1. Computer aided teaching of statistics: advantages and disadvantages
Ilona Székely Kovácsné
Institute of Methodology
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

2. The aim of teaching statistics
To prepare students for the application of statistical methods to the economic decision-making process and to use the results creatively

3. Teaching Statistics: vol
Teaching Statistics: vol. 24, Statistical Laboratories Using Minitab, SPSS and Excel: A Practical Comparison T. Privan, A. Reid, P. Petocz (Australia)
„It is our firm conviction that with just reading about statistics the student cannot master them; they need to practise them too using computers and the appropriate software, and the interpretation of the results.”

4. And what do the students say?
The teaching of statistics using computers is a good method because errors made by the student become apparent, and may be remedied in the course of teaching and learning, and not just in the end of term exams. The fact that the EXCEL tasks require continuous attention means that the students’ attention does not wander, as in the case of traditional lectures.

5. Advantages Visualization of the data
Using simulations and/or resampling of (real) data to understand the variability in statistics
Easy to use Excel functions (e.g. for mean and standard deviation)
Computable inverse distribution functions to determine critical values instead of using statistical tables
Output of DATA ANALYSIS contains a lot of useful extra information
The usage of computer saves time and leads to immediate results
Possibility of application to real-life problems
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

6. Weekly Lectures+Seminars 25 Seminar groups BA 2016/2017
Statistics II
Weekly Lectures+Seminars
 25 Seminar groups
BA 2016/2017
Sampling and Estimation
Hypothesis Testing
Correlation and Regression
Time Series
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

7. Rest of the talk: Presenting common mistakes and some examples of where a true understanding of the material is lacking
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

8. A detailed analysis of some exams
Exams of 84 students analysed
Exams from one examination, but consisting of two different problem sets (A and B) analysed
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

9. Sampling and Estimation
Common mistakes
Sampling and Estimation
Level of confidence: 1-α or α? %
Standard deviation or standard error? %
Interpretation of standard error of mean %
Confidence interval of population mean %
Needed sample size for a given maximum error (e.g. confidence interval of population mean) %
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

10. Difficulties/Common mistakes
Choosing the correct test
Determination of the decision rule
Distinguising between two-tailed and one tailed tests
p-values
Type I and type II errors
Hypothesis Testing
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

11. Common mistakes Hypothesis Testing
One-tailed test for population mean with unknown σ
H %
Significance Level α or 1-α? %
Inappropriately chosen z-test %
Error in the calculation of t-test statistics %
Error in determining the critical t-value 30.0%
Overall correct decision rule and conclusion for 25.0%
Two-tailed test for difference between two means-small sample (equal variances)
Overall correct solution for %
Two-tailed test for difference between two proportions
Overall correct solution for %
Hypothesis Testing
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

12. Correlation and Regression
Test questions:
Determine and interpret the correlation coefficient
Determine the linear regression equation
Interpret the regression cofficient b1
Is the relation significant?
Prediction
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

13. DATA ANALYSIS Regression Tool Summary Output
Test B (attempted by 95.1%)
Test A (attempted by 95.3%)
Test A was done by …
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

14. Correlation coefficient
Test A
Correctly determined 23.3%
Correct interpretation %
Test B
85.4%
51.0%
The corr. Coef. was correctly determined by 23.3%
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

15. Correlation coefficient
Test A
Correctly determined 23.26%
Correct interpretation %
Test B
85.4%
51.0%
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

16. Correlation coefficient
=CORREL(X; Y )=
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

17. Simple Linear Regression
Test A
Equation %
Is the relation significant? 69.8%
Interpretation of b %
Making Prediction 58.1%
Test B
56.1%
85.4%
51.0%
70.7%
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

18. Simple Linear Regression
Test A
Equation %
Is the relation significant? 69.8%
Interpretation of b %
Making Prediction 58.1%
Test B
56.1%
85.4%
51.0%
70.7%
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

19. Simple Linear Regression
Test A
Equation %
Is the relation significant? 69.8%
Interpretation of b %
Making Prediction 58.1%
Test B
56.1%
85.4%
51.0%
70.7%
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

20. What are the reasons behind this phenomenon
What are the reasons behind this phenomenon? First impression: DATA was missing! It was not a test question. First step It is important to make and examine the scatterplots. What patterns of variation do they show?
Only 9.3% plotted the data on a graph
Test A % Test B 2.4%
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

21. Regression Diagnostics
Looking at residuals
Are the residuals normally distributed?
Is the variability of residuals consistent for all data points?
Are the residuals independent of one another? Check the autocorrelation.
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

22. Interpretation of regression output
Multiple Regression
Interpretation of regression output
corr_matrix ry2 ry2.3 Int_ry2.3 b2 significant p<α Int_b2
92,5% % % % % % %
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

23. Test A (Additive model)
Time Series
Test A (Additive model)
Scatter diagram 85.7%
b %
bo %
Interpretation of b %
Interpretation of bo 76.2%
Trend value %
S %
Interpretation of S %
Forecast %
Test B (Multiplicative model)
72.5%
90.0%
70.0%
65.0%
32.5% ? Calculations
17.5%
17.5% ?
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

24. Disadvantages Problem-solving can become automatic and mechanical
Lack of critical thinking
What is behind the numbers?
How to interpret the results?
Drawing incorrect conclusions
Easily obtainable points for partial solutions in a test amplify the above mentioned problems
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

25. Some mathematical-statistical concepts in the support of teaching using software packages
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

26. The means by which we can achieve this
Teaching: “COMBINED” teaching – which can pass the test of dealing with the coming task
The student: should be able to use the appropriate probability and statistical methods together with the appropriate software
Technical means: a well-equipped, reliable, computer lab
Personal factors

27. How can we achieve this usable statistical knowledge?
Each student should work with their ‚own’ database, which should be an active, creative part of the solution
Application to real-life problems
Solving them Obtaining a result
Evaluation in the light of the original problem
Using a simulation of real data

28. Thank you for your attention!
Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017