2. Data and Analysis

3. Let’s Recall Some Numbers Early on, we wanted to look at the difference between men and women … w.r.t. cholesterol

4. From EXCEL CH_3.XLS

5. Hypothesis testing In the book's example (sample of 30 each), which is based on real life numbers, we find that:

6. Testing Differences Let's see if we can do things a bit more rigorously, looking at the "spread" of the data. So:

8. Testing Differences It turns out that we can calculate a standard error of the difference which equals: s d = (s w 2 + s m 2 ) 1/2 s d = (4.5 + 4.2) 1/2 = (19.36 + 16.81) 1/2 = 6.17. Let's compare the spread, or standard error, of the difference to the difference. The difference of 10.2 is about 1.65 times as big as the standard error. Clearly, if the difference was 0, we'd accept the fact that c w = c m.

9. Testing Differences The larger the difference relative to the spread, the more likely that c w  c m. If d/s d = 1.645, we could be about 90% certain that men's cholesterol is not equal to women's. As it turns out, that’s just about the certainty that we get here.

10. Key points for hypothesis testing: State hypotheses clearly Choose suitable sample Calculate appropriate measures of central tendency and dispersion Draw appropriate inferences

11. Regression Analysis Difference of means is useful, but sometimes we want to be a little more detailed. Suppose that we wanted to know how people’s expenditures changed as their incomes went up. One simple example is “rich people spend more than poor people.” You get a sample of rich people, and then a sample of poor people. Calculate the mean for the rich people, and the mean for the poor people. Hypothesis? E r > E p !

12. Let’s collect some data. Income per capita Expenditures What does this suggest? –Rich people spend more. How much more? Let’s draw a line. Example for Health Expenditures

13. Line has a form: Exp = a + b*income What does a mean? What does b mean? Income per capita Expenditures a b = slope

14. Says that for each $ of income per capita, we spend $b more. Although it is hard to think of, we could draw this diagram in n dimensions! What else determines health expenditures? Example for Health Expenditures Income per capita Expenditures a b = slope

16. EXCEL Example

17. Calculating Elasticities y = a + b x.  y = b  x. Why?  y/  x  = b. Is this an elasticity? Remember, the elasticity is in percentage terms, so: E = %  y/ %  x = (  y/y)/(  x  x). Can re-write this as: E = %  y/ %  x = (  y/y)/(  x  x) = (  y/  x)  (x/y).  y/  x  = b, so: E = b  (x/y).