. The following table shows which tests we used to solve the problem from the groups above. Group no. 1 2 3 and 4 5, 6 and 9 7 and 8

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Statistical Tests t-test D'Agostino's normality test, F-test and t-test when the population is assumed to be normally distributed; the Mann-Whitney U test for assessing whether two samples of observations come from the same distribution; the Kolmogorov–Smirnov test t-test for related samples computing confidence interval tests for discrete variables Table 1

volume 2 (2009), number 1

Aplimat – Journal of Applied Mathematics 3 E-learning course We decided not only to create excel sheets for different statistical tests, but our aim was to integrate these sheets into a complex and homogenous material. We have already designed five e-learning courses from different parts of mathematics and integrated them into the learning management system EKPTM of our university. More information about the LMS can be found in [7]. We have been successfully using the LMS and e-learning courses in teaching process at our department since 2003 and our experience with it is strongly positive, as well as experience, reactions and results of our students. So we have decided to design e-learning course Statistical Hypothesis Testing and integrated it into the LMS. The course is available for public at the address http://elearning.truni.sk/, where you can use guest as both login and password. The course keeps both AICC and SCORM standards, so it can be used also in LMS of other university. We have also prepared off-line version of the course, which you can obtain from the authors of the paper. As the course is designed for students who are not specialists neither in mathematics nor statistics, we adapted the content of the course. The course, which consists of ten modules, contains the minimum of theory and a lot of solved problems closely related to the experiments of our students. As the students are not specialists in operating ICT, we have also created 16 videos which show how to work with the sheets from the course. In this academic year more than 100 students are studying the course. The aim of the course is not to substitute the teacher, but to serve as an effective study material in combination with classical lectures. However, using the course enable to reduce the number of contact hours from 24 to 8 without negative impact on the knowlegde of students (see [5] or [6]). The preparation of an e-learning course is much more difficult than the preparation of a classical textbook. We tried to utilize elements which can be used in electronic materials, but they cannot be used in printed materials, such as videos or interactivity. Moreover, we tried to respect the knowledge from cognitive psychology about the way how people learn from electronic materials (see for example [1], [2], and [3]). It is ideal if methods used in the course lead into integration of texts and graphics into existing structure of knowlegde in the long-term memory of students. To reach it, we focus the attention of students on important information in the course, we tried to use effectively the limited capacity of working memory, integrate information from visual channel into structures in the long-term memory, use methods that enable to access the knowlegde and abilities from the long-term memory when necessary, provide support for student with less developped metacognitive skills, etc. Unfortunately, we were not able to add sound into the course. It is also important that students need to understand that it is useless to read the content of the course in a passive way. To master the content of the course, the students should apply the obtained knowledge in the examples from the course. So the students have to work with excel sheets when they are studying the course. 4 Conclusion Modern information and communication technologies can make human activities more efficient, especially in that case when it is necessary to operate a huge amount of information. In the paper we described a method how to save a lot of hours spent by routine calculations using functions in Excel to test statistical hypothesis, which represents a concrete example of efficient utilization of ICT. It is necessary to use ICT in educational process, as they can make the process more effective and interesting to students. We believe that the faculties which prepare future mathematics teachers volume 2 (2009), number 1

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Aplimat – Journal of Applied Mathematics will cooperate in preparation of e-learning courses and materials and that whole mathematics curriculum will be covered by these materials. The example of such a co-operation is between departments of mathematics at Trnava University and Matej Bel University in Banská Bystrica. Both departments use learning management system to educate their students. Moreover, they have prepared tens of e-learning courses from the field of mathematics. More information can be found in [4].

Acknowledgement The authors gratefully acknowledge the Scientific Grant Agency KEGA for supporting this work.

References [1] [2] [3] [4] [5] [6] [7]

CLARK, R. C., Mayer, R. E.: e-Learning and the Science of Instruction. Pfeiffer, 2003. ISBN 0-7879-6051-9 GAZDÍKOVÁ, V.: Základy dištančného elektronického vzdelávania, študijné texty. Pedagogická fakulta Trnavskej univerzity, Trnava 2003. GAZDÍKOVÁ, V., ŠKOLKOVÁ, K.: Preparation of E-learning Course. In: Proceedings of the 12th International Scientific Conference CO-MAT-TECH 2004. Trnava, Materiálovotechnologická fakulta STU, 2004. ISBN 80-227-2121-2 HANZEL, P., KLENOVČAN, P.: Distančné vzdelávanie na PF UMB. In: Inovácie v škole. Zborník z medzinárodnej konferencie. Podbanské 2003, s. 33 – 37. ISBN 80-968664-5-1 HÍC, P., POKORNÝ, M.: E-learning Helps to Reduce the Number of Contact Hours. In: 7th International Conference Aplimat 2008, STU, Bratislava 2008, s. 943-948. ISBN 978-8089313-03-7 HÍC, P., POKORNÝ, M.: Skúsenosti s počítačom podporovanou výučbou Základov štatistického spracovania údajov. Klady a zápory e-learningu na menších vysokých školách, ale nejen na nich. SVŠES, Praha 2008, s. 107-112. ISBN 978-80-86744-76-6 HORVÁTH, R., MIŠÚT, M.: The New Improvements of E-leaning System at Trnava University. ICETA 2005 – 4th International Conference on Emerging Telecommunications Technologies and Applications. Košice, 2005, pp. 157-160. ISBN 80-8086-016-6

