| [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 s[tuff]," 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. |
Two different approaches
to testing that
blur...
some call them"Significance
testing" vs. "Hypothesis
testing"--
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:
"Retain (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)
| the |
truth |
||
| Ho is true |
HA is true |
||
| my |
Reject Ho |
Type I error |
OK |
| decision |
Retain Ho |
OK |
Type II error |
Size of beta depends on what exact
parameter value in HA
is true--(difference between true value and null value is "effect
size") Usually a bigger "effect size" will have a smaller
beta.
A small Type II error means the "power"
of the test to detect the alternative hypothesis when
it's
true-- is high.
(power = 1-beta, for a given parameter value)
Larger sample size gives stronger power
to
detect a true alternative.
| Sievers home | Math151-Sp05/Sig_vs_hypothDV.htm | 4/30/04 |