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  • Pre post analysis with ANOVA

    Good morning,
    I was asked to perform a pre-post analysis with ANOVA in order to see the effect of the treatment on the treated. I thought about running a one way anova with the difference between pre and post values as dependent variable and the treatment dummy as independent but the difference between the means of the two groups are very negligible and i don't obtain any significant results. I saw on youtube that it can be done through ANCOVA but i have only found the procedure to run it on SPSS, and not on Stata.

    Thanks in advance for your help!

    Tommaso

  • #2
    If the differences in means between the groups is negligible, then that is your main result. No p-value is going the change the fact that the difference is substantively meaningless.

    ANCOVA is in Stata just part of the anova command. How to use that command obviously depends on what exactly you want to do and the exact structure of the data.
    ---------------------------------
    Maarten L. Buis
    University of Konstanz
    Department of history and sociology
    box 40
    78457 Konstanz
    Germany
    http://www.maartenbuis.nl
    ---------------------------------

    Comment


    • #3
      Tommaso:
      welcome to this forum.
      Why devoting your time and research skills to ANOVA/ANCOVA when -regress- (see Example under -regression- entry in Stata .pdf manual) can do it much better, especially as far as postestimation routines are concerned?
      That said, if, for any reason the difference between the means are negligible (which is not good or bad in itself, but simply a matter of fact given your data), there's no statistical approach for window-dressing then.
      Eventually, sharing an example/excerpt of your data via -dataex- (see the FAQ on that and other posting-related topics) will increase your chances of getting (more) helpful replies.
      Kind regards,
      Carlo
      (Stata 19.0)

      Comment


      • #4
        Thanks Carlo and Maarten for your replies.
        I tried to run the regression reg var2_post var2_pre i.treatment and the treatment variable turned out to be significant, conversely to what I have obtained after running oneway var2_diff treatment - a p-value of 0.8316. Any idea on why?

        Here is my full sample:

