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pre-test post-test
case mean SD mean SD n 'SE Delta m'/t/dof
1 50.9 333 5.6 4.9 100 33.3 t=1.36 dof 198
2 7.0 15 5.1 1.6 101 1.5 t=1.27 dof 200
3 5.3 3.9 5.0 1.2 100 0.41 t=0.74 dof 198
4 6.4 9.2 6.1 7.3 101 1.17 t=0.26 dof 200
5 9.7 26 8.2 24 99 3.56 t=0.48 dof 196
6 8.7 18 51 432 100 43.2 t=0.98 dof 198
I looked over the numbers looking for data gathering errors first:
Cases one and six seem to have unusual ratios of SD/mean for
school test results so I set them aside for follow up and verification.
Cases 2 and 5 are mildly in the same direction, but I processed them
anyway. Though the sample size is large enough not to need the small
sample size correction offered by the t statistic, I used it anyway,
as harmless.
In cases 2-5, I find the t value is too small to allow one to reject the null
hypothesis i.e. that the pre and post are significantly different.
(For large samples from a reasonably normal population, the t figure is >1.96
for the probability <5% of wrongly rejecting the null - no difference
conclusion )
As before, I used this formulation:
Standard error of the difference of the sample means =
sqrt [ SD1 squared /sample size + SD2 squared /sample size ]
t statistic = (diff of sample means) / (Std err of diff of sample means)
degrees of freedom = (sample size 1 - 1) + (sample size 2 -1)
...
The overall null conclusion - 'no difference', implies that your
processing of the trial population was either not dramatic enough
or not uniform enough to show up on this statistic.
You seem to have provided sample pairs with a t statistic of
1/4 , 1/2, 3/4, 1 , 1 1/4 etc.