Current address Pavel Híc, doc. RNDr. CSc. Katedra matematiky a informatiky, Pedagogická fakulta, Trnavská univerzita, Priemyselná 4, P. O. Box 9, 918 43 Trnava, tel. number +421 905 571155, e-mail: [email protected] Pokorný Milan, PaedDr. PhD. Katedra matematiky a informatiky, Pedagogická fakulta, Trnavská univerzita, Priemyselná 4, P. O. Box 9, 918 43 Trnava, tel. number +421 902 552505, e-mail: [email protected]

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1 Introduction The importance of modern information and communication technologies has rapidly grown in recent years. These technologies have penetrated into all spheres of human activities. Nowadays, it is quite easy to operate a huge amount of data using modern technologies, for example Excel which contains a lot of functions from different categories. Some calculations in mathematical statistics, which lasted for a long time in past because of complicated formulas, can be made in few seconds using modern spreadsheets. That is why the methods of teaching statistical hypothesis testing have changed significantly. It is not necessary to spend hours by routine calculations. On the other hand, it is necessary to obtain special abilities to operate the spreadsheets. The faculty of Education, Trnava University, prepares students who will work as teachers at nursery, primary and secondary schools or as educators in social institutions. These students not only have to learn how to teach, but they also have to learn how to design experiments, how to collect data from these experiments, operate and analyse them in an efficient way. In many cases these experiments are part of seminar or bachelor works and dissertations. For the students it is not important to understand the statistical methods in details, neither do the students need to master all statistical functions in Excel. The students just need to know how to choose the most appropriate method to operate their data from experiment and to test their hypothesis. That is why we have prepared Excel sheets for statistical tests that are operated easily and we teach our students how to use them at the subject Basics of statistics. It is important to notice that our students are not

Aplimat – Journal of Applied Mathematics specialists neither at the field of ICT nor operating computers. They are ordinary users. However, they are taught how to work effectively with ICT in the subject ICT in education. 2 Statistical hypothesis testing in Excel As we mentioned above, there is a lot of students in our faculty who have to test hypothesis of their experiments. These students are not specialists in mathematical statistics, they just need to choose an appropriate statistical test and implement it in Excel as simply as possible. That is why it is sufficient to teach them how to operate the excel sheets which we created for them and how to choose the appropriate sheet to solve their problem. The majority of problems that our students solve when they need to test their hypothesis can be sorted into the following groups. 1. The students make an experiment on a sample of people and they need to compare the selected sample with the whole population or a part of population. 2. The students make an experiment on a sample of two groups. The first group, which serves as a control group, is taught by a classical method. The second group, which serves as an experimental group, is taught by an experimental method. The students need to compare the knowledge or abilities of selected groups before the experiment and after the experiment. 3. The students make an experiment on a sample of people and they need to compare the knowledge or abilities of these people before and after the experiment. 4. The students make an experiment on a sample of people under two different conditions and they need to compare the results. 5. The students make an experiment on a sample of people and they need to formulate conclusions for the whole population or a part of population. 6. The students make a questionaire on a sample of people and they need to formulate conclusions for the whole population or a part of population. 7. The students make a questionaire on a sample of people and they need to compare the answers of two different groups, for example to compare the answers of men with the answers of women. 8. The students make a questionaire on a sample of people and they need to know whether there is some correlation between answers on two different questions. 9. The students explore a correlation between two variables and they need to determine a confidence interval for correlation coefficient. For each group we designed excel sheets that help students to test their hypothesis. We tried to prepare the sheets as simply as possible, so in majority of cases students need just to choose the appropriate sheet, put their own values and add or remove some cells. The students usually do not have to master the excel functions that are necessary to solve the problem. The following table shows which tests we used to solve the problem from the groups above. Group no. 1 2 3 and 4 5, 6 and 9 7 and 8

242

Statistical Tests t-test D'Agostino's normality test, F-test and t-test when the population is assumed to be normally distributed; the Mann-Whitney U test for assessing whether two samples of observations come from the same distribution; the Kolmogorov–Smirnov test t-test for related samples computing confidence interval tests for discrete variables Table 1