        Code:
        * Example generated by -dataex-. To install: ssc install dataex
        clear
        input str7 CODE byte(Var1_POST Var2_POST Var1_PRE Var2_PRE Treatment Var1_DIFF Var2_DIFF)
        "014-S02" 16  8 18 13 1  -2 -5
        "014-S03" 16 14 18 16 1  -2 -2
        "014-S04" 16 13 18 16 1  -2 -3
        "014-S05" 18 13 18 14 1   0 -1
        "014-S07" 11 18 18 18 1  -7  0
        "014-S09" 13 16 14 14 1  -1  2
        "014-S10" 20 18 16 17 1   4  1
        "014-S11" 17 18 20 19 1  -3 -1
        "014-S12" 17 20 19 18 1  -2  2
        "014-S13" 16 17 18 19 1  -2 -2
        "014-S14" 19 19 18 19 1   1  0
        "014-S15" 19 21 19 19 1   0  2
        "014-S19" 18 20 18 18 1   0  2
        "014-S20" 15 13 17 16 1  -2 -3
        "014-S21" 12 12 14 14 1  -2 -2
        "017-S01" 18 12 21 19 0  -3 -7
        "017-S02" 17 14 16 17 0   1 -3
        "017-S03" 18 16 17 16 0   1  0
        "017-S05" 17 17 17 16 0   0  1
        "017-S06" 16 17 17 18 0  -1 -1
        "017-S07" 19 19 16 18 0   3  1
        "017-S08" 18 17 16 20 0   2 -3
        "017-S09" 14 18 16 17 0  -2  1
        "017-S11" 16 17 12 17 0   4  0
        "017-S12" 16 19 17 18 0  -1  1
        "017-S13" 15 14 17 15 0  -2 -1
        "017-S14" 16 20 15 16 0   1  4
        "017-S15" 18 16 20 16 0  -2  0
        "017-S16" 14 13 14 12 0   0  1
        "023-S01" 16 17 18 18 1  -2 -1
        "023-S02" 15 18 18 18 1  -3  0
        "023-S03" 14 18 14 19 1   0 -1
        "023-S04" 14 16 16 15 1  -2  1
        "023-S05" 16 15 16 19 1   0 -4
        "023-S06" 16 18 17 19 1  -1 -1
        "023-S07" 14 17 18 16 1  -4  1
        "023-S08" 15 15 17 15 1  -2  0
        "023-S09" 15 18 17 19 1  -2 -1
        "023-S11" 18 17 19 16 1  -1  1
        "023-S12" 10 18 17 17 1  -7  1
        "023-S13" 19 17 16 19 1   3 -2
        "023-S14" 18 19 19 20 1  -1 -1
        "023-S15" 13 15 15 18 1  -2 -3
        "023-S16" 17 20 18 19 1  -1  1
        "023-S17" 14 10 12  9 1   2  1
        "023-S18" 13 12 13 11 1   0  1
        "023-S19" 18 20 16 17 1   2  3
        "024-S01" 15 16 15 16 1   0  0
        "024-S02" 18 18 19 18 1  -1  0
        "024-S03" 16 18 17 16 1  -1  2
        "024-S04" 13 13 14 12 1  -1  1
        "024-S05" 17 15 16 13 1   1  2
        "024-S08" 12 17 15 14 1  -3  3
        "024-S11" 17 17 19 16 1  -2  1
        "024-S12" 16 19 16 18 1   0  1
        "024-S13" 13 20 13 19 1   0  1
        "024-S14" 20 17 18 16 1   2  1
        "024-S16" 13 15 11 16 1   2 -1
        "024-S17" 14 15 12 14 1   2  1
        "024-S18" 19 19 17 17 1   2  2
        "024-S19" 10 12 13 10 1  -3  2
        "024-S20" 19 19 18 18 1   1  1
        "024-S22" 17 17 18 19 1  -1 -2
        "024-S23" 11 11 10 11 1   1  0
        "024-S24" 14 12 16 12 1  -2  0
        "024-S25" 12 13 10 11 1   2  2
        "025-S01"  7  9  9  9 1  -2  0
        "025-S02" 14 13 16 12 1  -2  1
        "025-S03" 18 21 17 19 1   1  2
        "025-S04" 17 18 18 13 1  -1  5
        "025-S05" 21 21 21 18 1   0  3
        "025-S06" 15 18 13 19 1   2 -1
        "025-S07" 17 17 18 17 1  -1  0
        "025-S08" 14 19 12 20 1   2 -1
        "025-S09" 21 21 21 20 1   0  1
        "025-S10" 20 19 18 15 1   2  4
        "025-S11" 19 18 17 18 1   2  0
        "025-S12" 19 17 11 11 1   8  6
        "025-S13" 17 18 15  7 1   2 11
        "025-S14" 16 17 16 19 1   0 -2
        "025-S16" 15 14 17 16 1  -2 -2
        "025-S17" 17 18 18 17 1  -1  1
        "025-S18" 16 17 15 14 1   1  3
        "025-S20" 18 18 20 21 1  -2 -3
        "025-S21" 15 17 20 18 1  -5 -1
        "026-S01" 14 16 11 13 1   3  3
        "026-S02" 14 10 13 12 1   1 -2
        "026-S03" 14 15 16 16 1  -2 -1
        "026-S04" 14 14 18 16 1  -4 -2
        "026-S05" 15 17 15 15 1   0  2
