st: Statistical significance vs the 95% confidence intervals -- how should i interpret these

["Eric Lawrence" <eric.d.lawrence@gmail.com>]

While many good points were made in the responses to the original
question, there is a
simple explanation for the discrepant results here.

In method 1, the standard deviation rather than the standard error was
used in computing the 95% CIs.  Compare the standard errors across 1
and 2 below.

--Eric

***
The question is "Are the estimates for year 1 and 3 statistically different?
year    estimate    st.error        95% conf interval
year1    .484721     .015637     .454068    .5153741
year2   .4128893    .0145616    .3843443    .4414343
year3   .4556235    .0138994    .4283765    .4828704

1. Using the 95% confidence interval that I obtained:

Year 1 and year 3 confidence intervals overlap thus year 1&3 estimates
are not statistically different at the 95% level.

2. Using ttesti they are statistically different with 99% confidence:

. ttesti 2398 .484721  .015637 2399 .4556235 .0138994
Two-sample t test with equal variances
------------------------------------------------------------------------------
        |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
      x |    2398     .484721    .0003193     .015637    .4840948    .4853472
      y |    2399    .4556235    .0002838    .0138994     .455067      .45618
---------+--------------------------------------------------------------------
combined |    4797    .4701692    .0002996    .0207488    .4695819    .4707565
---------+--------------------------------------------------------------------
   diff |            .0290975    .0004272                  .02826     .029935
------------------------------------------------------------------------------
Degrees of freedom: 4795
                     Ho: mean(x) - mean(y) = diff = 0
    Ha: diff < 0               Ha: diff != 0              Ha: diff > 0
      t =  68.1143                t =  68.1143              t =  68.1143
  P < t =   1.0000          P > |t| =   0.0000          P > t =   0.0000
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