1. Assignment: Read Chapter 12 Exercises p218-224: 9, 11, 17, 19, 20
Statistic for the day: Number of countries that have Spanish-speaking populations greater than 100,000: 21
Assignment:
Read Chapter 12
Exercises p : 9, 11, 17, 19, 20
These slides were created by Tom Hettmansperger and in some cases modified by David Hunter

2. A General Strategy Research Question or Hypothesis Quantification
Measure something relevant
Count something relevant
Collect Data: two-way table
Statistical Analysis: Chisquare test
Conclusions and/or Action

3. Exercise: Follow the 4 steps and answer the Research Question: Is there a relationship between gender and ownership of cell phones in Stat 100.2?
Data
Rows: gender Columns: cell phone
no yes All
female
male
All

4. Counts and percents Rows: Sex Columns: Cellphone
No Yes All
Female
Male
So 91.18% of women in the sample say yes but
only 86.14% of men in the sample say yes.
Are they statistically significantly different?

5. Counts and percents: Fall 2001
Rows: gender Columns: cellphone
no yes All
female
male
So 66.23% of women in the sample say yes but
only 45.71% of men in the sample say yes.
Are they statistically significantly different?

6. The strategy for determining statistical significance:
First, figure out what the skeptic expects
Second, figure out how far the research advocate’s data is from what is expected by the skeptic.
Third, decide if the distance in the second step is large.
Fourth, if large then claim there is a statistically significant difference.

7. Accepted definition of large for scientific purposes:
Something is large when it is in the outer 5%
tail of the appropriate distribution.

8. Step 1 We must compute what the skeptic expects: No Yes All
Female
Male
All

9. Counts and expected, chi-squared statistic
Rows: Sex Columns: Cellphone
No Yes All
Female
Male
All
Chi-Square = 1.506

10. Step 2 Preparing to compute the distance between data collected
by the research advocate and what the skeptic expects.

11. Expected counts are printed below observed
C C52 Total
Total
Chi-Sq =
= 1.506

12. Step 3: Compare chi-squared statistic with chi-squared distribution
But our chi-squared is so the skeptic wins!
There is not a statistically significant difference between men and women with regard to cell phone usage.

13. Step 4: No statistically significant difference
Rows: Sex Columns: Cellphone
No Yes All
Female
Male
Hence, the difference:
91.18% minus 86.14% = 5.04%
is not statistically significant.

14. FALL 2001 results Chi-Sq = 0.788 + 0.529 + 1.734 + 1.164 = 4.215
Expected counts are printed below observed
no yes Total w m
Total
Chi-Sq =
= 4.215

15. FALL 2001 Step 3: It is large this time!
But our chisquare is so the research advocate wins!
There is a statistically significant difference between men and women.

16. FALL 2001 Step 4: Statistically significant difference
Rows: gender Columns: cell ph
no yes All
female
male
Hence, the difference:
66.23% minus 45.71% = 20.52%
is statistically significant.

17. Why 1 degree of freedom? No Yes Women 136 Men 101 26 211 237
Note that black box is the ONLY one we can fill arbitrarily. Once that box is filled, all others are determined by margins!

18. How many degrees of freedom?
Always
Sometimes
Never
Women
One df
Two df
136
Men
101
106
105 26
237
Degrees of freedom (df) always equal
(Number of rows – 1) times (Number of columns – 1)

19. Exercise:
Follow the 4 steps and answer the research question: Is there a statistically significant difference in calories between small and large sandwiches? Data on slide #12.

20. Data: Low High Small 5 2 7 Large 14 Response: Calories Explanatory:
Size

21. Solution Expected counts are printed below observed low high Total
small
large
Total
Chi-Sq =
= 2.571
In this case the skeptic wins and the research advocate
loses. So we cannot claim that there is a relationship
between size and calories.

22. Health studies and risk
Research question: Do strong electromagnetic fields
cause cancer?
50 dogs randomly split into two groups: no field, yes field
The response is whether they get lymphoma.
Rows: mag field Columns: cancer
no yes All no
yes
All

23. Rows: mag field Columns: cancer
observed above the expected
no yes All no
yes
All
Chi-Square = (compare to 3.84)
Research advocate wins!

24. Terminology and jargon:
Identify the ‘bad’ response category: yes cancer
Risk for categories of explanatory variable
Identify treatment category
Identify baseline (control) category
Treatment risk: 15/25 or .60 or 60%
Baseline risk: 5/25 or .20 or 20%
Relative risk: Treatment risk over Baseline risk = .60/.20=3
So risk due to mag field is 3 times higher than baseline risk.
One more on the next page:

25. So the percentage change is 200%
Increased risk (percentage change in risk):
So the percentage change is 200%
A 200% increase in treatment risk over
baseline risk for getting cancer.

26. Final note:
When the chi-squared test is statistically significant
then it makes sense to compute the various risk
statements.
If there is no statistical significance then the skeptic
wins.
There is no evidence in the data for differences in
risk for the categories of the explanatory variable.