Testing means with missing values

[En Lee]

Hello everyone,

I have a small problem executing a one-would-think simple t-test and I hope you can help me!

So let's say I have two variables x and y and the data set looks like the following:
x y
------------------------------
1 5
2 .
3 .
. 4
4 .
. 3

Now I want to test whether the mean of x is different to the mean of y ( so H0: 2.5 = 4)
Is there any smart way to do this?
If I just do ttest x=y I obviously get "no observation" and when I create a new variable which displays the mean respectively I get a test where 6 observations are tested against each other but I want to test 4 obs vs. 3 obs.

Thank you in advance!

[Nick Cox]

You can restructure the data so that you have two groups. if you have some pairing (as in your example) you are thereby ignoring information in the data.

clear 
input x y
1 5
2 .
3 .
. 4
4 .
. 3
end 

stack (x y) , into(xy) 

list 

ttest xy, by(_stack)

[Joseph Coveney]

Nick's recommendation is the most principled, but you can just use the -unpaired- option of -ttest- if you want to be quick-and-dirty.

.ÿ
.ÿversionÿ16.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿinputÿbyteÿ(xÿy)

ÿÿÿÿÿÿÿÿÿÿÿÿxÿÿÿÿÿÿÿÿÿy
ÿÿ1.ÿ1ÿ5
ÿÿ2.ÿ2ÿ.
ÿÿ3.ÿ3ÿ.
ÿÿ4.ÿ.ÿ4
ÿÿ5.ÿ4ÿ.
ÿÿ6.ÿ.ÿ3
ÿÿ7.ÿend

.ÿ
.ÿttestÿxÿ=ÿy,ÿunpaired

Two-sampleÿtÿtestÿwithÿequalÿvariances
------------------------------------------------------------------------------
Variableÿ|ÿÿÿÿÿObsÿÿÿÿÿÿÿÿMeanÿÿÿÿStd.ÿErr.ÿÿÿStd.ÿDev.ÿÿÿ[95%ÿConf.ÿInterval]
---------+--------------------------------------------------------------------
ÿÿÿÿÿÿÿxÿ|ÿÿÿÿÿÿÿ4ÿÿÿÿÿÿÿÿÿ2.5ÿÿÿÿ.6454972ÿÿÿÿ1.290994ÿÿÿÿ.4457397ÿÿÿÿÿ4.55426
ÿÿÿÿÿÿÿyÿ|ÿÿÿÿÿÿÿ3ÿÿÿÿÿÿÿÿÿÿÿ4ÿÿÿÿ.5773503ÿÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿ1.515862ÿÿÿÿ6.484138
---------+--------------------------------------------------------------------
combinedÿ|ÿÿÿÿÿÿÿ7ÿÿÿÿ3.142857ÿÿÿÿ.5084323ÿÿÿÿ1.345185ÿÿÿÿ1.898768ÿÿÿÿ4.386946
---------+--------------------------------------------------------------------
ÿÿÿÿdiffÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-1.5ÿÿÿÿ.9036961ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-3.823025ÿÿÿÿ.8230248
------------------------------------------------------------------------------
ÿÿÿÿdiffÿ=ÿmean(x)ÿ-ÿmean(y)ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿtÿ=ÿÿ-1.6599
Ho:ÿdiffÿ=ÿ0ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿdegreesÿofÿfreedomÿ=ÿÿÿÿÿÿÿÿ5

ÿÿÿÿHa:ÿdiffÿ<ÿ0ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿHa:ÿdiffÿ!=ÿ0ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿHa:ÿdiffÿ>ÿ0
ÿPr(Tÿ<ÿt)ÿ=ÿ0.0789ÿÿÿÿÿÿÿÿÿPr(|T|ÿ>ÿ|t|)ÿ=ÿ0.1578ÿÿÿÿÿÿÿÿÿÿPr(Tÿ>ÿt)ÿ=ÿ0.9211

.ÿ
.ÿexit

endÿofÿdo-file


.

[En Lee]

Thank you so much, both of you!
You really saved my master thesis! :D

[Marcos Almeida]

Joseph's approach can tackle the unpaired t test under this display of data.

But sometimes we need to perform a Wilcoxon ranksum test.

Nick's approach in #2 can cope as well with a - ranksum - test under the display in #1.

I came across this scenario several times and I needed to rebuild the dataset "by hand", hence I'm glad to have now learned how to use -stack- command!