1. Confidence Interval Construction
How do I construct a 95% confidence interval and test for significance?

2. Hmmm, BPA has been linked to cancer, but I wonder if it affects the ability of mice to convert food to energy. Null hypothesis: a hypothesis that proposes that no association exists between variables of interest.

3. Alternative Hypothesis: Proposition that there is an association between variables of interest.

4. Examples Null hypothesis: There is no association between BPA and mice body mass. Alternative hypothesis: BPA is positively associated with mice body mass.

5. Samantha has decided to test her null hypothesis
Samantha has decided to test her null hypothesis. She obtains 100 mice and randomly assigns 50 to either group A or group B. Random by definition means chosen without any particular conscience consideration given to the choice. A mouse in group A could have just as likely been assigned to group B.

6. She weighs the mice before feeding to establish a baseline – a starting measurement used as a comparison for a variable that is expected to change. She determines the average weights to be group A = 64.5 lbs. and group B = 65.7 lbs.

7. Group A has a mean (ñ) of 64. 5 and a standard deviation (SD) of 7
Group A has a mean (ñ) of 64.5 and a standard deviation (SD) of 7. What is the standard error(SEM)? Yes, write the equation. SEM = for group A sample.

8. What is the margin of error (MOE). Margin of error is simply +/-1
What is the margin of error (MOE)? Margin of error is simply +/-1.96 x SEM. MOE for our example in group A is +/- 1.9

9. To construct the confidence interval, add and subtract the margin of error to the mean. In our example, the MOE is approximately 2 so... Confidence interval is going to be 64.5 plus and minus 2 pounds or 62.5 to What does this mean???

10. This means that if one were to take a sample of 50 mice from the same population and calculate the average 100 times, 95 times of those calculated averages would be between 62.5 and 66.5 lbs. We are 95% confident that the mean weight for the mice in our total population of mice is between 62.5 and 66.5 lbs

11. Group A mice are given BPA-laced food while Group B mice are given food that is known to be 100% BPA-free. She feeds the mice in this manner for 1 month.

12. After 1 month, she weighs mice from each group and measures the averages. The average weight for group A is 53.3 and the average weight for group B is 60.5.

13. Is the difference of 60.5 – 53.3 = 7.2 significant?

14. Samantha takes the 100 mice and randomly assigns them to 2 totally different groups (group C and group D). She then finds the average for each of the 2 new groups and compares them. C = 65.3 lbs., D=67.6 lbs.

15. She repeats this process (50 times) of randomly assigning mice to 2 groups and comparing their weights. She finds that out of those 50 comparisons, the difference in averages is less than 7.2 lbs. 48 times.

16. The p-value is the probability that a correlation is observed randomly rather than as a result of the independent variable (treatment). A p-value of 0.05 or less suggests that there is a only 5% chance of making a type 1 error.

17. So should we reject or fail to reject Samantha’s null hypothesis
So should we reject or fail to reject Samantha’s null hypothesis? Is the 7.2 lbs. difference significant?

18. Odds Ratio Table Example
Head Ache
No Head Ache
Totals
Drank tea
330
270
600
Did not drink tea
220
480
700
550
750
1300

19. An OR of more than 1 means positive association
An OR of more than 1 means positive association. An OR of less than 1 means a negative association. An OR = 1 means no association. In this case, People that drank the tea are 2.6 times more likely to have a headache than people that did not drink the tea. What if the OR is 0.98 or 1.2 or 1.27 or 2.3??