QQ Plot and Shapiro-Wilk Test Disagree
Clash Royale CLAN TAG#URR8PPP
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$begingroup$
My QQ Plot shows that the data is not normally distributed
qqplot(residual_values, fit = True, line = '45')
pylab.show()
It has a skewness of 0.54
residual_values.skew() # 0.5469389365591185
But the p_value of Shapiro-Wilk test is greater than 0.05, telling me that it is normally distributed
shapiro(residual_values) # (0.9569438099861145, 0.2261517345905304)
What is the correct inference from this? Is it normally distributed or not?
regression machine-learning
edited Mar 11 at 8:58
Nick Cox
39.2k587131
asked Mar 10 at 18:27
ShinigamiShinigami
237
$endgroup$
add a comment |
$begingroup$
My QQ Plot shows that the data is not normally distributed
qqplot(residual_values, fit = True, line = '45')
pylab.show()
It has a skewness of 0.54
residual_values.skew() # 0.5469389365591185
But the p_value of Shapiro-Wilk test is greater than 0.05, telling me that it is normally distributed
shapiro(residual_values) # (0.9569438099861145, 0.2261517345905304)
What is the correct inference from this? Is it normally distributed or not?
regression machine-learning
edited Mar 11 at 8:58
Nick Cox
39.2k587131
asked Mar 10 at 18:27
ShinigamiShinigami
237
$endgroup$
3
$begingroup$
The QQ plot looks consistent with being normally distributed. Did you expect every point to fall exactly on the line?
$endgroup$
– The Laconic
Mar 10 at 20:24
3
$begingroup$
It is approximately normally distributed if you are prepared to discount slight skewness. No procedure ever indicates more.
$endgroup$
– Nick Cox
Mar 10 at 21:07
1
$begingroup$
It's approximately normal, the skewness in the sample is quite mild; this doesn't automatically mean the population is also skewed (though I expect it is). A high p-value on a test of normality doesn't mean that it is normal, only that you couldn't detect whatever population non-normality there was. (The answer to "is it normally distributed" is "no" - unless you generated it to be normal it won't actually be normal -- but why would it have to be?)
$endgroup$
– Glen_b♦
Mar 10 at 23:09
add a comment |
$begingroup$
My QQ Plot shows that the data is not normally distributed
qqplot(residual_values, fit = True, line = '45')
pylab.show()
It has a skewness of 0.54
residual_values.skew() # 0.5469389365591185
But the p_value of Shapiro-Wilk test is greater than 0.05, telling me that it is normally distributed
shapiro(residual_values) # (0.9569438099861145, 0.2261517345905304)
What is the correct inference from this? Is it normally distributed or not?
regression machine-learning
edited Mar 11 at 8:58
Nick Cox
39.2k587131
asked Mar 10 at 18:27
ShinigamiShinigami
237
$endgroup$
My QQ Plot shows that the data is not normally distributed
qqplot(residual_values, fit = True, line = '45')
pylab.show()
It has a skewness of 0.54
residual_values.skew() # 0.5469389365591185
But the p_value of Shapiro-Wilk test is greater than 0.05, telling me that it is normally distributed
shapiro(residual_values) # (0.9569438099861145, 0.2261517345905304)
What is the correct inference from this? Is it normally distributed or not?
regression machine-learning
regression machine-learning
edited Mar 11 at 8:58
Nick Cox
39.2k587131
asked Mar 10 at 18:27
ShinigamiShinigami
237
edited Mar 11 at 8:58
Nick Cox
39.2k587131
asked Mar 10 at 18:27
ShinigamiShinigami
237
edited Mar 11 at 8:58
Nick Cox
39.2k587131
edited Mar 11 at 8:58
Nick Cox
39.2k587131
edited Mar 11 at 8:58
Nick Cox
39.2k587131
39.2k587131
asked Mar 10 at 18:27
ShinigamiShinigami
237
asked Mar 10 at 18:27
ShinigamiShinigami
237
asked Mar 10 at 18:27
ShinigamiShinigami
237
237
3
$begingroup$
The QQ plot looks consistent with being normally distributed. Did you expect every point to fall exactly on the line?
$endgroup$
– The Laconic
Mar 10 at 20:24
3
$begingroup$
It is approximately normally distributed if you are prepared to discount slight skewness. No procedure ever indicates more.
$endgroup$
– Nick Cox
Mar 10 at 21:07
1
$begingroup$
It's approximately normal, the skewness in the sample is quite mild; this doesn't automatically mean the population is also skewed (though I expect it is). A high p-value on a test of normality doesn't mean that it is normal, only that you couldn't detect whatever population non-normality there was. (The answer to "is it normally distributed" is "no" - unless you generated it to be normal it won't actually be normal -- but why would it have to be?)
