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What is the interpretation of the p-value of 2.2e-16?

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0

$begingroup$

I am a beginner in using Wilcoxon test to get the p-value. After applying the test to my data, I got the p-value < 2.2e-16. Does that mean that the samples I have are significantly different from each other? I am suspicious of such a result. I have looked at other related questions (such as this question) but I didn't really understand what this value means.

Can someone please explain?

r p-value wilcoxon-mann-whitney

share|cite|improve this question

edited 13 hours ago

Nick Cox

39.4k588132

asked 15 hours ago

Adam AminAdam Amin

1213

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Possible duplicate of How should tiny $p$-values be reported? (and why does R put a minimum on 2.22e-16?)
  $endgroup$
  – corey979
  11 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Depending on your field, this might commonly be reported as p < 0.001.
  $endgroup$
  – APH
  9 hours ago
  

  
  
  
  

add a comment | 

0

$begingroup$

I am a beginner in using Wilcoxon test to get the p-value. After applying the test to my data, I got the p-value < 2.2e-16. Does that mean that the samples I have are significantly different from each other? I am suspicious of such a result. I have looked at other related questions (such as this question) but I didn't really understand what this value means.

Can someone please explain?

r p-value wilcoxon-mann-whitney

share|cite|improve this question

edited 13 hours ago

Nick Cox

39.4k588132

asked 15 hours ago

Adam AminAdam Amin

1213

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Possible duplicate of How should tiny $p$-values be reported? (and why does R put a minimum on 2.22e-16?)
  $endgroup$
  – corey979
  11 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Depending on your field, this might commonly be reported as p < 0.001.
  $endgroup$
  – APH
  9 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

I am a beginner in using Wilcoxon test to get the p-value. After applying the test to my data, I got the p-value < 2.2e-16. Does that mean that the samples I have are significantly different from each other? I am suspicious of such a result. I have looked at other related questions (such as this question) but I didn't really understand what this value means.

Can someone please explain?

r p-value wilcoxon-mann-whitney

share|cite|improve this question

edited 13 hours ago

Nick Cox

39.4k588132

asked 15 hours ago

Adam AminAdam Amin

1213

$endgroup$

share|cite|improve this question

edited 13 hours ago

Nick Cox

39.4k588132

asked 15 hours ago

Adam AminAdam Amin

1213

share|cite|improve this question

edited 13 hours ago

Nick Cox

39.4k588132

asked 15 hours ago

Adam AminAdam Amin

1213

edited 13 hours ago

Nick Cox

39.4k588132

edited 13 hours ago

Nick Cox

39.4k588132

asked 15 hours ago

Adam AminAdam Amin

1213

asked 15 hours ago

Adam AminAdam Amin

1213

3 Answers
3

active

oldest

votes

8

$begingroup$

2.2e-16 is the scientific notation of 0.00000000000000022, meaning it is very close to zero. Your statistical software probably uses this notation automatically for very small numbers. You may be able to change this in the settings.

The notation alone is no reason to be suspicious. The result itself might be, but you will have to be the judge of that.

< 2.2e-16 as the p value would indicate a significant result, meaning that the actual p value is even smaller than 2.2e-16 (a typical threshold is 0.05, anything smaller counts as statistically significant).

share|cite|improve this answer

answered 13 hours ago

morphistmorphist

1061

New contributor

morphist is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

0

$begingroup$

Adding to Morphist's answer (+1 to Morphist), I would be suspicious of this if:

• N was small




• The difference was expected to be small




• Other studies find small differences.

and so on.

I would make a density plot of the values in each of the groups and see if they look really different.

share|cite|improve this answer

edited 7 hours ago

Sycorax

42.7k12112207

answered 7 hours ago

Peter Flom♦Peter Flom

77.6k12110219

$endgroup$

add a comment | 

0

$begingroup$

You will reject your null hypothesis in this situation as the p < 0.01. If you are comparing difference with respect to some variable in two groups, then it means both groups have significance differences in the mean values of that variable.

share|cite|improve this answer

answered 7 hours ago

Ahmed ArifAhmed Arif

1314

$endgroup$

add a comment | 

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8

$begingroup$

2.2e-16 is the scientific notation of 0.00000000000000022, meaning it is very close to zero. Your statistical software probably uses this notation automatically for very small numbers. You may be able to change this in the settings.

The notation alone is no reason to be suspicious. The result itself might be, but you will have to be the judge of that.

