Transcript
Chapter 3 – Statistical Tools for Health Economics
Key Ideas
We find out about economic phenomena by measuring them. We must collect data and analyze it to gain insights into how the world works.
Many analyses are simple. Are two (or more) groups the same or different?
Other analyses involve measuring orders of magnitude. It may make a difference if the (negative) demand elasticity is –0.1, –1.0, or –10.
Teaching Tips
Instructors may wish to “pick and choose” through this chapter, or to use it as a reference. As with Chapter 2, it does not substitute for a course in statistics or econometrics.
Here is an ideal way to use a spreadsheet in real time. Do we think that men are taller than women? Ask each student to estimate his or her height in inches or meters, to put it on a slip of paper, and indicate whether it is a man or a woman (those with “clicker technology” available may find this even easier. Students can easily enter data onto a spreadsheet and sort the data. Even if you don’t want to calculate “difference of means,” you may still show that while some women may be taller than some men, the central tendency (mean or median – you may wish to calculate both) for men will be larger.
In the feature on hormone replacement (Box 3-2), although the underlying analyses were complex, the findings are straightforward, and reasonably clear to motivated readers. Students may also be intrigued by the fact that the experiment was stopped when the findings became clear rather than continued to the end as scheduled. (“Stop rules are important parts of clinical trials). Numerous follow-ups have been done with the Women’s Health Initiative since the 2002 report and they are often reported on television and on the web. Interested students may wish to investigate them.
Chapter 3 – Statistical Tools for Health Economists - Multiple Choice
The hypothesis that decreased cigarette smoking results in fewer deaths is a(n) ________ hypothesis
simple
complex
composite*
unusual
The hypothesis that women spend different amounts on prescription drugs than men is a(n) ______ hypothesis.
simple*
complex
composite
unusual
Here are some data on cholesterol levels for young men and young women.
Cholesterol Levels
Men Women
110 120
120 130
130 140
130 150
140 160
150 170
160 190
170 200
180 200
200 220
220 230
The mean men’s cholesterol level is ______. The mean women’s level is _____.
a. 110; 120.
b. 130; 130.
c. 145; 165.
d. 155; 174.*
The median men’s cholesterol level is ____. The median women’s level is ____.
a. 110; 120.
b. 130; 130.
c. 150; 170.*
d. 155; 174.
The ______ measure of central tendency is more sensitive to outliers.
median
mean*
mode
minimum
To determine whether means are significantly different, we divide the difference by the:
median of the difference.
mode of the difference
standard error of the difference.*
histogram of the difference.
(Difficult). In the problem above, the standard error of the difference is ________; the difference is statistically _________.
6.31; significant.
18.18; insignificant.*
22.54; normal.
34.11; insignificant.
In a regression y = a + bx, if b is positive, then a decrease in variable x means that variable:
y will decrease.*
y will increase.
y will increase if a equals 0.
y will increase if a is less than 0.
In a regression y = a + bx + cz, if b is positive, and c is negative, then if both x and z increase by one unit:
y will decrease.
y will increase.
y will increase if a equals 0.
y will increase if the absolute value of b is greater than the absolute value of c. *
In the diagram above, we relate pharmaceutical expenditures to income with the regression:
Expenditures = a + b x Income
Coefficient b refers to:
The increase in income with a one unit increase in expenditures.
The increase in expenditures with a one unit increase in income.*
The increase in expenditures if the price of pharmaceuticals rises.
The decrease in expenditures with a one unit increase in income.
The elasticity of expenditures with respect to income ElasEI with the regression above is:
coefficient b multiplied by (mean expenditure/mean income).
coefficient b multiplied by (mean income/mean expenditure). *
coefficient b multiplied by coefficient a.
coefficient b divided by coefficient a.
If we relate pharmaceutical expenditures to income with the regression:
log (Expenditures) = a + b x log (Income),
the elasticity of expenditures with respect to income is:
coefficient b multiplied by (mean expenditure/mean income).
coefficient b multiplied by (mean income/mean expenditure).
coefficient b. *
coefficient b divided by coefficient a.
Dummy (or binary) variables may be used:
to measure income elasticities.
to measure price elasticities.
to measure the differences attributable to gender (men v. women).*
Answers (b) and (c) are correct.
Consider a regression where:
Expenditures = a + bx (x = 0 if male; 1 if female) + cz (z = 0 if African-American; 1 if non-African-American)
For an African-American male, the predicted expenditures will be:
a. *
a + b.
a + b + c.
a + c.
