# p-value and significance level

#### sak

##### New Member
In 1 sample t-test, where null: mean of sample is zero, I would think a high p-value like 0.30 would imply that null can't be rejected at 5% significance level. However, p-value of 0.012 would imply null will be rejected at 5% significance level but not at 1% significance level.

So, I am confused that 1% being stricter gives low p-value even though high p-value is consider to give us more confidence. Can you guys please explain.

Thanks

#### Englund

##### TS Contributor
where null: mean of sample is zero
You don't need much of a test to test this. Just compute the mean and check whether it is zero or not. Usually significance tests are carried out to test whether the population mean is, for example, zero.

#### SiBorg

##### New Member
even though high p-value is consider to give us more confidence
care to elaborate on this please?
Yes, the low p value gives more confidence, the high one less confidence.

P.S. I'm quite proud of the nested quotes in this post.

#### sak

##### New Member
Guys. I am very confused now.

In single sample t-test if our null is that mean is zero. For high p-value like 0.3 we would say we fail to reject null at 5%,1%,etc significance level. Correct?

But for low p-value like 0.012 we reject null at 5% significance level and accept alternative hypothesis? However, we would fail to reject null at 1% significance level when p value is 0.012.

But, 1% significance is considered to be stricter than 5%. So, where is the disconnect. Please explain.

Thanks

Edit: I have fixed some of my typos based on later posts here.

Last edited:

#### SiBorg

##### New Member
Guys. I am very confused now.

In single sample t-test if our null is that mean is zero. For high p-value like 0.3 we would say we fail to reject null at 5% confidence level. Correct?

But for low p-value like 0.012 we would fail to reject null at 5% confidence level? Please explain.

Thanks
I'm guessing that you mean 1% 'confidence level' for the second statement?

Where you've stated 'confidence level', you mean significance level.

The significance level is the risk that you will make a type 1 error - i.e. say there is an effect where there isn't. So the lower the significance level, the higher your confidence.

A 5% significance level (p=0.05) equates to a 95% confidence interval.

A 1% significance level(p=0.01) equates to a 99% confidence interval.

The lower the p, the higher (and narrower) the confidence interval.

#### SiBorg

##### New Member
The null hypothesis should be constructed as the opposite of what you are trying to show. The alternative is what you are trying to show. Therefore, you usually want to reject the null and accept the alternative.