Statistical Tools for Health Economics

Hypothesis TestingDifference of MeansRegression Analysis

Multiple Regression AnalysisStatistical Inference in the Science and

Social Sciences

Hypothesis Testing

Case I: Indicate that 20-year-old men’s cholesterol level are difference from their counter part women’s levels

H0: Cm=Cw (null hypothesis)

Ha: Cm<>Cw (alternative hypothesis)sr

Case II: rich people spend more on health care than do poor people

H0: Er=Ep

Ha: Er>Ep

Difference of Means• To compare men and women’s cholesterol levels, we

need a test that can determine the differences between two distributions of continuous data.

• Continuous data are natural measures that in principle could take on different value for each observation. Categorical data refer to arbitrary categories.

• Dispersion :The variance of a distribution. The variance is often deflated by taking the square root to get the standard deviation

• Central Limit theorem: no matter what the underlying distribution, the means of that distribution are distributed like a normal or bell-shaped curve. e.g. Figure 3-2B: the most probable value of the difference is 10.2. About 68 percent of the distribution lies between 4.18 (10.2-1*6.02) and 16.22 (10.2+1*6.02). About 95.4 percent of the distribution lies between -1.84 (10.2-2*6.02) and 22.24 (10.2+2*6.02)

Hypotheses and Inference

1. State the hypothesis

2. Choose a sample

3. Calculate mean and standard deviation

4. Draw the appropriate inference: 10 percent confidence level

Regression Analysis

• Ordinary Least SquareQ=a+bP+eThe last parameter is the error term e. No regression analysis will fit the data exactly. Errors

may occur because of omittted variable and wrong measurement of explanatory variables or the dependent variable.

Example: A demand regressionQ=17.02-3.75*tax per pack, R-square=0.01(1)This equation indicates that a $1 increase in the tax price P of a pack of cigarettes lead to

a decrease in quantity demand of 3.75 fewer cigarettes per day among those who smoke.

(2)The standard error for the coefficient is 0.34. In this regression, the standard error of 0.34 is relatively small compared to the coefficient of 3.75. H0: b=0 ( tax price doesn’t matter) H1: b<0

The t-statistic is (3.75-0)/0.34=10.9. We can be more than 95 percent sure that tax price has an effect on quantity of cigarette consumered

(3)R square measures the proportion of the total variation explained by the regression model. An R-square of 0.01 implies that about 1 percent of the variance was explained.

• Estimating ElasticitiesEp=dQ/dP*(P/Q)In above example, the mean of Q is 15.3 while the mean tax price is 0.454Ep=-3.75*(0.454/15.3)=-0.11A 10 percent increases in the tax price of cigarette would lead to a 1.1 percent decrease in q

uantity demanded.

Multiple Regression

• Q=a+bP+cY+dA+eE+fG+e• Interpreting Regression Coefficients:

See Table 3-1

Dummy Variable: Gender in Table 3-1

A. Figure 3.4 coefficient on Race is 0.56 (Ba)(Race is 1 while Gender is 0). This means that African American women smoke 5.06 fewer cigarette than white women Coefficient for Gender is 2.17 (Bm) (Race is 0 while Gender is 1)

White men smoke 2.17 more cigarette than white women.

Finally, African men smoke 2.89 (=-5.06+2.17) fewer cigarette than white women.

B. Interactive: add interactive term, so the impact of being black and male is 2.33(new Ba)-4.03(new Bm)-1.44(Bam)=3.41

Statistical Inference in the Sciences and Social Sciences

• Natural scientist attempts to control experimentally for all of the other possible sorts of variation other than the relation being studied. By contrast, econometricians are seldom to do since such projects are expensive. For example, multimillion dollar health insurance experiment was executed in late 1970s and early 1980s.