REASONING ABOUT INFORMAL STATISTICAL
INFERENCE: ONE STATISTICIAN’S
VIEW
ALLAN J. ROSSMAN
arossman@calpoly.edu
ABSTRACT
This paper identifies key concepts and
issues associated with the reasoning of informal statistical inference. I focus
on key ideas of inference that I think all students should learn, including at
secondary level as well as tertiary. I argue that a fundamental component of
inference is to go beyond the data at hand, and I propose that statistical
inference requires basing the inference on a probability model. I present
several examples using randomization tests for connecting the randomness used
in collecting data to the inference to be drawn. I also mention some related
points from psychology and indicate some points of contention among
statisticians, which I hope will clarify rather than obscure issues.
Keywords: Statistical
reasoning; Statistical significance; Randomization tests
__________________________
Statistics Education Research
Journal, 7(2), 5-19, http://www.stat.auckland.ac.nz/serj
Ó International Association
for Statistical Education (IASE/ISI), November, 2008
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ALLAN J. ROSSMAN
Department of Statistics
Cal Poly