Transcript Statistical Tools for Health Economics

Statistical Tools for Health
Economics
Hypothesis Testing
Difference of Means
Regression Analysis
Multiple Regression Analysis
Statistical 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.
2.
3.
4.
State the hypothesis
Choose a sample
Calculate mean and standard deviation
Draw the appropriate inference: 10
percent confidence level
Regression Analysis
• Ordinary Least Square
Q=a+bP+e
The 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 regression
Q=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 Elasticities
Ep=dQ/dP*(P/Q)
In above example, the mean of Q is 15.3 while the mean tax price is 0.454
Ep=-3.75*(0.454/15.3)=-0.11
A 10 percent increases in the tax price of cigarette would lead to a 1.1 percent decrease in
quantity 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.