$endgroup$
– Glen_b♦
Mar 10 at 23:09
add a comment |
3
$begingroup$
The QQ plot looks consistent with being normally distributed. Did you expect every point to fall exactly on the line?
$endgroup$
– The Laconic
Mar 10 at 20:24
3
$begingroup$
It is approximately normally distributed if you are prepared to discount slight skewness. No procedure ever indicates more.
$endgroup$
– Nick Cox
Mar 10 at 21:07
1
$begingroup$
It's approximately normal, the skewness in the sample is quite mild; this doesn't automatically mean the population is also skewed (though I expect it is). A high p-value on a test of normality doesn't mean that it is normal, only that you couldn't detect whatever population non-normality there was. (The answer to "is it normally distributed" is "no" - unless you generated it to be normal it won't actually be normal -- but why would it have to be?)
$endgroup$
– Glen_b♦
Mar 10 at 23:09
3
3
$begingroup$
The QQ plot looks consistent with being normally distributed. Did you expect every point to fall exactly on the line?
$endgroup$
– The Laconic
Mar 10 at 20:24
$begingroup$
The QQ plot looks consistent with being normally distributed. Did you expect every point to fall exactly on the line?
$endgroup$
– The Laconic
Mar 10 at 20:24
3
3
$begingroup$
It is approximately normally distributed if you are prepared to discount slight skewness. No procedure ever indicates more.
$endgroup$
– Nick Cox
Mar 10 at 21:07
$begingroup$
It is approximately normally distributed if you are prepared to discount slight skewness. No procedure ever indicates more.
$endgroup$
– Nick Cox
Mar 10 at 21:07
1
1
$begingroup$
It's approximately normal, the skewness in the sample is quite mild; this doesn't automatically mean the population is also skewed (though I expect it is). A high p-value on a test of normality doesn't mean that it is normal, only that you couldn't detect whatever population non-normality there was. (The answer to "is it normally distributed" is "no" - unless you generated it to be normal it won't actually be normal -- but why would it have to be?)
$endgroup$
– Glen_b♦
Mar 10 at 23:09
$begingroup$
It's approximately normal, the skewness in the sample is quite mild; this doesn't automatically mean the population is also skewed (though I expect it is). A high p-value on a test of normality doesn't mean that it is normal, only that you couldn't detect whatever population non-normality there was. (The answer to "is it normally distributed" is "no" - unless you generated it to be normal it won't actually be normal -- but why would it have to be?)
$endgroup$
– Glen_b♦
Mar 10 at 23:09
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
The QQ plot is an informal test of normality that can give you some insight into the nature of deviations from normality; for example, whether the distribution has some skew, or fat tails, or there are specific observations that deviate from what you would expect from a normal distribution (outliers). The QQ plot can often convince you that the distribution is definitely not normal, but this isn't such a case. Here, the points fall more or less along the line, which is broadly consistent with normality--intuitively, the sort of variation you would expect to see in a small sample.
The Shapiro-Wilk test is a formal test of normality. I'm not familiar with the shapiro function's output, so I'm not sure which number, if either, is supposed to be the p-value, but if you say it's largish, then we are led to accept the null hypothesis of normality. And this is consistent with what we see qualitatively in the QQ plot.
edited Mar 11 at 8:56
Nick Cox
39.2k587131
answered Mar 10 at 22:02
The LaconicThe Laconic
1,2752615
$endgroup$
add a comment |
$begingroup$
The q-q is consistent with (not "proving") approximate normality, more or less.
The Shapiro-Wilk is a formal test of normality and as such, it cannot confirm the null hypothesis of normality. The data may be reasonably consistent with normality yet still be from a different nonnormal underlying distribution. Frequentist hypothesis tests, as a general rule, cannot prove a hypothesis, and failure to reject (p>alpha) does not support the null hypothesis.
@The Laconic gave some decent advice to interpret the q-q plot. However, large p-values do not lead you to accept the null hypothesis (therefore, you don't conclude normality based on this test; the best you can do is say insufficient evidence of nonnormality at the a priori chosen alpha level).
answered Mar 10 at 22:18
LSCLSC
3348
$endgroup$
add a comment |
$begingroup$
My understanding is that, given power issues with normality tests, they are not highly recommended. As a result I don't use them any more, preferring QQ plots (which are recommended in the literature I have seen).
answered Mar 10 at 22:55
user54285user54285
865
$endgroup$
1
$begingroup$
I was under the impression formal tests of normality are usually too powerful and too frequently detect immaterial departures from normality. Visualization is generally preferred, as you said (and theoretical knowledge when available).
