Assignment: Begin to review for final exam.

1. Apr. 26 Statistic for the day:Chance that a college student expects to be a millionaire by the age of 40: 1 in 2 Source: Harper’s index May 2000 Assignment: Begin to review for final exam. These slides were created by Tom Hettmansperger and in some cases modified by David Hunter

2. Exercise:Follow the 4 steps and answer theResearch 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 12 124 136 male 14 87 101 All 26 211 237

3. Step 1: Formulate hypotheses Null: There is no relationship between gender and cell phone usage. Alternative: There is a relationship. Data Rows: gender Columns: cell phone no yes All female 12 124 136 male 14 87 101 All 26 211 237

4. Step 2: Calculate test statistic Rows: gender Columns: cell phone no yes All female 12 | 14.9 124 | 121.1 136 male 14 | 11.1 87 | 89.9 101 All 26 211 237 Observed | Expected

5. Step 3: Find p-value From p. 137, a standardized score of 1.22 has area .11 to the right. This means that the 2-sided p-value is .22. Step 4: Make decision The p-value of .22 means we have no evidence of a difference between men and women in Stat 100 with regard to cell phone usage.

6. Meta-analysis • A collection of statistical techniques for combining studies. • By combining many studies, we may sometimes be able to obtain a large “meta-study” that helps to answer difficult questions that are not clear from smaller studies.

7. Vote-counting method • Simply find all studies on a particular topic and count how many had found a statistically significant result. • Bad idea unless sample size is also taken into account: Imagine taking a single study involving 1000 participants and breaking it up into 100 studies of 10 participants each. Probably, none of the 10-participant studies would amount to anything statistically significant even if the larger study would.

8. Which studies should be included? Different studies may differ widely in their quality of work. Often, many studies must be eliminated from a meta-analysis because it is not absolutely clear that what is being studied in them is the desired focus of the research. A meta-analysis of the effect of behavior on blood pressure eliminated all but 26 out of 857 possible studies!

9. Should studies be compared or combined? If one wishes to combine studies, make sure they’re really measuring the same thing on the same population! Consider two studies comparing surgery to relaxation for treating chronic back pain. One is conducted at a back-care specialty clinic, the other at a suburban medical center. Where will the people with the most severe back pain go? The two studies are probably conducted on different populations.

10. Is smoking related to lower sperm count in men? One study found a 22.8% reduction in sperm count for smokers, but it only used 88 subjects and the finding was not statistically significant. An accompanying meta-analysis estimated a similar reduction, but with the power of the combined studies, the p-value was found to be less than 0.0001. (Remember, these findings are based on observational studies and do not imply causation.)

11. Are mammograms an effective screening device for women aged 40-49? A 1993 meta-analysis said NO. This raises a potential problem with meta-analyses: The possibility of type 2 errors might be ignored because it seems unlikely that such a large study could miss any significant result! The 1993 meta-analysis did not dissuade the American Cancer Society from recommending mammograms for women 40-49. The ACS and others have pointed to various potential flaws with the meta-analysis.