# Accept Null hypothesis VS Reject Null hypothesis ?

#### hanialbarni

##### New Member
Hello
Good evening everyone,

can someone correct me this is what I do understand below

- if I reject null hypothesis it means the hypothesis p value < 0.05 and my hypothesis is not significant

- if I accept null hypothesis it means my hypothesis p > 0.05 and my hypothesis is significant

am I correct , can someone please correct me if I am mistaken !!!!

#### Injektilo

##### New Member
We never accept the null hypothesis. We either reject it in favour of the alternate hypothesis or we fail to reject it. It sounds like we're splitting hairs, but the distinction is important.

When the p-value > 0.05, we do not reject the null hypothesis because there is not enough evidence to do so. It doesn't mean that the null hypothesis is true. This is something that is much harder to prove.

It's a similar situation in a criminal court. The judge decides if the accused is guilty or not guilty. The judge does not decide whether the accused is guilty or innocent, because innocence is much harder to prove and the onus is on the prosecution to demonstrate that the evidence is overwhelmingly pointing to the accused being guilty. Similarly, the onus is on the researcher to prove that the alternate hypothesis should be adopted instead of the null hypothesis.

Let's put it another way. Let's say that you have a sample of 100 observations, and a test you ran came up with a p-value of 0.051. Would you conclude that the null hypothesis is true? Maybe if you had collected a handful more observations and you re-ran the test, the p-value would have been < 0.05. So why would you jump to the conclusion that because something is not proven to be something other than 0, it HAS to be 0? That's a leap in logic.

#### hanialbarni

##### New Member
OMG so much difficult to understand ;S , Ok let me get this

if i reject the null hypothesis it mean my p > 0.05and hypothesis is significant ?

if i fail to reject the null hypothesis it mean my p < 0.05and hypothesis is not significant ?

Please someone explain the above statements because this is what i understand currently !!!

#### maartenbuis

##### TS Contributor
0.05 is a common but not the only significance possible level. Common alternatives are 0.10, 0.01, but in principle you can choose any value you like.

A hypothesis is neither significant nor insignificant. It is the parameters that can be significant or not. Say our parameter is a regression coefficient, our null hypothesis is that that coefficient is 0, and we have chosen a significance level of 5%. That regression coefficient can be called significant when it's p-value is less than 0.05. That regression coefficient can be called not significant when the p-value is more than 0.05. So saying that a regression coefficient is significant is just a short hand for "I tested whether the regression coefficient was equal to 0 and failed to reject that hypothesis at the 0.05 level". The term significant can lead to a lot of confusion (it is not a synonym for important), so it is often safer and clearer to just use the full sentence rather than "significant".

The logical order of your statements are reversed: the p-value is less than 0.05 and therefore you reject the null-hypothesis, not the other way around.

#### Karabiner

##### TS Contributor
if i reject the null hypothesis it mean my p > 0.05and hypothesis is significant ?
You have a mistake there, it must be p < 0.05 instead of p > 0.05.
So, if p < 0.05 then you have a statistically significant result and can
reject H0.

if i fail to reject the null hypothesis it mean my p < 0.05and hypothesis is not significant ?
If p > 0.05 (not, as you wrote, p < 0.05), then you do not have a significant
result and cannot reject H0.

With kind regards

K,

#### PeterFlom

##### New Member
OMG so much difficult to understand ;S , Ok let me get this

if i reject the null hypothesis it mean my p > 0.05and hypothesis is significant ?

if i fail to reject the null hypothesis it mean my p < 0.05and hypothesis is not significant ?

Please someone explain the above statements because this is what i understand currently !!!
No, you have this incorrect in three ways:

1. You don't get a p value depending on whether you reject or fail to reject the null; rather, you decide about the null based on your p value
2. You reject the null if the p value is small, you fail to reject the null if it is large.
3. The number 0.05 is traditional and common, but not necessary nor universal. It could be 0.01 or 0.10 or anything.

This may help:

The null hypothesis is usually something like: Nothing is going on or There is no relationship. You (the researcher) want to show that the null is false. So, you bring in evidence that it is false (that is, that there is something going on or there is a relationship. If the evidence is strong, the p value will be low and you will reject the null (this makes you happy) if there is not enough evidence, then you will fail to reject the null and have to come up with something else (this makes you sad)