1. Runs Test for Randomness
12.4
Runs Test for Randomness

2. Is this sequence random?
SSSSSSSSSSSWWWWWWW
SWSWSWSWSWSWSWSWS
SWSSWWSWWWSSWWSSSWWSSWWSS

3. R R R D D R R D D D D D R D R R D R R R D D R
Random Party?
For each successive presidential term from Teddy Roosevelt to George W. Bush (first term), the party affiliation controlling the White House is shown below, where R designates Republican and D designates Democrat.
R R R D D R R D D D D D R D R R D R R R D D R
Historical Note: In cases in which the president died in office or resigned, the period during which the vice president finsished the term is not counted as a new term.
Test the sequence for randomness.

4. Runs Test for Randomness
Sample Statistic – R = _______
R R R D D R R D D D D D R D R R D R R R D D R
Run is a sequence of…
How many runs do we have?
R =

5. Looking forward Lack of randomness can be determined in two ways:
R is very _____
SSSSSSSSSSSSWWWWWW
SWSWSWSWSWSWSWSW
This piece of information will help us understand the hypotheses.

6. The Test
Hypothesis
H0:
H1:
Find the critical values from table 10 in the back of the book
To use the table
n1=
n2=
In the table
c1 = this is our lower critical value
c2 = this is our upper critical value
Calculate the sample statistic: R = # of runs

7. The decision process
Using R, c1, and c2 we can determine whether or not the sequence is random.
If R< c1 we have …
If R> c2 we have …
We _____________ null.
If c1 < R< c2
Draw a conclusion in context

8. Assignment Day #1
P 695 #1, 4-6, 11
Assignment Day#2
P. 695 #2, 7-10

9. R R R D D R R D D D D D R D R R D R R R D D R
Political Party
R R R D D R R D D D D D R D R R D R R R D D R
RRR DD RR DDDDD R D RR D RRR DD R
R =
n1=
n2=
Therefore,
c1 =
c2 =
Conclusion:

10. What about this?
Silver iodide seeding of summer clouds was done over the Santa Catalina mountains of Arizona. Of great importance is the direction of the wind during the seeding process. A sequence of consecutive days gave the following compass readings for wind direction at seeding level at 5 A.M. (0 degrees represents true north).
Test this sequence for randomness.

11. Runs Test About the Median
To do this test, we will simply find ______and then replace every number in the sequence with either _______.
A  ____________
B ____________
Once we have this new sequence the test is exactly the same as a Runs Test for Randomness.

12. Median TI Tip – Use 1-Var Stats on the TI to find the median.
The median of our data is ______.
Now our sequence will read…
n1=
n2=
Therefore,
c1 =
c2 =
Conclusion:
R =