        "026-S06" 15 15 16 13 1  -1  2
        "026-S07" 14 14 16 11 1  -2  3
        "026-S08" 15 15 15 14 1   0  1
        "026-S09" 14 14 14 14 1   0  0
        "026-S10" 17 14 14 13 1   3  1
        "026-S11" 16 16 13 13 1   3  3
        "026-S12" 14 15 15 15 1  -1  0
        "026-S13" 16 15 13 13 1   3  2
        "026-S14" 15 15 13 12 1   2  3
        "026-S15" 14 14 13 14 1   1  0
        "026-S16" 16 16 15 13 1   1  3
        "026-S17" 15 14 13 15 1   2 -1
        "026-S18" 18 15 13 16 1   5 -1
        "026-S19" 16 18 14 14 1   2  4
        "026-S20" 14 18 14 16 1   0  2
        "026-S21" 14 14 16 15 1  -2 -1
        "026-S22" 15 13 15 12 1   0  1
        "026-S23" 16 16 12 15 1   4  1
        "026-S24" 14 14 14 11 1   0  3
        "027-S01" 20 18 21 17 1  -1  1
        "027-S02" 19 19 15 14 1   4  5
        "027-S03" 15 14 14 14 1   1  0
        "027-S04" 18 16 18 18 1   0 -2
        "027-S05" 17 18 19 18 1  -2  0
        "027-S06" 16 15 16 14 1   0  1
        "027-S07" 17 20 19 18 1  -2  2
        "027-S08" 17 18 19 17 1  -2  1
        "027-S09" 18 18 16 19 1   2 -1
        "027-S10" 20 21 21 20 1  -1  1
        "027-S11" 17 14 18 16 1  -1 -2
        "027-S12" 17 17 17 18 1   0 -1
        "027-S13" 14 17 16 16 1  -2  1
        "027-S14" 18 17 15 15 1   3  2
        "027-S15" 15 17 17 18 1  -2 -1
        "027-S16" 17 18 18 14 1  -1  4
        "027-S17" 21 17 19 15 1   2  2
        "027-S18" 18 18 18 19 1   0 -1
        "027-S19" 18 17 17 19 1   1 -2
        "027-S20" 20 19 19 18 1   1  1
        "028-S01" 20 19 19 19 1   1  0
        "028-S02" 19 18 19 15 1   0  3
        "028-S03" 19 18 19 17 1   0  1
        "028-S04" 20 19 21 20 1  -1 -1
        "028-S05" 16 15 17 14 1  -1  1
        "028-S06" 18 17 16 17 1   2  0
        "028-S07" 20 21 19 16 1   1  5
        "028-S08" 17 14 18 15 1  -1 -1
        "028-S09" 21 20 19 20 1   2  0
        "028-S10" 13 14 14 15 1  -1 -1
        "028-S11" 21 18 21 16 1   0  2
        "028-S12" 18 20 19 20 1  -1  0
        "028-S13" 17 17 19 16 1  -2  1
        "028-S14" 17 16 19 18 1  -2 -2
        "028-S15" 17 16 17 19 1   0 -3
        "028-S16" 17 19 17 19 1   0  0
        "028-S17" 20 19 20 20 1   0 -1
        "028-S18" 19 17 16 16 1   3  1
        "028-S19" 18 15 18 19 1   0 -4
        "028-S20" 14 16 12 10 1   2  6
        "028-S21" 20 18 18 17 1   2  1
        "029-S01" 19 20 18 21 1   1 -1
        "029-S02" 15 18 17 19 1  -2 -1
        "029-S03" 21 21 20 21 1   1  0
        "029-S04" 15 21 18 20 1  -3  1
        "029-S05" 20 19 17 20 1   3 -1
        "029-S06" 15 13 13 13 1   2  0
        "029-S07" 21 17 21 20 1   0 -3
        "029-S08" 19 18 20 19 1  -1 -1
        "029-S10" 20 18 19 19 1   1 -1
        "029-S11" 20 16 17 17 1   3 -1
        "029-S12" 16 18 18 19 1  -2 -1
        "029-S13" 17 19 20 21 1  -3 -2
        "029-S15" 17 18 19 18 1  -2  0
        "029-S16" 19 19 19 20 1   0 -1
        "029-S17" 19 16 19 16 1   0  0
        "029-S18" 20 17 20 21 1   0 -4
        "029-S19" 18 20 19 20 1  -1  0
        "029-S20" 18 17 20 17 1  -2  0
        "029-S21" 17 21 18 21 1  -1  0
        "029-S22" 19 17 18 18 1   1 -1
        "029-S23" 17 15 19 17 1  -2 -2
        "029-S24" 17 15 15 16 1   2 -1
        "029-S25" 16 17 17 16 1  -1  1
        "029-S26" 16 17 17 15 1  -1  2
        "029-S27" 11 14 14 12 1  -3  2
        "029-S28" 17 18 16 17 1   1  1
        "031-S01" 18 16 17 19 1   1 -3
        "031-S02" 10 11 11 14 1  -1 -3
        "031-S03" 20 16 17 16 1   3  0
        "031-S04" 17 19 15 17 1   2  2
        "031-S05" 12 11 10  9 1   2  2
        "031-S07" 17 17 13 14 1   4  3
        "031-S08" 16 18 18 14 1  -2  4
        "031-S09" 18 15 13 13 1   5  2
