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

How should tiny $p$-values be reported? (and why does R put a minimum on 2.22e-16?)Interpreting p-value < 2.2e-16 in RSanity check: how low can a p-value go?Statistical comparison of two means with a range not starting at 0Algorithm and R code for dealing with ties in Wilcoxon rank-sum testInterpretation of ur.df - “p-value”?What test should I use for two groups of different number of measurements and low number of samples?Getting a P value of 1 when medians/means are different (Wilcoxon rank sum test)wilcox.test R questionAn issue with computing the Wilcoxon test using RInterpreting the relation between p-value and rho value

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1

$begingroup$

This question already has an answer here:

• 
  How should tiny $p$-values be reported? (and why does R put a minimum on 2.22e-16?)
  
  4 answers
  
  

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

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edited Apr 16 at 14:10

Nick Cox

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asked Apr 16 at 11:54

Adam AminAdam Amin

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$endgroup$

marked as duplicate by amoeba, Michael Chernick, mkt, Frans Rodenburg, Jarle Tufto Apr 17 at 8:34

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Depending on your field, this might commonly be reported as p < 0.001.
  $endgroup$
  – APH
  Apr 16 at 18:14
  

  
  
  
  

add a comment
 | 

1

$begingroup$

This question already has an answer here:

• 
  How should tiny $p$-values be reported? (and why does R put a minimum on 2.22e-16?)
  
  4 answers
  
  

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 Apr 16 at 14:10

Nick Cox

40.8k66 gold badges9090 silver badges136136 bronze badges

asked Apr 16 at 11:54

Adam AminAdam Amin

14355 bronze badges

$endgroup$

marked as duplicate by amoeba, Michael Chernick, mkt, Frans Rodenburg, Jarle Tufto Apr 17 at 8:34

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Depending on your field, this might commonly be reported as p < 0.001.
  $endgroup$
  – APH
  Apr 16 at 18:14
  

  
  
  
  

add a comment
 | 

$begingroup$

This question already has an answer here:

• 
  How should tiny $p$-values be reported? (and why does R put a minimum on 2.22e-16?)
  
  4 answers
  
  

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 Apr 16 at 14:10

Nick Cox

40.8k66 gold badges9090 silver badges136136 bronze badges

asked Apr 16 at 11:54

Adam AminAdam Amin

14355 bronze badges

$endgroup$

share|cite|improve this question

edited Apr 16 at 14:10

Nick Cox

40.8k66 gold badges9090 silver badges136136 bronze badges

asked Apr 16 at 11:54

Adam AminAdam Amin

14355 bronze badges

share|cite|improve this question

edited Apr 16 at 14:10

Nick Cox

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asked Apr 16 at 11:54

Adam AminAdam Amin

14355 bronze badges

edited Apr 16 at 14:10

Nick Cox

40.8k66 gold badges9090 silver badges136136 bronze badges

edited Apr 16 at 14:10

Nick Cox

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asked Apr 16 at 11:54

Adam AminAdam Amin

14355 bronze badges

asked Apr 16 at 11:54

Adam AminAdam Amin

14355 bronze badges

3 Answers
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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).

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answered Apr 16 at 14:04

morphistmorphist

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add a comment
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1

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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 Apr 16 at 19:30

Sycorax

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answered Apr 16 at 19:29

Peter Flom♦Peter Flom

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$endgroup$

add a comment
 | 

1

$begingroup$

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 Apr 16 at 19:36

Ahmed ArifAhmed Arif

15155 bronze badges

$endgroup$

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 Apr 16 at 14:04

morphistmorphist

36633 bronze badges

$endgroup$

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 Apr 16 at 14:04

morphistmorphist

36633 bronze badges

$endgroup$

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 Apr 16 at 14:04

morphistmorphist

36633 bronze badges

$endgroup$

share|cite|improve this answer

answered Apr 16 at 14:04

morphistmorphist

36633 bronze badges

answered Apr 16 at 14:04

morphistmorphist

36633 bronze badges

answered Apr 16 at 14:04

morphistmorphist

36633 bronze badges

1

$begingroup$

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 Apr 16 at 19:30

Sycorax

47.4k1515 gold badges123123 silver badges221221 bronze badges

answered Apr 16 at 19:29

Peter Flom♦Peter Flom

80.9k1313 gold badges117117 silver badges229229 bronze badges

$endgroup$

add a comment
 | 

1

$begingroup$

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 Apr 16 at 19:30

Sycorax

47.4k1515 gold badges123123 silver badges221221 bronze badges

answered Apr 16 at 19:29

Peter Flom♦Peter Flom

80.9k1313 gold badges117117 silver badges229229 bronze badges

$endgroup$

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 Apr 16 at 19:30

Sycorax

47.4k1515 gold badges123123 silver badges221221 bronze badges

answered Apr 16 at 19:29

Peter Flom♦Peter Flom

80.9k1313 gold badges117117 silver badges229229 bronze badges

$endgroup$

share|cite|improve this answer

edited Apr 16 at 19:30

Sycorax

47.4k1515 gold badges123123 silver badges221221 bronze badges

answered Apr 16 at 19:29

Peter Flom♦Peter Flom

80.9k1313 gold badges117117 silver badges229229 bronze badges

edited Apr 16 at 19:30

Sycorax

47.4k1515 gold badges123123 silver badges221221 bronze badges

edited Apr 16 at 19:30

Sycorax

47.4k1515 gold badges123123 silver badges221221 bronze badges

answered Apr 16 at 19:29

Peter Flom♦Peter Flom

80.9k1313 gold badges117117 silver badges229229 bronze badges

answered Apr 16 at 19:29

Peter Flom♦Peter Flom

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1

$begingroup$

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 Apr 16 at 19:36

Ahmed ArifAhmed Arif

15155 bronze badges

$endgroup$

add a comment
 | 

1

$begingroup$

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 Apr 16 at 19:36

Ahmed ArifAhmed Arif

15155 bronze badges

$endgroup$

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 Apr 16 at 19:36

Ahmed ArifAhmed Arif

15155 bronze badges

$endgroup$

share|cite|improve this answer

answered Apr 16 at 19:36

Ahmed ArifAhmed Arif

15155 bronze badges

answered Apr 16 at 19:36

Ahmed ArifAhmed Arif

15155 bronze badges

answered Apr 16 at 19:36

Ahmed ArifAhmed Arif

15155 bronze badges