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

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

Teaching Statistics: vol Teaching Statistics: vol. 24, 2002 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.”

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.

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

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

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

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

Sampling and Estimation Common mistakes Sampling and Estimation Level of confidence: 1-α or α? 17.5% Standard deviation or standard error? 5.0% Interpretation of standard error of mean 24.4% Confidence interval of population mean 50.0% Needed sample size for a given maximum error (e.g. confidence interval of population mean) 28.5% Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

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

Common mistakes Hypothesis Testing One-tailed test for population mean with unknown σ H1 42.5% Significance Level α or 1-α? 15.0% Inappropriately chosen z-test 10.0% Error in the calculation of t-test statistics 35.0% 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 7.5% Two-tailed test for difference between two proportions Overall correct solution for 17.5% Hypothesis Testing Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

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

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

Correlation coefficient Test A Correctly determined 23.3% Correct interpretation 21.0% 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

Correlation coefficient Test A Correctly determined 23.26% Correct interpretation 20.93% Test B 85.4% 51.0% Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

Correlation coefficient =CORREL(X; Y )= -0.6891 Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

Simple Linear Regression Test A Equation 58.1% Is the relation significant? 69.8% Interpretation of b1 20.93% 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

Simple Linear Regression Test A Equation 58.1% Is the relation significant? 69.8% Interpretation of b1 20.93% 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

Simple Linear Regression Test A Equation 58.1% Is the relation significant? 69.8% Interpretation of b1 20.93% 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

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 9.3% Test B 2.4% Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

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

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% 85.0% 35.0% 32.5% 60.0% 60.0% 35.0% Challenges and Innovations in Statistics, Education Multiplier Conference of PROCIVICSTAT, Szeged, September 7-9, 2017

Test A (Additive model) Time Series Test A (Additive model) Scatter diagram 85.7% b1 78.6% bo 78.6% Interpretation of b1 69.0% Interpretation of bo 76.2% Trend value 66.7% S3 45.2% Interpretation of S3 45.2% Forecast 31.0% 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

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

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

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

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

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