A Review of Descriptive Statistics, OLS and an Introduction to Stata

Andy Grogan-Kaylor

Andy Grogan-Kaylor

2 Sep 2021

Social Service Agency Data

Simulated data on social service clients

. use clients.dta, clear // use (get) the data
(Simulated Clients)
. describe

Contains data from clients.dta
 Observations:           521                  Simulated Clients
    Variables:             8                  3 Jun 2020 15:14
──────────────────────────────────────────────────────────────────────────────────────────────
Variable      Storage   Display    Value
    name         type    format    label      Variable label
──────────────────────────────────────────────────────────────────────────────────────────────
ID              double  %9.0g                 ID
age             double  %9.0g                 age
gender          long    %9.0g      gender     gender
program         long    %9.0g      program    program
mental_health~1 double  %9.0g                 mental_health_T1
mental_health~2 double  %9.0g                 mental_health_T2
latitude        double  %9.0g                 latitude
longitude       double  %9.0g                 longitude
──────────────────────────────────────────────────────────────────────────────────────────────
Sorted by:

One Line Stata

do_something to_variable(s), options

Quite often the default options are so well chosen that you do not need to specify any options.

The Stata Interface

The Stata Interface

Measures of Central Tendency

. summarize 

    Variable │        Obs        Mean    Std. dev.       Min        Max
─────────────┼─────────────────────────────────────────────────────────
          ID │        521    2965.449     1158.32       1005       4989
         age │        521     28.0438    7.047373   18.05584   45.45653
      gender │        521    1.821497    .7549825          1          3
     program │        521    2.197697    .7973963          1          4
mental_hea~1 │        521    95.11707    5.161698   80.93709   108.5736
─────────────┼─────────────────────────────────────────────────────────
mental_hea~2 │        521    98.87066    7.423767   79.57518   118.2272
    latitude │        521    42.25321    .1027698   41.99847    42.6237
   longitude │        521   -83.74921    .0987047  -84.04328  -83.42666
. summarize age, detail

                             age
─────────────────────────────────────────────────────────────
      Percentiles      Smallest
 1%     18.17739       18.05584
 5%     18.72159       18.05992
10%     19.54324       18.10945       Obs                 521
25%     22.37428       18.13374       Sum of wgt.         521

50%     26.61352                      Mean            28.0438
                        Largest       Std. dev.      7.047373
75%     32.88188       44.35607
90%     38.46387       44.78399       Variance       49.66547
95%     41.26977       45.30344       Skewness       .5501433
99%     44.16425       45.45653       Kurtosis       2.317297

Measures of Variation

Some programs, e.g. R make you search for standard deviation. With Stata, sd is easily accessible with summarize.

. histogram mental_health_T1, normal scheme(burd)
(bin=22, start=80.937087, width=1.2562034)
. graph export myhistogram.png, width(500) replace
file
    /Users/agrogan/Desktop/GitHub/newstuff/categorical/review-stats-intro-stata/myhistogram.
    > png saved as PNG format

histogram of mental health

Comparing Continuous and Continuous Variables

. twoway scatter mental_health_T1 age, msymbol(o) scheme(burd)
. graph export myscatter.png, width(500) replace
file
    /Users/agrogan/Desktop/GitHub/newstuff/categorical/review-stats-intro-stata/myscatter.pn
    > g saved as PNG format

scatterplot of age and mental health

Correlation

. pwcorr mental_health_T1 age, sig

             │ mental~1      age
─────────────┼──────────────────
mental_hea~1 │   1.0000 
             │
             │
         age │  -0.0093   1.0000 
             │   0.8329
             │

Comparing Continuous Variables Across Categorical Variables

. graph bar mental_health_T2, over(program) scheme(burd)
. graph export mybargraph.png, width(500) replace
file
    /Users/agrogan/Desktop/GitHub/newstuff/categorical/review-stats-intro-stata/mybargraph.p
    > ng saved as PNG format

bar graph of mental health at time 2

t-test

. preserve // preserve data set
. keep if program == 1 | program == 2 // only keep 2 programs for now
(201 observations deleted)
. ttest mental_health_T2, by(program)

