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University of North Carolina Chapel Hill
Soci708-001 Statistics for Sociologists
Fall 2009
Professor François Nielsen
Stata Commands for Module 7 – Inference for Distributions
For further information on any command in this handout, simply type help
followed by the name of the command in Stata.
For confidence intervals, also see page 35 of the Stata and SAS Guide pdf
(click on Documents in side bar; guide is linked under Software Documenta-
tion).
1 Statistical Functions in Stata
1.1 Normal Distribution Functions
The function normal(z) returns the cumulative standard normal distribution
P ( Z ≤ z ).
. display normal(1.207) .
The function invnormal(p) returns z such that P ( Z ≤ z ) = p.
. display invnormal(0.975)
1.2 Student t Distribution Functions
The function ttail(df, t) returns the reverse cumulative (upper-tail) Stu-
dent’s t distribution for df degrees of freedom; given t it returns the probability
P ( T > t ).
. display ttail(7, 1.960) .
The function invttail(df, p) returns the inverse reverse cumulative
(upper-tail) Student’s t distribution for df degrees of freedom; given p it returns
t such that P ( T > t ) = p.
. display invttail(7, 0.025)
1.3 Curve for Problem 7.113 p.
For IPS6e Problem 7.113 p.481 – Degrees of freedom and confidence interval
width.
This is how to draw the curve requested in this problem in Stata:
. twoway function y=invttail(x,0.025), range(2 100) yline(1.96)
This is how to do it in R:
curve(qt(0.975,x),2,100,xlab="Degrees of freedom", ylab="t*") abline(1.96,0,col="blue")
2 Entering Data for Confidence Intervals and One-Sample Tests
There are several ways to enter data in Stata to calculate confidence intervals
for the mean and one-sample test statistics. Here are three of them.
2.1 Method 1
A quick-and-dirty method from Andrew Ritchey. Take IPS6e Problem 7.
p.442 as an example. You have to enter 20 observations. In Stata, first clear
any data in memory. Then create a data frame with 20 observations and create
a variable with all values missing:
. clear . set obs 20 . gen mpg=.
Then go to the data editor (Data/Data Editor, or click the icon) and replace the
missing values with the actual values. Then close the Data Editor (click on the
×). Your data are ready to use. See below.
2.2 Method 2
Another technique from Michele Easter. You want to enter 9 observations. After
clearing any data in memory, we create a new variable called var and input
the data. (Type input var and then enter the values. After the last value,
type end.)
. clear . input var
var
- 3
- 3
- end
2.3 Method 3
Still another technique that is a time-saver for moderately long data sets from
the textbook. Use the disk that comes with the text and navigate to the data
sets, and go the the Excel folder. The data for Problem 7.24 p. 442 are under
. * lower bound of CI . display 43.17 - 2.
. * upper bound . display 43.17 + 2.
Now we do the CI the easy way.
. ci mpg
Variable | Obs Mean Std. Err. [95% Conf. Interval] -------------+--------------------------------------------------------------- mpg | 20 43.17 .9872104 41.10374 45.
3 One-Sample t-Test in Stata
The following two examples involve inputting data using the keyboard, but in
general it is easier just to go into the Data Editor, or copy and paste from an
already-entered Excel spreadsheet.
In the first command, we create a new variable called var and input the
data. (Type input var and then enter the values. After the last value, type
end.)
. input var
var
- 3
- 3
- end
Check the mean by using the summarize command (a.k.a. sum or su).
. su var
Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- var | 9 3.133333 .1581139 2.9 3.
The mean for this sample is 3.133333. Now we would like to do a t-test to
assess how likely it is that the true mean is greater than 3. Stata tests whether
the μ > 3, μ = 3, or μ < 3 at the same time.
. ttest var=
One-sample t test
Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- var | 9 3.133333 .0527046 .1581139 3.011796 3.
mean = mean(var) t = 2. Ho: mean = 3 degrees of freedom = 8
Ha: mean < 3 Ha: mean != 3 Ha: mean > 3 Pr(T < t) = 0.9824 Pr(|T| > |t|) = 0.0353 Pr(T > t) = 0.
Stata by default assigns a 95% confidence interval, but this can be changed
using the option level. To tell Stata to use a 90% confidence interval, you
would enter the command (output not shown):
. ttest var=3, level(90) ...
See Stata Help for more on the ttest command.
4 Matched Pairs in Stata
This example is very similar.
. input x
x
- 9000
- 8000
- 6000
- 6000
- 8000
- 7000
- end . ttest x=
One-sample t test
Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- x | 6 7333.333 494.4132 1211.06 6062.404 8604.
mean = mean(x) t = 14. Ho: mean = 0 degrees of freedom = 5
Ha: mean < 0 Ha: mean != 0 Ha: mean > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.
5 Two-Samples Problems in Stata
Now, using the dataset woprops (available from sidebar of course website,
under Datasets), do a t-test to see whether State cabinets under Democratic
. ttesti 17 .1712353 .0822401 22 .2398636 .1350461, unequal ... . ttesti 17 .1712353 .0822401 22 .2398636. ...