$endgroup$
– LSC
Mar 11 at 0:57
add a comment |
$begingroup$
The Shapiro-Wilk p-value being >0.05 indicates lack of evidence against normality. That is consistent with the QQ plot you showed, which is not too far off the line. I don't see what the inconsistency is here. Also, you should give a CI for the skewness coefficient.
edited Mar 11 at 8:57
Nick Cox
39.2k587131
answered Mar 10 at 22:22
beta1_equals_beta2beta1_equals_beta2
683
$endgroup$
add a comment |
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The QQ plot is an informal test of normality that can give you some insight into the nature of deviations from normality; for example, whether the distribution has some skew, or fat tails, or there are specific observations that deviate from what you would expect from a normal distribution (outliers). The QQ plot can often convince you that the distribution is definitely not normal, but this isn't such a case. Here, the points fall more or less along the line, which is broadly consistent with normality--intuitively, the sort of variation you would expect to see in a small sample.
The Shapiro-Wilk test is a formal test of normality. I'm not familiar with the shapiro function's output, so I'm not sure which number, if either, is supposed to be the p-value, but if you say it's largish, then we are led to accept the null hypothesis of normality. And this is consistent with what we see qualitatively in the QQ plot.
edited Mar 11 at 8:56
Nick Cox
39.2k587131
answered Mar 10 at 22:02
The LaconicThe Laconic
1,2752615
$endgroup$
add a comment |
$begingroup$
The QQ plot is an informal test of normality that can give you some insight into the nature of deviations from normality; for example, whether the distribution has some skew, or fat tails, or there are specific observations that deviate from what you would expect from a normal distribution (outliers). The QQ plot can often convince you that the distribution is definitely not normal, but this isn't such a case. Here, the points fall more or less along the line, which is broadly consistent with normality--intuitively, the sort of variation you would expect to see in a small sample.
The Shapiro-Wilk test is a formal test of normality. I'm not familiar with the shapiro function's output, so I'm not sure which number, if either, is supposed to be the p-value, but if you say it's largish, then we are led to accept the null hypothesis of normality. And this is consistent with what we see qualitatively in the QQ plot.
edited Mar 11 at 8:56
Nick Cox
39.2k587131
answered Mar 10 at 22:02
The LaconicThe Laconic
1,2752615
$endgroup$
add a comment |
$begingroup$
The QQ plot is an informal test of normality that can give you some insight into the nature of deviations from normality; for example, whether the distribution has some skew, or fat tails, or there are specific observations that deviate from what you would expect from a normal distribution (outliers). The QQ plot can often convince you that the distribution is definitely not normal, but this isn't such a case. Here, the points fall more or less along the line, which is broadly consistent with normality--intuitively, the sort of variation you would expect to see in a small sample.
The Shapiro-Wilk test is a formal test of normality. I'm not familiar with the shapiro function's output, so I'm not sure which number, if either, is supposed to be the p-value, but if you say it's largish, then we are led to accept the null hypothesis of normality. And this is consistent with what we see qualitatively in the QQ plot.
edited Mar 11 at 8:56
Nick Cox
39.2k587131
answered Mar 10 at 22:02
The LaconicThe Laconic
1,2752615
$endgroup$
The QQ plot is an informal test of normality that can give you some insight into the nature of deviations from normality; for example, whether the distribution has some skew, or fat tails, or there are specific observations that deviate from what you would expect from a normal distribution (outliers). The QQ plot can often convince you that the distribution is definitely not normal, but this isn't such a case. Here, the points fall more or less along the line, which is broadly consistent with normality--intuitively, the sort of variation you would expect to see in a small sample.
The Shapiro-Wilk test is a formal test of normality. I'm not familiar with the shapiro function's output, so I'm not sure which number, if either, is supposed to be the p-value, but if you say it's largish, then we are led to accept the null hypothesis of normality. And this is consistent with what we see qualitatively in the QQ plot.
edited Mar 11 at 8:56
Nick Cox
39.2k587131
answered Mar 10 at 22:02
The LaconicThe Laconic
1,2752615
edited Mar 11 at 8:56
Nick Cox
39.2k587131
edited Mar 11 at 8:56
Nick Cox
39.2k587131
edited Mar 11 at 8:56
Nick Cox
39.2k587131
39.2k587131
answered Mar 10 at 22:02
The LaconicThe Laconic
1,2752615
answered Mar 10 at 22:02
The LaconicThe Laconic
1,2752615
answered Mar 10 at 22:02
The LaconicThe Laconic
1,2752615
1,2752615
add a comment |
add a comment |
$begingroup$
The q-q is consistent with (not "proving") approximate normality, more or less.