        "031-S10" 17 14 20 20 1  -3 -6
        "031-S11" 14  7 14  7 1   0  0
        "031-S12" 21 17 18 16 1   3  1
        "031-S13" 18 16 18 17 1   0 -1
        "031-S14" 15 20 17 14 1  -2  6
        "031-S15" 18 17 16 18 1   2 -1
        "031-S16" 20 17 18 17 1   2  0
        "031-S17" 18 17 18 14 1   0  3
        "033-S01" 17 16 15 19 0   2 -3
        "033-S02" 17 18 14 16 0   3  2
        "033-S03" 18 16 13 16 0   5  0
        "033-S04" 17 16 16 16 0   1  0
        "033-S05" 16 15 16 15 0   0  0
        "033-S06" 13 14 16 17 0  -3 -3
        "033-S07" 20 17 15 14 0   5  3
        "033-S08" 19 18 14 18 0   5  0
        "033-S09" 11 13  9 12 0   2  1
        "033-S10" 19 16 15 18 0   4 -2
        "033-S11"  9 10 13 14 0  -4 -4
        "033-S12" 18 15 15 14 0   3  1
        "033-S13" 15 10 15 14 0   0 -4
        "033-S14" 18 13 15 20 0   3 -7
        "033-S15" 14 18 18 16 0  -4  2
        "033-S18" 15 14 18 17 0  -3 -3
        "033-S19" 15 17 16 17 0  -1  0
        "034-S01" 20 20 19 20 1   1  0
        "034-S04" 14 16 16 15 1  -2  1
        "034-S05" 16 17 17 17 1  -1  0
        "034-S09" 14 16 14 14 1   0  2
        "034-S10" 14 15 16 15 1  -2  0
        "034-S13" 16 19 18 18 1  -2  1
        "034-S18" 18 15 20 19 1  -2 -4
        "034-S19" 11 12 16 14 1  -5 -2
        "035-S02" 19 11 18 15 1   1 -4
        "035-S03" 17 19 18 18 1  -1  1
        "035-S04" 17 17 17 14 1   0  3
        "035-S05" 17 15 15 16 1   2 -1
        "035-S07" 18 20 20 20 1  -2  0
        "035-S08" 16 20 15 19 1   1  1
        "035-S09" 19 20 17 20 1   2  0
        "035-S10" 15 18 19 19 1  -4 -1
        "035-S11" 16 18 18 18 1  -2  0
        "035-S12" 13 14 15 17 1  -2 -3
        "035-S13" 13 13 16 11 1  -3  2
        "035-S14" 16 17 15 18 1   1 -1
        "035-S15" 12 12 15 14 1  -3 -2
        "035-S16" 18 16 18 19 1   0 -3
        "035-S17" 17 17 16 16 1   1  1
        "037-S02" 16 18 18 20 0  -2 -2
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        "044-S12" 18 20 19 19 1  -1  1
        "044-S13" 14 14 15 17 1  -1 -3
        "044-S15"  9  7 15 13 1  -6 -6
        "044-S16" 16 15 13 13 1   3  2
        "044-S17" 13 13 17 18 1  -4 -5
        "044-S18" 17 14 11 18 1   6 -4
        "044-S19" 15 13 16 16 1  -1 -3
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        "047-S18" 18 18 17 18 1   1  0
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        "051-S02" 16 16 15 18 1   1 -2
        "051-S03" 12 15 10  8 1   2  7
        "051-S04" 17 16 15 17 1   2 -1
        "051-S05" 14 12 12 13 1   2 -1
        "051-S06" 13 16 13 17 1   0 -1
        "051-S07" 18 20 18 19 1   0  1
        "051-S08" 16 17 14 19 1   2 -2
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        "119-S10" 14 16 17 18 0  -3 -2
        "119-S11" 15 16 13 13 0   2  3
        "119-S13" 16 16  9 13 0   7  3
        "119-S14" 15 18 16 17 0  -1  1
        "119-S15" 13 16 15 19 0  -2 -3
        "120-S01" 14 14 14 16 0   0 -2
        "120-S04" 20 20 20 19 0   0  1
        "120-S05" 15 17 15 17 0   0  0
        "120-S08" 16 17 13 18 0   3 -1
        "121-S02" 11 12 11 11 0   0  1
        "121-S06" 18 20 16 16 0   2  4
        "121-S11" 10 12 12 15 0  -2 -3
        "121-S12" 13 14 17 17 0  -4 -3
        "121-S13" 20 16 21 18 0  -1 -2
        "122-S01" 10 12  9 13 0   1 -1
        "122-S05" 20 17 19 18 0   1 -1
        "122-S06" 17 12 17 16 0   0 -4
        "122-S07" 19 18 18 16 0   1  2
        "122-S08" 14 14 13 10 0   1  4
        "122-S09" 15 15 16 17 0  -1 -2
        "122-S10" 18 17 21 18 0  -3 -1
        "122-S13"  9  9  9  9 0   0  0
        "122-S16" 15 16 18 16 0  -3  0
        "122-S19" 14 14 13 14 0   1  0
        "122-S20" 20 13 18 13 0   2  0
        end

