Simple stats question

Assuming you are quoting figures for Standard Deviation, a figure of 1.96 or more indicates that your results lie outside a 95% chance occurence for a normal distribution. In practical terms, you can conclude with a 95% confidence level (or more) that your result is NOT a random one.
The choice of statistical test which yields such SD figures will depend on the nature of your data and your procedure. Each test yields a particular measure like 't' or 'rho' which is assumed to be normally distributed such that SD can be found for it. The assumption of 'normal distribution' is often just that (an assumotion) which can become more reliable the bigger the data set.

It really depends on the type of experiment you were running and how consistent the data is. If you did condition one and every value was between 1.95 and 1.97 and condition two was 2.03 to 2.05, yes those could be significant, but if condition one was 1.7 to 2.2 and condition two was 1.75 to 2.25, then significance would depend on sample size and the value distribution.

The real answer to your question is that the test you use depends on the type of data you are generating and there is always some interpretation to be done on the results. You probably need to find someone who has some expertise to help you. Even if you did a t-test correctly, it doesn't sound like you have the experience to make sure you meet the ground rules for that test or interpret the results.