STATISTICAL CONCEPTS AND TECHNIQUES FOR TESTING DEPARTURES FROM NORMALITY IN THE MATHEMATICS TEACHER PREPARATION

• Journal title : Honam Mathematical Journal
• Volume 29, Issue 1,  2007, pp.83-100
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2007.29.1.083
Title & Authors
STATISTICAL CONCEPTS AND TECHNIQUES FOR TESTING DEPARTURES FROM NORMALITY IN THE MATHEMATICS TEACHER PREPARATION
Lee, Sang-Gone;

Abstract
Normality is one of the most common assumptions made in sampling and statistical inference procedures without suffering from lack of attention. Its results may lead to an invalid conclusion. We present several testing procedures that can be used to evaluate the effects of departure from normality using concrete examples by hand or with the aid of Minitab. The goal is to influence prospective teachers in order to learn statistical concepts and techniques for testing normality on the basis of the didactical theory.
Keywords
Testing Normality;Problem Solving;Didactical Theory;
Language
English
Cited by
References
1.
Korea Meteorogical Administration. Http://www.kma.go.kr. 11 2006.

2.
T. W. Anderson and D. A. Daring. A Test of Goodness of Fit. JASA, 49:765-769, 1954.

3.
F. J. Anscombe and W. J. Glynn. Distribution of the Kurtosis Statistic $b_2$ for Normal Samples. Biometrika, pages 227-234, 1983.

4.
KookMin Bank. Http://www.lot.kbstar.com. Web site, 11 2003.

5.
R. B. D'Agostino. Transformation to Normality of the Null Distribution of $g_1$.Biometrika, 57:679-681, 1970.

6.
R. B. D'Agostino. Approaches to the Null Distribution of $\sqrt{b_1}$. Biometrika, 60:169-173, 1973.

7.
R. B. D'Agostino. Tests for Departure from Normality. Empirical Results for the Distribution of $b_2$ and $\sqrt{b_1}$. Biometrika, 60:613-622, 1973.

8.
D.E.A. Giles. A Saddle Point Approximation to the Distribution Function of the Anderson-Daring Test Statistic. Econometrics Working Paper, 2000. Univ. of Victoria.

9.
R. C. Grary. Testing for Normality. Biometrika, 34:209-242, 1947.

10.
H. C. Hamaker. Approximating the Cumulative Normal Distribution and Its Inverse. Appl Stat, 27(1):76-77, 1978.

11.
H. W. Lilliefors. On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown. JASA, 1:399-402, 1967.

12.
S. W.Looney and Jr T. R.Gulledage.Probability Plotting Positions and Goodness-of-fit for the Normal Distribution. Stat, 34:297-303, 1985.

13.
F.J. Massey. The Kolomogorov-Smirnov Test for Goodness of Fit. JASA, 46:68-78, 1951.

14.
National Council of Teachers of Mathematics. Curriculum and Evaluation Stan­dards for School Mathematics. NCTM, 1989.

15.
D. B. Owen. The Handbook of Statistical Tables. Reading Massachusetts:. Addi­son Wesley, 1962.

16.
E. S. Pearson and H. O. Hartley. Tables for Statisticians. Biometrika, 1966.

17.
M. Rouncefield. Is it Normal ?, How to Use Probability Paper. Teaching Stat, 12(1):6-8, 1990.

18.
T. A. Ryan. Note on a Test for Normality. Technometrics, 10:825-839, 1990.

19.
T. A. Ryan and B. L. Joiner. Normal Probability Plots and Tests for Normality. Technical Report, 1976.

20.
M. B. Wilk S. S. Shapiro and H. J. Chan. A Comparative Study of Various Tests for Normality. JASA, 63:1343-1372, 1968.

21.
K. Sandrock. A Common Pitfall in the Use of the Kologorov-Smirnov One Sample Test. Teaching Stat, 12(1):9-11, 1990.

22.
S. S. Shapiro and M. B. Wilk. An Analysis of Variance Test for Normality. Biometrika, 52:591-606, 1965.