Significance t test of two scalars' difference

[Jae Li]

Hi everyone!

I want to test if the difference between two scalars is statistically significant at 10%, 5% or 1%, do you possibly know how to achieve that? The following is my code and data, but it didn't show up the t-statistics. Many thanks for your time in advance!


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* Example generated by -dataex-. For more info, type help dataex
clear
input long Name double(mean1 mean2)
1  1.8383807419289167   1.7266930261427125
2  .23570075560114517   .16440843279268563
3  .17996988718763549   .20369058384697425
4   5.620516515152281    5.805663871321566
5  2.5813825628443197   2.6832247877277484
6 -.06357658493897562 -.011365789056073154
7  .18118794957284806   .17398404645983095
8   5.286552811590096    5.824117617449302
end

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ttest mean1== mean2 if Name== 8

Paired t test
------------------------------------------------------------------------------
Variable |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
 mean1|       1    5.286553           .           .           .           .
mean2 |       1    5.824118           .           .           .           .
---------+--------------------------------------------------------------------
    diff |       1   -.5375648           .           .           .           .
------------------------------------------------------------------------------
     mean(diff) = mean(mean1- mean2)                     t =        .
 H0: mean(diff) = 0                              Degrees of freedom =        0

 Ha: mean(diff) < 0           Ha: mean(diff) != 0           Ha: mean(diff) > 0
 Pr(T < t) =      .         Pr(|T| > |t|) =      .          Pr(T > t) =      .

[Carlo Lazzaro]

Jae:
you're actually comparing two constants. No test in hell/heaven will ever do what you're after.

The correct approach (that does not fullfil your oiu of reach research goals) is:

. ttest mean1 == mean2, unpaired unequal

Two-sample t test with unequal variances
------------------------------------------------------------------------------
Variable |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
   mean1 |       8    1.982514    .8265995    2.337976    .0279171    3.937112
   mean2 |       8    2.071302    .8822033    2.495248   -.0147771    4.157381
---------+--------------------------------------------------------------------
Combined |      16    2.026908    .5840887    2.336355    .7819527    3.271864
---------+--------------------------------------------------------------------
    diff |           -.0887877    1.208946               -2.682747    2.505171
------------------------------------------------------------------------------
    diff = mean(mean1) - mean(mean2)                              t =  -0.0734
H0: diff = 0                     Satterthwaite's degrees of freedom =  13.9411

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.4712         Pr(|T| > |t|) = 0.9425          Pr(T > t) = 0.5288

.

[Leonardo Guizzetti]

A scalar is just a number, and if you want to know if they're different, just look at them. But that's not statistics or statistical inference. For that, you need to work with samples.

[Jae Li]

@Carlo Lazzaro @Leonardo Guizzetti Hi Carlo and Leonardo, many thanks for your swift replies! I'll change the samples to fulfill it.

[Carlo Lazzaro]

Jae:
I fail to get how drawing two different samples can fix the issue, if you still want to compare two scalars.