        Comment


        • #5
          Tommaso:
          the only (and trivial) reason is that you've run two different models:
          First model:
          Code:
          . reg Var2_POST Var2_PRE i.Treatment
          
                Source |       SS           df       MS      Number of obs   =       869
          -------------+----------------------------------   F(2, 866)       =    247.40
                 Model |  2347.71904         2  1173.85952   Prob > F        =    0.0000
              Residual |  4108.98522       866  4.74478662   R-squared       =    0.3636
          -------------+----------------------------------   Adj R-squared   =    0.3621
                 Total |  6456.70426       868  7.43859938   Root MSE        =    2.1783
          
          ------------------------------------------------------------------------------
             Var2_POST |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
          -------------+----------------------------------------------------------------
              Var2_PRE |   .5822514   .0271209    21.47   0.000     .5290211    .6354818
           1.Treatment |   .3470834   .1534411     2.26   0.024     .0459234    .6482434
                 _cons |   6.363223   .4338934    14.67   0.000     5.511618    7.214829
          ------------------------------------------------------------------------------
          Second model with -oneway-:
          Code:
          . oneway Var2_DIFF Treatment
          
                                  Analysis of Variance
              Source              SS         df      MS            F     Prob > F
          ------------------------------------------------------------------------
          Between groups      .273068089      1   .273068089      0.05     0.8316
           Within groups      5234.72578    867     6.037746
          ------------------------------------------------------------------------
              Total           5234.99885    868   6.03110467
          
          Bartlett's test for equal variances:  chi2(1) =   0.0621  Prob>chi2 = 0.803
          Second model with -regress-:
          Code:
          . reg Var2_DIFF i.Treatment
          
                Source |       SS           df       MS      Number of obs   =       869
          -------------+----------------------------------   F(1, 867)       =      0.05
                 Model |  .273068089         1  .273068089   Prob > F        =    0.8316
              Residual |  5234.72578       867    6.037746   R-squared       =    0.0001
          -------------+----------------------------------   Adj R-squared   =   -0.0011
                 Total |  5234.99885       868  6.03110467   Root MSE        =    2.4572
          
          ------------------------------------------------------------------------------
             Var2_DIFF |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
          -------------+----------------------------------------------------------------
           1.Treatment |  -.0363227   .1707969    -0.21   0.832    -.3715465    .2989011
                 _cons |  -.0676471   .1332594    -0.51   0.612    -.3291959    .1939018
          ------------------------------------------------------------------------------
          As both -oneway- and -regress- are linear models (and the latter is much more flexible), the results you get depend on specification rather than statistical procedure.
          Kind regards,
          Carlo
          (Stata 19.0)

          Comment


          • #6
            I see, thanks Carlo! I thought the two models were testing the same thing.
            Which is the right model to use in order to see whether there is an effect of the treatment on the treated?

            Comment


            • #7
              Let me add one more example to those Carlo gave you.

              Code:
              . regress Var2_POST Var2_PRE i.Treatment, noheader
              ------------------------------------------------------------------------------
                 Var2_POST |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
              -------------+----------------------------------------------------------------
                  Var2_PRE |      0.582      0.027   21.469   0.0000        0.529       0.635
               1.Treatment |      0.347      0.153    2.262   0.0239        0.046       0.648
                     _cons |      6.363      0.434   14.665   0.0000        5.512       7.215
              ------------------------------------------------------------------------------
              
              . display _b[Var2_PRE] -1
              -.41774855
              
              . regress Var2_DIFF Var2_PRE i.Treatment, noheader
              ------------------------------------------------------------------------------
                 Var2_DIFF |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
              -------------+----------------------------------------------------------------
                  Var2_PRE |     -0.418      0.027  -15.403   0.0000       -0.471      -0.365
               1.Treatment |      0.347      0.153    2.262   0.0239        0.046       0.648
                     _cons |      6.363      0.434   14.665   0.0000        5.512       7.215
              ------------------------------------------------------------------------------
              
              . display _b[Var2_PRE]
              -.41774855
              The point is that regardless of whether you use Var2_POST or Var2_DIFF as the outcome variable in the oneway ANCOVA model, the coefficient & SE for treatment group are the same. But the coefficients for Var2_Pre (or more generally, the covariate) are not the same in the two models. They are related though. Notice that the coefficient for PRE in the second model = the coefficient for PRE in the first model minus 1.
              --
              Bruce Weaver
              Email: [email protected]
              Version: Stata/MP 18.5 (Windows)

              Comment

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