Is this statistically significant? 0.78 (approx) standard deviations from mean

Hi guys,

Just a quick question about some data I've collected from an experiment I've conducted. Basically the experiment is 172 separate tests, each with varying conditions, and each test has been completed by 20 subjects (I wont bore you with the details).

Some of the tests contain a particular condition, which when present the data is off by (on average) 0.78 of a standard deviation from the mean. This has occurred every time this condition is present, so it does appear to be affecting the performance of the subjects slightly.

I'm wondering if this is large enough to say this condition has a statistically significant effect on the performance on the subject, or whether it can be attributed to chance?

Thanks in advance :)