Consider a regression where:
Expenditures = a + bx (x = 0 if male; 1 if female) + cz (z = 0 if African-American; 1 if non-African-American)
For a non-African-American female, the predicted expenditures will be:
a.
a + b.
a + b + c. *
a + c.
Use the following discussion to consider the next three problems.
A statistician estimates a demand curve for visits per year to the health club:
Qd = 50 – 10p + 0.5 y,
where p is the price of towels per visit (in dollars) and y is household income (in thousands of dollars). There are two groups of users. Group A has a mean income of $40 (thousand), and group B has a mean income of $80 (thousand). Members of both groups must pay $2 per towel each time they visit.
The calculated quantities demanded are:
70 visits for group A and 50 visits for group B.
70 visits for both groups A and B.
50 visits for both groups A and B.
50 visits for group A and 70 visits for group B.*
Group A members have a towel price elasticity of ___________ which is _________ than group B.
–0.4; more elastic*
–0.4; less elastic
–0.8; more elastic
–1.6; less elastic
Group B members have an income elasticity of _________ which is ____________ than group A.
0; smaller
+0.27; smaller
+0.57; larger*
1.0; larger
In examining the impact of the electromagnetic fields (EMFs) on childhood cancer the study team found that the true rates of leukemia were _________, and _______ to the level of EMFs.
unequal;. negatively related.
unequal; positive related.
equal; unrelated.*
variable; related.
In the feature (Box 3-2) on the Women’s Health Initiative, the study found that women in the experimental who were taking HRT had ______ levels of breast cancer, coronary heart disease, stroke, and pulmonary embolism than those in the control group.
higher*
lower
equal
different
The R2 statistic represents goodness-of-fit for a regression. An R2 of 0.40 indicates that we have explained _____________.
20% of the variance of the independent variables.
40% of the variance of the dependent variable.*
40% of the variance of the independent variables.
all of the variance of the dependent variable.
In Table 3-1, Regression B, the R2 indicates that about ____ percent of the variation is being explained.:
17.4.
2.17
0.65
11.14.*
In the book’s cigarette example, the following regression is displayed in Table 3-1, column (b)
Q = 17.22 – 2.28*tax per pack + other variables, R2 = 0.11
(0.33)
The coefficient of tax per pack, indicates that:
a one percent increase in cigarette tax would decrease number of cigarettes smoked by 2.28 percent per day.
a one percent increase in cigarette tax would increase the number of cigarettes smoked by 17.22 percent per day.
A one dollar increase in cigarette tax would increase the number of cigarettes smoked by 17.22 cigarettes per day.
A one dollar increase in cigarette tax would decrease the number of cigarettes smoked by 2.28 cigarettes per day.*
In problem (14), the cigarette tax coefficient is:
statistically significant because the t-statistic is very large (over 6).*
not statistically significant because it is negative.
not important because it is small.
answers (a) and (c) are correct.
From Table 3-1, Regression B, we can say the following about male smokers.
They smoke significantly fewer cigarettes than females.
They smoke significantly more cigarettes than females.*
They smoke more cigarettes than females, but the result is not statistically significant.
The regression coefficient provides no useful information about male smoking.
From Table 3-1, regression B, a one dollar increase in the excise tax on cigarettes leads to a(n) ____________ cigarettes smoked per day.
statistically insignificant increase of 2.28
statistically significant increase of 2.28
statistically insignificant decrease of 2.28
statistically significant decrease of 2.28*
(Difficult) From Table 3-1, regression C, Hispanic men smoke ___________ cigarettes than white, non-Hispanic women
4.13 fewer*
2.38 more
2.38 fewer
1.43 fewer
(Difficult) From Table 3-1, regression C, African-American men smoke ___________ cigarettes than African-American women
1.91 fewer
1.43 more
1.43 fewer
0.95 more*
(Difficult) Based on statistics and your knowledge of demand curves, evaluate the impact of a one dollar increase in excise taxes on excise tax receipts to the government.
They will decrease because people will buy fewer cigarettes.
They will increase because the decline in cigarettes purchased (and consumed) will not offset the tax increase.*
They will decrease because the decline in cigarettes purchased (and consumed) will offset the tax increase.
They will be unchanged because the increased taxes and decreased consumptions will offset each other.
A t-statistic can relate a difference of two distributions to ____________.
the median of the two distributions.
the standard error of the median of the two distributions.
the standard error of the mean of the two distributions.
the standard error of the mean of the difference of the two distributions.*
