How do I interpret the results of this SPSS paired samples t test? 


*

*Paired samples statistics (table 1):  pretest score mean= 41.6667, post test score mean= 93.3333, N=3 

*Paired samples correlations (table 2) Correlations= -.277 , Sig.=.821

*Paired samples Test (Table 3) t=-7.750, df=2, sig(2-tailed)=.016
PRETEST SCORE
A=30
B=50
C=45
POSTTEST SCORE
A=95
B=95
C=90
The significance level in Table 2 is high while that in Table 3 is low.  Should I 
 reject the null or reject the alternative hypothesis in this t-test?
 A: That will depend on which null hypothesis you are testing. At a guess, since this is a t-test, you want to see if the mean changed, and that would be table 3 which is significant (that is, the means changed).
However, I'd be a little leery. There was a huge change not only in the mean scores but in the standard deviation - it was much lower in the post-test (see Table 1). Was this expected? Also, table 2 shows that the correlation between pre and post test is quite low -- in fact, it is negative -- which is odd. You would expect a positive correlation between two tests.
Finally N is only 3. 
A: The first table tells you that the pre- and post-average test scores are radically different.  The hypothesis you test is that they are indeed different.  Such scores are so different as not needing statistical testing for confirmation.  If needed, you do have that statistical confirmation in the third table. 
The second table has no direct relevance to whether the pre- and post-test average scores are different.  It just shows a negative correlation between the two; which is a bit strange.  I gather maybe the patients that were in the worst shape improved the most. 
The one concern I have is that your sample has only 3 individuals.  That seems way too low to derive any sort of reliable inference on the effectiveness of the treatment.  You can just observe that based on these 3 patients it overall makes a very big difference.  But, you probably need to have a sample of at least 10 x that to derive more reliable results.  
