Q:

What is level of significance?

I am always confused with meaning of level of significance especially when my null hypothesis got accepted at 5% level and rejected at 1% level, how it could be possible that investigators would have two different decisions by merely changing levels of significance ?
Can anybody please explain procedures for selecting correct level of significance?

A:

The standard significance level is $5\%$, which indicates a $5\%$ chance of concluding that a difference exists when there actually is no difference at all. Thus, lower levels of significance reduce the risk of an incorrect conclusion.
The $P$-value on the other hand indicates the probability of obtaining such an extreme value, assuming the null hypothesis is true. Thus, we can reject the null hypothesis (that there is no difference) and accept the alternate hypothesis (that there is actually a difference) when the $P$-value is less than the level of significance.
However, this $5\%$ level is not necessarily set and the statistician must indicate the level of significance. For example, the long-sought Higgs Boson particle has been labeled with $5\sigma$ with a $P$-value of $3\cdot10^{-7}$. This indicates the probability that the physicists would collect data this extreme if the particle did not exist. As you can see, the significance level for testing the null hypothesis can be widely flexible. 

A:

When you perform a hypothesis test, you get a number out at the end, called the p-value. This is the probability that, under the null hypothesis, you could get results at least as far from the expectation as the ones you actually got.
For example - you flip a coin 10 times, get 8 heads, your null hypothesis is that P(H) = 0.5, the p-value is the probability of flipping 8 out of 10 heads with a fair coin. By the way, that value is about 0.044.
The significance level is an arbitrary line drawn between p-values that are "consistent" with the null hypothesis, and ones that are "inconsistent". Or in more casual terms, it's the line where you stop believing that the results you got are likely to happen by random chance.
So if we, like many fields these days, choose to set the significance level at 5%, we're saying that an event that happens less than one time in 20 is "unlikely", and if our hypothesis test produces a p-value less than that then we should reject the null hypothesis. In the case of the coin that flips 8 heads, the p-value is 0.44 < 0.5, so we would reject the hypothesis of a fair coin at the 5% level.
However, maybe we want to be more certain. It's an experiment that's hard to replicate, or we're in a field that requires a different standard of rigor. We set our significant level at 1%, so only events less common than once in a hundred times are considered significant evidence against the null hypothesis. So our 8-heads result, with its p-value of 0.044 > 0.01, is not enough for us to reject the hypothesis of a fair coin at the 1% level.
In some fields, the preferred significant level could go up as high as 10%, or as low as 0.00000001. If you're not sure what you should be using, then I'd recommend looking in some relevant journals to see what's commonly used for your field. And I would especially recommend doing so before you run the experiment, because setting things like significance levels after you have your data is considered evidence of fishing for results.

