| [New York Times, Nov. 13, 01--report on the finding of the first anthrax
case in New York City: The test that was first used was new; they
hadn't had time to confirm the results by the usual method of growing a
culture.]
Dr. Koplan, director of the Centers for Disease Control and Prevention, on the phone with Mayor Giuliani: "Are you sure it's anthrax?" the mayor asked. "Well, we have a high degree of probability," Dr. Koplan replied. "No, no, no, don't give me that stuff," was the mayor's rejoinder. "Is it anthrax or is it not?' "Yes," Dr. Koplan said. "Fine, that's all I needed to hear," Mr. Giuliani said. |
"Significance
testing" vs. "Hypothesis
testing"-- two different approaches that
blur...
Both start with null and alternative hypotheses.
You want to show the alternative is true.
Significance testing:
Calculate P-value (or closest alpha), describe
how
unusual your result is if H0 is true.
Let the audience for your work decide if they
believe in the alternative hypothesis or not. (Scientist's approach.)
Language: "strong evidence for
Ha, against H0"
or not strong...
Hypothesis testing:
Make a decision
between H0 and Ha (often associated with predetermined
fixed alpha level)
We need to do something.
Language: "Accept
Ha, reject H0" if
P-value smaller than alpha.
What
if we can't reject H0? Do we accept H0?
Safer:
"fail to reject H0"
H0
"Innocent"
"Guilty" Ha
\ "Not Proven" / but
defendant goes free...
If we make a decision
we
run the risk of error:
Type I error, Accepting
alternative Ha when null H0 is true
(probability = alpha) Test designed to focus on this one.
Type II error, Accepting
null H0
when alternative Ha is true
(probability = beta, depends on what exact parameter value in Ha
is true) Can't make this one if we refuse to commit, but
A small Type II error means the "power"
of the test to detect the alternative hypothesis when it's
true-- is high.
(Sec. 6.4, optional, takes this further)
Larger sample size gives stronger power to
detect a true alternative.
| Sievers home | Math151-Sp02/Sig_vs_hypoth.htm | 4/22/02 |