id: 06439632
dt: j
an: 2015d.00872
au: Rochowicz, John A. jun.
ti: $p$-value approximations for $t$-tests of hypothesis.
so: Spreadsheets Educ. 5, No. 3, 20 p., electronic only (2012).
py: 2012
pu: Bond University, Faculty of Business, Gold Coast, Queensland
la: EN
cc: K75 K95 U75
ut: stochastics; university teaching; quantitative research; spreadsheets;
simulation; mathematical statistics; statistical inference; hypothesis
testing; parametric $t$-tests; $p$-values; decision analysis; numerical
integration; gamma function; Monte Carlo integration; computer as
educational medium; approximations; multiple approaches;
$t$-distribution; Simpson’s rule; NBS approximation; one-sample
$t$-test; two-independent-samples $t$-test; paired-samples $t$-test
ci:
li: http://epublications.bond.edu.au/ejsie/vol5/iss3/5/
ab: Summary: Mathematics can be analyzed in different ways and each method
supports the other with the same results. This paper describes a number
of approaches for finding the $p$-values necessary for making decisions
about statistical $t$-tests of hypothesis. The concepts of areas under
the Student’s $t$-curve and the mathematical connections between
tests of hypothesis,probabilities and areas under a curve are
presented. The Excel function TDISTand various approximation techniques
from numerical analysis are discussed. Numerical analysis techniques
include Simpson’s Rule for integration and Monte Carlo integration.
Also an approximation from the National Bureau of Standards is
provided. Comparisons of results from each method are presented.
Numerical approximations are shown to be as important and as accurate
as exact solutions.
rv: