Statistical Education Resource Kit
Hypothesis Testing and Court Trials
Synopsis: A large-group activity whose goal is to give
a visual demonstration of Type I and Type II errors. It involves
preparing large cards with different information on the two sides of each
card, as follows:
-
Card 1 has the words "I am not guilty" on one side and "I was found not
guilty" on the second side
-
Card 2 has the words "I am not guilty" on one side and "I was found guilty"
on the second side
-
Card 3 has the words "I am guilty" on one side and "I was found not
guilty" on the second side
-
Card 4 has the words "I am guilty" on one side and "I was found guilty"
on the second side
The instructor has students stand and sit down according to their true
state and the jury's verdict. The cards are prepared in advance to
have the probability of a type I error a and
type II error b.
Type of activity: In-class, large group
Statistical topics: Type I and Type II errors, probabilities
of Type I and Type II errors
Time needed: 10-15 minutes
Materials needed:
-
approximately 100 sheets of yellow, say, copy paper
-
approximately 100 sheets of pink, say, copy paper
Procedure:
Part I
Prior to class, prepare n "cards", as follows:
-
Using the pink paper, create (1-a)*n/2
cards with the words "I Am Not Guilty" printed on one side of the paper
and the words "Jury Verdict: Not Guilty" printed on the other side.
-
Create a*n/2 cards with the words "I
Am Not Guilty" printed on one side of a sheet of pink paper, and create
a*n/2 cards with the words "Jury Verdict:
Guilty" printed on one side of a sheet of yellow paper. Staple the two
sheets of paper together, so that the printed sides are visible.
-
Create b*n/2 cards with the words "I
Am Guilty" printed on one side of a sheet of yellow paper, and create
b*n/2 cards with the words "Jury Verdict:
Not Guilty" printed on one side of a sheet of pink paper. Staple
the two sheets of paper together, so that the printed sides are visible.
-
Using the yellow, create (1 - b)*n/2
cards with the words "I Am Guilty" printed on one side of the paper and
the words "Jury Verdict: Guilty" printed on the other side.
In summary, the color of the cards should correspond to the following:
| Color |
Status |
| Pink/Pink |
Defendant is Not Guilty/Jury Verdict is Not Guilty |
| Pink/Yellow |
Defendant is Not Guilty/Jury Verdict is Guilty |
| Yellow/Pink |
Defendant is Guilty/Jury Verdict is Not Guilty |
| Yellow/Yellow |
Defendant is Guilty/Jury Verdict is Guilty |
For example, if you create n = 200 cards with a
= 0.1 and b = 0.5, the resulting 200 observations
can be displayed in a two-by-two frequency table as follows:
|
|
Jury Verdict |
|
|
Not Guilty |
Guilty |
Total |
| Defendant's True Status |
Not Guilty |
90 |
10 |
100 |
| Guilty |
50 |
50 |
100 |
|
Total |
140 |
60 |
200 |
Letting H0: Defendant is Not Guilty and H1: Defendant is Guilty, then
a Type I Error is made if the jury verdict is guilty when the defendant
is not guilty, and a Type II Error is made if the jury verdict is not guilty
when the defendant is actually guilty. Then, in this example, the
probability of a Type I Error, a, is 10/100
= 0.10 and the probability of a Type II Error, b,
is 50/100 = 0.50 . (Note that cards with different colors on the
two sides correspond to errors while cards with only one color correspond
to correct decisions.)
Part II
Suggested conduct of activity in class:
-
Ask all students who are not guilty, i.e. those students with "I am Not
Guilty" on a pink sheet of paper, to stand.
-
Of those students who are standing, ask those whose verdict is not guilty,
i.e. those students with "Jury Verdict: Not Guilty" on a yellow sheet of
paper, to sit down. The 10% who are left standing are Type I errors.
That is, a = P(Type I error) = 0.10. Pause
and comment on what is seen. Then, ask the remaining students to sit down.
-
Ask those who are guilty, i.e. those students with "I am Guilty" on a yellow
sheet of paper, to stand.
-
Of those students who are standing, ask all those whose verdict is not
guilty, i.e. those students with "Jury Verdict: Guilty" on a yellow sheet
of paper, to sit down. The 50% who are left standing
are Type II errors. That is, b = Prob(Type
II error) = 0.50 .
Comments from others who have tried activity: None.
Submit comments.
Supplementary materials: See Bill Harkness for already prepared
cards.
This web page was submitted by William L. Harkness: wlh@stat.psu.edu