The Shapiro-Wilk is a formal test of normality and as such, it cannot confirm the null hypothesis of normality. The data may be reasonably consistent with normality yet still be from a different nonnormal underlying distribution. Frequentist hypothesis tests, as a general rule, cannot prove a hypothesis, and failure to reject (p>alpha) does not support the null hypothesis.
@The Laconic gave some decent advice to interpret the q-q plot. However, large p-values do not lead you to accept the null hypothesis (therefore, you don't conclude normality based on this test; the best you can do is say insufficient evidence of nonnormality at the a priori chosen alpha level).
answered Mar 10 at 22:18
LSCLSC
3348
$endgroup$
add a comment |
$begingroup$
The q-q is consistent with (not "proving") approximate normality, more or less.
The Shapiro-Wilk is a formal test of normality and as such, it cannot confirm the null hypothesis of normality. The data may be reasonably consistent with normality yet still be from a different nonnormal underlying distribution. Frequentist hypothesis tests, as a general rule, cannot prove a hypothesis, and failure to reject (p>alpha) does not support the null hypothesis.
@The Laconic gave some decent advice to interpret the q-q plot. However, large p-values do not lead you to accept the null hypothesis (therefore, you don't conclude normality based on this test; the best you can do is say insufficient evidence of nonnormality at the a priori chosen alpha level).
answered Mar 10 at 22:18
LSCLSC
3348
$endgroup$
add a comment |
$begingroup$
The q-q is consistent with (not "proving") approximate normality, more or less.
The Shapiro-Wilk is a formal test of normality and as such, it cannot confirm the null hypothesis of normality. The data may be reasonably consistent with normality yet still be from a different nonnormal underlying distribution. Frequentist hypothesis tests, as a general rule, cannot prove a hypothesis, and failure to reject (p>alpha) does not support the null hypothesis.
@The Laconic gave some decent advice to interpret the q-q plot. However, large p-values do not lead you to accept the null hypothesis (therefore, you don't conclude normality based on this test; the best you can do is say insufficient evidence of nonnormality at the a priori chosen alpha level).
answered Mar 10 at 22:18
LSCLSC
3348
$endgroup$
The q-q is consistent with (not "proving") approximate normality, more or less.
The Shapiro-Wilk is a formal test of normality and as such, it cannot confirm the null hypothesis of normality. The data may be reasonably consistent with normality yet still be from a different nonnormal underlying distribution. Frequentist hypothesis tests, as a general rule, cannot prove a hypothesis, and failure to reject (p>alpha) does not support the null hypothesis.
@The Laconic gave some decent advice to interpret the q-q plot. However, large p-values do not lead you to accept the null hypothesis (therefore, you don't conclude normality based on this test; the best you can do is say insufficient evidence of nonnormality at the a priori chosen alpha level).
answered Mar 10 at 22:18
LSCLSC
3348
answered Mar 10 at 22:18
LSCLSC
3348
answered Mar 10 at 22:18
LSCLSC
3348
answered Mar 10 at 22:18
LSCLSC
3348
3348
add a comment |
add a comment |
$begingroup$
My understanding is that, given power issues with normality tests, they are not highly recommended. As a result I don't use them any more, preferring QQ plots (which are recommended in the literature I have seen).
answered Mar 10 at 22:55
user54285user54285
865
$endgroup$
1
$begingroup$
I was under the impression formal tests of normality are usually too powerful and too frequently detect immaterial departures from normality. Visualization is generally preferred, as you said (and theoretical knowledge when available).
$endgroup$
– LSC
Mar 11 at 0:57
add a comment |
$begingroup$
My understanding is that, given power issues with normality tests, they are not highly recommended. As a result I don't use them any more, preferring QQ plots (which are recommended in the literature I have seen).
answered Mar 10 at 22:55
user54285user54285
865
$endgroup$
1
$begingroup$
I was under the impression formal tests of normality are usually too powerful and too frequently detect immaterial departures from normality. Visualization is generally preferred, as you said (and theoretical knowledge when available).
