Teaching undergraduates with Stata

Histogram

Create a histogram of mpg overlaid with a normal density curve.

. sysuse auto

. histogram mpg, normal
(bin=8, start=12, width=3.625)

Bar chart

Create a bar chart of percentages of observations for each level of foreign grouped by level of rep78.

. sysuse auto

. graph bar, over(rep78) over(foreign)

Scatterplot

Create a scatterplot of price versus mpg overlaid with a line showing their linear relationship.

. sysuse auto

. twoway (scatter price mpg) (lfit price mpg)

z test

Test that the mean mpg is 20 miles per gallon, assuming that the population standard deviation is 6.

. sysuse auto

. ztest mpg==20, sd(6)

One-sample z test


Variable 
 
     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
 
 
 
     mpg 
 
      74     21.2973    .6974858           6    19.93025    22.66434

    mean = mean(mpg)                                              z =   1.8600
H0: mean = 20                                    

    Ha: mean < 20               Ha: mean != 20                 Ha: mean > 20
 Pr(Z < z) = 0.9686         Pr(|Z| > |z|) = 0.0629          Pr(Z > z) = 0.0314

Test means without a dataset by using the immediate command. In a sample size of 74, test that an observed mean of 21.3 with an assumed population standard deviation of 6 is equal to the hypothesized mean of 20.

. ztesti 74 21.3 6 20

One-sample z test


         
 
     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
 
 
 
       x 
 
      74        21.3    .6974858           6    19.93295    22.66705

    mean = mean(x)                                                z =   1.8638
H0: mean = 20                                    

    Ha: mean < 20               Ha: mean != 20                 Ha: mean > 20
 Pr(Z < z) = 0.9688         Pr(|Z| > |z|) = 0.0623          Pr(Z > z) = 0.0312

To learn more, see [R] ztest and [U] 19 Immediate commands →

t test

Test that the mean price is equal between the two groups defined by foreign.

. sysuse auto

. ttest price, by(foreign)

Two-sample t test with equal variances


   Group 
 
     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
 
 
 
Domestic 
 
      52    6072.423    429.4911    3097.104    5210.184    6934.662
 Foreign 
 
      22    6384.682    558.9942    2621.915     5222.19    7547.174

Combined 
 
      74    6165.257    342.8719    2949.496    5481.914      6848.6

    diff 
 
           -312.2587    754.4488               -1816.225    1191.708

    diff = mean(Domestic) - mean(Foreign)                          t =  -0.4139
H0: diff = 0                                      Degrees of freedom =       72

    Ha: diff < 0                 Ha: diff != 0                  Ha: diff > 0
 Pr(T < t) = 0.3401         Pr(|T| > |t|) = 0.6802           Pr(T > t) = 0.6599

Test means without a dataset by using the immediate command. Test that the mean of group 1, which has a sample size of 52, an observed mean of 6072, and a standard deviation of 3097, is equal to the mean of group 2, which has a sample size of 22, an observed mean of 6385, and a standard deviation of 2622.

. ttesti 52 6072 3097 22 6385 2622

Two-sample t test with equal variances


         
 
     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
 
 
 
       x 
 
      52        6072    429.4766        3097     5209.79     6934.21
       y 
 
      22        6385    559.0123        2622     5222.47     7547.53

Combined 
 
      74    6165.054    342.8675    2949.458     5481.72    6848.388

    diff 
 
                -313    754.4348               -1816.938    1190.938

    diff = mean(x) - mean(y)                                      t =  -0.4149
H0: diff = 0                                     Degrees of freedom =       72

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.3397         Pr(|T| > |t|) = 0.6795          Pr(T > t) = 0.6603

To learn more, see [R] ttest and [U] 19 Immediate commands →

Model interpretation

(Run example on “Linear regression” first.)

Get predictions and residuals after fitting any model.

. predict y_hat
(option xb assumed; fitted values)

. predict epsilon_hat, residual

Interpret and visualize model results by using marginal means.

. margins foreign, at(weight=(2000(500)4500)) plot

Power analysis

Estimate the required sample size for a one-sample t test assuming a null mean of 0 to detect target means of 1, 2, and 3 with the default 80% power, given the default significance level of 0.05 and the sample standard deviation of 1.

. power onemean 0 (1 2 3), graph