volume 2 (2009), number 1

Aplimat – Journal of Applied Mathematics 3 E-learning course We decided not only to create excel sheets for different statistical tests, but our aim was to integrate these sheets into a complex and homogenous material. We have already designed five e-learning courses from different parts of mathematics and integrated them into the learning management system EKPTM of our university. More information about the LMS can be found in [7]. We have been successfully using the LMS and e-learning courses in teaching process at our department since 2003 and our experience with it is strongly positive, as well as experience, reactions and results of our students. So we have decided to design e-learning course Statistical Hypothesis Testing and integrated it into the LMS. The course is available for public at the address http://elearning.truni.sk/, where you can use guest as both login and password. The course keeps both AICC and SCORM standards, so it can be used also in LMS of other university. We have also prepared off-line version of the course, which you can obtain from the authors of the paper. As the course is designed for students who are not specialists neither in mathematics nor statistics, we adapted the content of the course. The course, which consists of ten modules, contains the minimum of theory and a lot of solved problems closely related to the experiments of our students. As the students are not specialists in operating ICT, we have also created 16 videos which show how to work with the sheets from the course. In this academic year more than 100 students are studying the course. The aim of the course is not to substitute the teacher, but to serve as an effective study material in combination with classical lectures. However, using the course enable to reduce the number of contact hours from 24 to 8 without negative impact on the knowlegde of students (see [5] or [6]). The preparation of an e-learning course is much more difficult than the preparation of a classical textbook. We tried to utilize elements which can be used in electronic materials, but they cannot be used in printed materials, such as videos or interactivity. Moreover, we tried to respect the knowledge from cognitive psychology about the way how people learn from electronic materials (see for example [1], [2], and [3]). It is ideal if methods used in the course lead into integration of texts and graphics into existing structure of knowlegde in the long-term memory of students. To reach it, we focus the attention of students on important information in the course, we tried to use effectively the limited capacity of working memory, integrate information from visual channel into structures in the long-term memory, use methods that enable to access the knowlegde and abilities from the long-term memory when necessary, provide support for student with less developped metacognitive skills, etc. Unfortunately, we were not able to add sound into the course. It is also important that students need to understand that it is useless to read the content of the course in a passive way. To master the content of the course, the students should apply the obtained knowledge in the examples from the course. So the students have to work with excel sheets when they are studying the course. 4 Conclusion Modern information and communication technologies can make human activities more efficient, especially in that case when it is necessary to operate a huge amount of information. In the paper we described a method how to save a lot of hours spent by routine calculations using functions in Excel to test statistical hypothesis, which represents a concrete example of efficient utilization of ICT. It is necessary to use ICT in educational process, as they can make the process more effective and interesting to students. We believe that the faculties which prepare future mathematics teachers volume 2 (2009), number 1

243

Aplimat – Journal of Applied Mathematics will cooperate in preparation of e-learning courses and materials and that whole mathematics curriculum will be covered by these materials. The example of such a co-operation is between departments of mathematics at Trnava University and Matej Bel University in Banská Bystrica. Both departments use learning management system to educate their students. Moreover, they have prepared tens of e-learning courses from the field of mathematics. More information can be found in [4].

Acknowledgement The authors gratefully acknowledge the Scientific Grant Agency KEGA for supporting this work.

References [1] [2] [3] [4] [5] [6] [7]

CLARK, R. C., Mayer, R. E.: e-Learning and the Science of Instruction. Pfeiffer, 2003. ISBN 0-7879-6051-9 GAZDÍKOVÁ, V.: Základy dištančného elektronického vzdelávania, študijné texty. Pedagogická fakulta Trnavskej univerzity, Trnava 2003. GAZDÍKOVÁ, V., ŠKOLKOVÁ, K.: Preparation of E-learning Course. In: Proceedings of the 12th International Scientific Conference CO-MAT-TECH 2004. Trnava, Materiálovotechnologická fakulta STU, 2004. ISBN 80-227-2121-2 HANZEL, P., KLENOVČAN, P.: Distančné vzdelávanie na PF UMB. In: Inovácie v škole. Zborník z medzinárodnej konferencie. Podbanské 2003, s. 33 – 37. ISBN 80-968664-5-1 HÍC, P., POKORNÝ, M.: E-learning Helps to Reduce the Number of Contact Hours. In: 7th International Conference Aplimat 2008, STU, Bratislava 2008, s. 943-948. ISBN 978-8089313-03-7 HÍC, P., POKORNÝ, M.: Skúsenosti s počítačom podporovanou výučbou Základov štatistického spracovania údajov. Klady a zápory e-learningu na menších vysokých školách, ale nejen na nich. SVŠES, Praha 2008, s. 107-112. ISBN 978-80-86744-76-6 HORVÁTH, R., MIŠÚT, M.: The New Improvements of E-leaning System at Trnava University. ICETA 2005 – 4th International Conference on Emerging Telecommunications Technologies and Applications. Košice, 2005, pp. 157-160. ISBN 80-8086-016-6

Current address Pavel Híc, doc. RNDr. CSc. Katedra matematiky a informatiky, Pedagogická fakulta, Trnavská univerzita, Priemyselná 4, P. O. Box 9, 918 43 Trnava, tel. number +421 905 571155, e-mail: [email protected] Pokorný Milan, PaedDr. PhD. Katedra matematiky a informatiky, Pedagogická fakulta, Trnavská univerzita, Priemyselná 4, P. O. Box 9, 918 43 Trnava, tel. number +421 902 552505, e-mail: [email protected]

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