< 2.2e-16 as the p value would indicate a significant result, meaning that the actual p value is even smaller than 2.2e-16 (a typical threshold is 0.05, anything smaller counts as statistically significant).

share|cite|improve this answer

answered 13 hours ago

morphistmorphist

1061

New contributor

morphist is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

8

$begingroup$

2.2e-16 is the scientific notation of 0.00000000000000022, meaning it is very close to zero. Your statistical software probably uses this notation automatically for very small numbers. You may be able to change this in the settings.

The notation alone is no reason to be suspicious. The result itself might be, but you will have to be the judge of that.

< 2.2e-16 as the p value would indicate a significant result, meaning that the actual p value is even smaller than 2.2e-16 (a typical threshold is 0.05, anything smaller counts as statistically significant).

share|cite|improve this answer

answered 13 hours ago

morphistmorphist

1061

New contributor

morphist is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

2.2e-16 is the scientific notation of 0.00000000000000022, meaning it is very close to zero. Your statistical software probably uses this notation automatically for very small numbers. You may be able to change this in the settings.

The notation alone is no reason to be suspicious. The result itself might be, but you will have to be the judge of that.

< 2.2e-16 as the p value would indicate a significant result, meaning that the actual p value is even smaller than 2.2e-16 (a typical threshold is 0.05, anything smaller counts as statistically significant).

share|cite|improve this answer

answered 13 hours ago

morphistmorphist

1061

New contributor

morphist is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this answer

answered 13 hours ago

morphistmorphist

1061

New contributor

morphist is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 13 hours ago

morphistmorphist

1061

New contributor

morphist is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 13 hours ago

morphistmorphist

1061

0

$begingroup$

Adding to Morphist's answer (+1 to Morphist), I would be suspicious of this if:

• N was small




• The difference was expected to be small




• Other studies find small differences.

and so on.

I would make a density plot of the values in each of the groups and see if they look really different.

share|cite|improve this answer

edited 7 hours ago

Sycorax

42.7k12112207

answered 7 hours ago

Peter Flom♦Peter Flom

77.6k12110219

$endgroup$

add a comment | 

0

$begingroup$

Adding to Morphist's answer (+1 to Morphist), I would be suspicious of this if:

• N was small




• The difference was expected to be small




• Other studies find small differences.

and so on.

I would make a density plot of the values in each of the groups and see if they look really different.

share|cite|improve this answer

edited 7 hours ago

Sycorax

42.7k12112207

answered 7 hours ago

Peter Flom♦Peter Flom

77.6k12110219

$endgroup$

add a comment | 

$begingroup$

Adding to Morphist's answer (+1 to Morphist), I would be suspicious of this if:

• N was small




• The difference was expected to be small




• Other studies find small differences.

and so on.

I would make a density plot of the values in each of the groups and see if they look really different.

share|cite|improve this answer

edited 7 hours ago

Sycorax

42.7k12112207

answered 7 hours ago

Peter Flom♦Peter Flom

77.6k12110219

$endgroup$

share|cite|improve this answer

edited 7 hours ago

Sycorax

42.7k12112207

answered 7 hours ago

Peter Flom♦Peter Flom

77.6k12110219

edited 7 hours ago

Sycorax

42.7k12112207

edited 7 hours ago

Sycorax

42.7k12112207

answered 7 hours ago

Peter Flom♦Peter Flom

77.6k12110219

answered 7 hours ago

Peter Flom♦Peter Flom

77.6k12110219

0

$begingroup$

You will reject your null hypothesis in this situation as the p < 0.01. If you are comparing difference with respect to some variable in two groups, then it means both groups have significance differences in the mean values of that variable.

share|cite|improve this answer

answered 7 hours ago

Ahmed ArifAhmed Arif

1314

$endgroup$

add a comment | 

0

$begingroup$

You will reject your null hypothesis in this situation as the p < 0.01. If you are comparing difference with respect to some variable in two groups, then it means both groups have significance differences in the mean values of that variable.

share|cite|improve this answer

answered 7 hours ago

Ahmed ArifAhmed Arif

1314

$endgroup$

add a comment | 

$begingroup$

You will reject your null hypothesis in this situation as the p < 0.01. If you are comparing difference with respect to some variable in two groups, then it means both groups have significance differences in the mean values of that variable.

share|cite|improve this answer

answered 7 hours ago

Ahmed ArifAhmed Arif

1314

$endgroup$

share|cite|improve this answer

answered 7 hours ago

Ahmed ArifAhmed Arif

1314

answered 7 hours ago

Ahmed ArifAhmed Arif

1314

answered 7 hours ago

Ahmed ArifAhmed Arif

1314