An obstacle to teaching hypothesis testing to future managers: The plurality of conceptions related to the concept of variable

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An obstacle to teaching hypothesis testing to future managers: The plurality of conceptions related to the

concept of variable

Roxane Jallet-Cattan, Corinne Hahn

To cite this version:

Roxane Jallet-Cattan, Corinne Hahn. An obstacle to teaching hypothesis testing to future managers:

The plurality of conceptions related to the concept of variable. CERME 9 - Ninth Congress of the

European Society for Research in Mathematics Education, Charles University in Prague, Faculty of

Education; ERME, Feb 2015, Prague, Czech Republic. pp.777-778. �hal-01287136�

777

An obstacle to teaching hypothesis testing to future managers: The plurality of conceptions related to the concept of variable

Roxane Jallet-Cattan

and Corinne Hahn

1 ESSCA & ESCP Europe

2 ESCP Europe, Hahn@escpeurope.eu

The teaching of hypothesis testing is an important part of business statistics curricula but it is most of the time reduced to its operational dimension. We claim that other historical and systematic dimensions should be better taken into account. We have focused our research on exploring the teaching and learning of hypothesis tests for the difference between two means. In our poster, we present the results of the first stage of our research:

we have studied how this test was introduced in busi- ness statistics books and how it was integrated into the structure of each book.

Keywords: Hypothesis testing, business statistics, variable

For the past few years in France the teaching of sta- tistics has been reduced in many areas of higher ed- ucation, particularly in management sciences. It is often replaced by learning to use technological “black boxes”, reducing the teaching of statistics to learning a set of techniques and emphasizing what Fabre (2010) calls the operational dimension of knowledge. We claim that it is important to take into account the other two dimensions, historical and systematic, as well.

THE NOTION OF HYPOTHESIS TESTING

We have focused our research on statistical hypothe- sis testing. We have known for a long time that it is a difficult notion (for an extensive review see Batanero, 2000). Some authors have recommended abandoning it in favor of confidence interval (Cumming & Finch, 2005). Misconceptions by students and professionals or statisticians, have been widely studied (see for ex- ample Batanero, 2000, Falk & Greenbaum, 1995, Sotos et al, 2009). It seems to us that most of these miscon- ceptions can be explained by the primacy given to

the operational dimension. History tells us that the commonly taught hybrid form incorporates elements of Fisher’s theory and elements of Neyman-Pearson’s.

This dual epistemology, rejected by some elsewhere as impossible to combine, is rarely made explicit and leads to confusion between pvalue and significance level (see Hubbard et al, 2003, Lehman, 1993).

SYSTEMATIC DIMENSION

Beyond this extensively documented error, it seemed that the systematic dimension, i.e. the entry into a structured corpus of knowledge, also posed problems given the different statuses that some concepts can take in descriptive statistics and inferential statistics.

Some authors challenge the very notion of the exis- tence of two different areas within statistics (Konold and Pollatsek, 2002). We feel that to not identify de- scriptive statistics leads to deny the complex episte- mology of the discipline. Standard deviation can be viewed either as an indicator of the intensity of noise (inferential statistics) or as an indicator of the amount of information (descriptive statistics). The question is how we link the two conceptions.

THE RESEARCH

We have focused our research on exploring the teach-

ing and learning of hypothesis tests for the difference

between two means. In our poster, we present the re-

sults of the first stage of our research: we have studied

how this test was introduced in 8 business statistics

books and how it was integrated into the structure of

each book. A central element seems to be the way the

author “gives meaning to the letters,” in the words of

Malisani and Spagnolo (2009), and incorporates the

concept of variable in its different forms. To perform

An obstacle to teaching hypothesis testing to future managers… (Roxane Jallet-Cattan and Corinne Hahn)

778 the structure analysis, we relied on the typology pro-

posed by these authors and have adapted it to the field of statistics.

REFERENCES

Batanero, C. (2000). Controversies around the role of statistical tests in experimental research. Mathematical Thinking and Learning, 2(1-2), 75-98.

Cumming, G. & Finch, S. (2005). Inference by eye. Confidence intervals and how to read pictures of data. American Psychologist, 60(2), 170-180.

Fabre, M. (2010). Problématisation des savoirs. In A. Van Zanten (Ed.), Dictionnaire pédagogique (pp. 539–541). Paris:

Presses Universitaires de France.

Falk, R. & Greenbaum, C.W. (1995). Significance tests die hard:

The amazing persistence of a probabilistic misconception.

Theory and Psychology, 5(1), 75-98.

Hubbard, R., Bayarri, M.J., Berk, K. N. Carlton, M.A. (2003).

Confusion over measures of evidence (p’s) versus er- rors (α’s) in classical statistical testing. The American Statistician, 57-3, 171-182.

Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signal in noisy process. Journal for Research in Mathematics Education 33, 259-289.

Lehman, E.L. (1993). The Fisher, Neyman-Pearson Theories of Testing Hypotheses : One theory or two ? Journal of the American Statistical Asociation, 424, 1242-1249.

Malisani, E. & Spagnolo, F. (2009). From an arithmetical thought to algebraic thought: The role of the “variable”. Educational Studies in Mathematics 71, 19-41.

Sotos A., Vanhoof S. Van den Noortgate W., Onghena P. (2009).

How confident are students in their misconceptions about hypothesis tests? Journal of Statistics Education 17-2.