$endgroup$
– LSC
Mar 11 at 0:57
add a comment |
$begingroup$
My understanding is that, given power issues with normality tests, they are not highly recommended. As a result I don't use them any more, preferring QQ plots (which are recommended in the literature I have seen).
answered Mar 10 at 22:55
user54285user54285
865
$endgroup$
My understanding is that, given power issues with normality tests, they are not highly recommended. As a result I don't use them any more, preferring QQ plots (which are recommended in the literature I have seen).
answered Mar 10 at 22:55
user54285user54285
865
answered Mar 10 at 22:55
user54285user54285
865
answered Mar 10 at 22:55
user54285user54285
865
answered Mar 10 at 22:55
user54285user54285
865
865
1
$begingroup$
I was under the impression formal tests of normality are usually too powerful and too frequently detect immaterial departures from normality. Visualization is generally preferred, as you said (and theoretical knowledge when available).
$endgroup$
– LSC
Mar 11 at 0:57
add a comment |
1
$begingroup$
I was under the impression formal tests of normality are usually too powerful and too frequently detect immaterial departures from normality. Visualization is generally preferred, as you said (and theoretical knowledge when available).
$endgroup$
– LSC
Mar 11 at 0:57
1
1
$begingroup$
I was under the impression formal tests of normality are usually too powerful and too frequently detect immaterial departures from normality. Visualization is generally preferred, as you said (and theoretical knowledge when available).
$endgroup$
– LSC
Mar 11 at 0:57
$begingroup$
I was under the impression formal tests of normality are usually too powerful and too frequently detect immaterial departures from normality. Visualization is generally preferred, as you said (and theoretical knowledge when available).
$endgroup$
– LSC
Mar 11 at 0:57
add a comment |
$begingroup$
The Shapiro-Wilk p-value being >0.05 indicates lack of evidence against normality. That is consistent with the QQ plot you showed, which is not too far off the line. I don't see what the inconsistency is here. Also, you should give a CI for the skewness coefficient.
edited Mar 11 at 8:57
Nick Cox
39.2k587131
answered Mar 10 at 22:22
beta1_equals_beta2beta1_equals_beta2
683
$endgroup$
add a comment |
$begingroup$
The Shapiro-Wilk p-value being >0.05 indicates lack of evidence against normality. That is consistent with the QQ plot you showed, which is not too far off the line. I don't see what the inconsistency is here. Also, you should give a CI for the skewness coefficient.
edited Mar 11 at 8:57
Nick Cox
39.2k587131
answered Mar 10 at 22:22
beta1_equals_beta2beta1_equals_beta2
683
$endgroup$
add a comment |
$begingroup$
The Shapiro-Wilk p-value being >0.05 indicates lack of evidence against normality. That is consistent with the QQ plot you showed, which is not too far off the line. I don't see what the inconsistency is here. Also, you should give a CI for the skewness coefficient.
edited Mar 11 at 8:57
Nick Cox
39.2k587131
answered Mar 10 at 22:22
beta1_equals_beta2beta1_equals_beta2
683
$endgroup$
The Shapiro-Wilk p-value being >0.05 indicates lack of evidence against normality. That is consistent with the QQ plot you showed, which is not too far off the line. I don't see what the inconsistency is here. Also, you should give a CI for the skewness coefficient.
edited Mar 11 at 8:57
Nick Cox
39.2k587131
answered Mar 10 at 22:22
beta1_equals_beta2beta1_equals_beta2
683
edited Mar 11 at 8:57
Nick Cox
39.2k587131
edited Mar 11 at 8:57
Nick Cox
39.2k587131
edited Mar 11 at 8:57
Nick Cox
39.2k587131
39.2k587131
answered Mar 10 at 22:22
beta1_equals_beta2beta1_equals_beta2
683
answered Mar 10 at 22:22
beta1_equals_beta2beta1_equals_beta2
683
answered Mar 10 at 22:22
beta1_equals_beta2beta1_equals_beta2
683
683
add a comment |
add a comment |
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$begingroup$
The QQ plot looks consistent with being normally distributed. Did you expect every point to fall exactly on the line?
$endgroup$
– The Laconic
Mar 10 at 20:24
3
$begingroup$
It is approximately normally distributed if you are prepared to discount slight skewness. No procedure ever indicates more.
$endgroup$
– Nick Cox
Mar 10 at 21:07
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It's approximately normal, the skewness in the sample is quite mild; this doesn't automatically mean the population is also skewed (though I expect it is). A high p-value on a test of normality doesn't mean that it is normal, only that you couldn't detect whatever population non-normality there was. (The answer to "is it normally distributed" is "no" - unless you generated it to be normal it won't actually be normal -- but why would it have to be?)
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– Glen_b♦
Mar 10 at 23:09