T-Test with two sum groups in Quintiles

[Hoa Phan]

Hi there,
I have portfolios divided into quintiles
I need to conduct t-test to check the differences in mean value of portfolios (Q1+Q2) and mean value of portflios (Q4+Q5) but I cannot. Could you guys help me please?
The picture is an example.
Thank you in advance!

[Carlo Lazzaro]

Hoa:
assuming that -ttest- is actually the way to go here, you may want to consider the following toy example:

. use "C:\Program Files\Stata17\ado\base\a\auto.dta"
(1978 automobile data)

. xtile quint_price= price , nq(5)

. ttest price if quint_price<=2, by(foreign) unequal

Two-sample t test with unequal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
Domestic |      23    4115.217    75.90388    364.0222    3957.802    4272.632
 Foreign |       7    4117.143     129.361    342.2569    3800.608    4433.678
---------+--------------------------------------------------------------------
Combined |      30    4115.667     64.4885     353.218    3983.773     4247.56
---------+--------------------------------------------------------------------
    diff |           -1.925466    149.9855               -333.9568    330.1059
------------------------------------------------------------------------------
    diff = mean(Domestic) - mean(Foreign)                         t =  -0.0128
H0: diff = 0                     Satterthwaite's degrees of freedom =  10.5031

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.4950         Pr(|T| > |t|) = 0.9900          Pr(T > t) = 0.5050

. ttest price if quint_price>=4, by(foreign) unequal

Two-sample t test with unequal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
Domestic |      17    9441.176     839.605     3461.78    7661.293    11221.06
 Foreign |      12    8039.167     724.526    2509.832    6444.496    9633.838
---------+--------------------------------------------------------------------
Combined |      29    8861.034    581.8073    3133.128    7669.256    10052.81
---------+--------------------------------------------------------------------
    diff |             1402.01    1108.997               -873.6304     3677.65
------------------------------------------------------------------------------
    diff = mean(Domestic) - mean(Foreign)                         t =   1.2642
H0: diff = 0                     Satterthwaite's degrees of freedom =  26.9579

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.8915         Pr(|T| > |t|) = 0.2170          Pr(T > t) = 0.1085

.

[Nick Cox]

. sysuse auto, clear
(1978 automobile data)

. xtile price5bin = price, nq(5)

. tab price5bin

5 quantiles |
   of price |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 |         15       20.27       20.27
          2 |         15       20.27       40.54
          3 |         15       20.27       60.81
          4 |         15       20.27       81.08
          5 |         14       18.92      100.00
------------+-----------------------------------
      Total |         74      100.00

. gen tocompare = cond(inlist(price5bin, 4, 5), 3, cond(inlist(price5bin, 1, 2), 1, 2))

. tab price5bin tocompare

         5 |
 quantiles |            tocompare
  of price |         1          2          3 |     Total
-----------+---------------------------------+----------
         1 |        15          0          0 |        15 
         2 |        15          0          0 |        15 
         3 |         0         15          0 |        15 
         4 |         0          0         15 |        15 
         5 |         0          0         14 |        14 
-----------+---------------------------------+----------
     Total |        30         15         29 |        74 

. ttest mpg if inlist(tocompare, 1, 3), by(tocompare)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       1 |      30    24.56667    .9549428    5.230437    22.61359    26.51974
       3 |      29     18.2069    .7821584    4.212052    16.60472    19.80908
---------+--------------------------------------------------------------------
Combined |      59    21.44068    .7424946    5.703209    19.95441    22.92694
---------+--------------------------------------------------------------------
    diff |             6.35977    1.238925                3.878866    8.840674
------------------------------------------------------------------------------
    diff = mean(1) - mean(3)                                      t =   5.1333
H0: diff = 0                                     Degrees of freedom =       57

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

[Hoa Phan]

Hoa:
assuming that -ttest- is actually the way to go here, you may want to consider the following toy example:

. use "C:\Program Files\Stata17\ado\base\a\auto.dta"
(1978 automobile data)

. xtile quint_price= price , nq(5)

. ttest price if quint_price<=2, by(foreign) unequal

Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. err. Std. dev. [95% conf. interval]
---------+--------------------------------------------------------------------
Domestic | 23 4115.217 75.90388 364.0222 3957.802 4272.632
Foreign | 7 4117.143 129.361 342.2569 3800.608 4433.678
---------+--------------------------------------------------------------------
Combined | 30 4115.667 64.4885 353.218 3983.773 4247.56
---------+--------------------------------------------------------------------
diff | -1.925466 149.9855 -333.9568 330.1059
------------------------------------------------------------------------------
diff = mean(Domestic) - mean(Foreign) t = -0.0128
H0: diff = 0 Satterthwaite's degrees of freedom = 10.5031

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.4950 Pr(|T| > |t|) = 0.9900 Pr(T > t) = 0.5050

. ttest price if quint_price>=4, by(foreign) unequal

Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. err. Std. dev. [95% conf. interval]
---------+--------------------------------------------------------------------
Domestic | 17 9441.176 839.605 3461.78 7661.293 11221.06
Foreign | 12 8039.167 724.526 2509.832 6444.496 9633.838
---------+--------------------------------------------------------------------
Combined | 29 8861.034 581.8073 3133.128 7669.256 10052.81
---------+--------------------------------------------------------------------
diff | 1402.01 1108.997 -873.6304 3677.65
------------------------------------------------------------------------------
diff = mean(Domestic) - mean(Foreign) t = 1.2642
H0: diff = 0 Satterthwaite's degrees of freedom = 26.9579

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.8915 Pr(|T| > |t|) = 0.2170 Pr(T > t) = 0.1085

.

Yes, it works. Thank all you guys. I will close this dicussion here!