Two-sample t test with equal variances
─────────┬────────────────────────────────────────────────────────────────────
   Group │     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
─────────┼────────────────────────────────────────────────────────────────────
 Program │     111     94.7963    .4969934     5.23615    93.81138    95.78123
 Program │     209    105.3512    .3562424    5.150136    104.6489    106.0535
─────────┼────────────────────────────────────────────────────────────────────
Combined │     320      101.69    .4033737    7.215767    100.8964    102.4836
─────────┼────────────────────────────────────────────────────────────────────
    diff │           -10.55491    .6083793               -11.75187   -9.357953
─────────┴────────────────────────────────────────────────────────────────────
    diff = mean(Program) - mean(Program)                          t = -17.3492
H0: diff = 0                                     Degrees of freedom =      318

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

ANOVA

. restore // restore old version of data
. oneway mental_health_T2 program, tabulate // oneway analysis of variance

            │     Summary of mental_health_T2
    program │        Mean   Std. dev.       Freq.
────────────┼────────────────────────────────────
  Program A │   94.796305   5.2361502         111
  Program B │   105.35121   5.1501362         209
  Program C │   94.299149   5.2002254         188
  Program D │   95.582917   5.6199143          13
────────────┼────────────────────────────────────
      Total │   98.870656   7.4237673         521

                        Analysis of variance
    Source              SS         df      MS            F     Prob > F
────────────────────────────────────────────────────────────────────────
Between groups      14689.6155      3   4896.53849    181.23     0.0000
 Within groups       13968.791    517   27.0189382
────────────────────────────────────────────────────────────────────────
    Total           28658.4065    520   55.1123202

Bartlett's equal-variances test: chi2(3) =   0.1991    Prob>chi2 = 0.978

Importantly, ,tabulate gives us a table of results.

Regression

. regress mental_health_T2 mental_health_T1 i.program

      Source │       SS           df       MS      Number of obs   =       521
─────────────┼──────────────────────────────────   F(4, 516)       =    135.94
       Model │  14704.3725         4  3676.09313   Prob > F        =    0.0000
    Residual │   13954.034       516  27.0427015   R-squared       =    0.5131
─────────────┼──────────────────────────────────   Adj R-squared   =    0.5093
       Total │  28658.4065       520  55.1123202   Root MSE        =    5.2003

─────────────────┬────────────────────────────────────────────────────────────────
mental_health_T2 │ Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
─────────────────┼────────────────────────────────────────────────────────────────
mental_health_T1 │  -.0327405    .044321    -0.74   0.460    -.1198123    .0543314
                 │
         program │
      Program B  │   10.57171   .6111758    17.30   0.000     9.371008    11.77241
      Program C  │   -.494409   .6224837    -0.79   0.427    -1.717323     .728505
      Program D  │   .7226213   1.526873     0.47   0.636     -2.27703    3.722272
                 │
           _cons │   97.90435   4.236239    23.11   0.000     89.58195    106.2267
─────────────────┴────────────────────────────────────────────────────────────────

What if We Want to Allow For Different Slopes?

Instructor will draw this out.

. regress mental_health_T2 c.mental_health_T1##i.program

      Source │       SS           df       MS      Number of obs   =       521
─────────────┼──────────────────────────────────   F(7, 513)       =     77.65
       Model │  14743.6327         7  2106.23324   Prob > F        =    0.0000
    Residual │  13914.7738       513  27.1243155   R-squared       =    0.5145
─────────────┼──────────────────────────────────   Adj R-squared   =    0.5078
       Total │  28658.4065       520  55.1123202   Root MSE        =    5.2081

───────────────────────────┬────────────────────────────────────────────────────────────────
          mental_health_T2 │ Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
───────────────────────────┼────────────────────────────────────────────────────────────────
          mental_health_T1 │   .0038108   .0940124     0.04   0.968    -.1808858    .1885074
                           │
                   program │
                Program B  │   14.13882   11.07298     1.28   0.202    -7.615155    35.89279
                Program C  │   2.227825    11.6862     0.19   0.849    -20.73087    25.18653
                Program D  │   27.30439    22.3002     1.22   0.221    -16.50657    71.11535
                           │
program#c.mental_health_T1 │
                Program B  │  -.0375708   .1162481    -0.32   0.747    -.2659517    .1908101
                Program C  │  -.0286832   .1228833    -0.23   0.816    -.2700997    .2127332
                Program D  │  -.2851331   .2385022    -1.20   0.232    -.7536944    .1834281
                           │
                     _cons │   94.43455   8.938253    10.57   0.000     76.87446    111.9946
───────────────────────────┴────────────────────────────────────────────────────────────────

Regression Assumptions and the Issue of “Normality”

Questions?