Does a log transform always bring a distribution closer to normal?
$begingroup$
I have a highly right skewed data set with a large range of values (from 1 ~ 10^6) (can't share the actual data for work related reasons).
When I plot the log of the data instead, the distribution looks a lot more like a normal distribution.
Have I stumbled on a meaningful insight in the data set, or is just a general property of the log transform that it brings the distribution closer to normal?
distributions normal-distribution data-transformation skewness
asked 2 days ago
Akaike's ChildrenAkaike's Children
254
$endgroup$
add a comment |
$begingroup$
I have a highly right skewed data set with a large range of values (from 1 ~ 10^6) (can't share the actual data for work related reasons).
When I plot the log of the data instead, the distribution looks a lot more like a normal distribution.
Have I stumbled on a meaningful insight in the data set, or is just a general property of the log transform that it brings the distribution closer to normal?
distributions normal-distribution data-transformation skewness
asked 2 days ago
Akaike's ChildrenAkaike's Children
254
$endgroup$
1
$begingroup$
I have to guess that you mean right-skewed. Left or right indicates which tail is longer; the terminology implies a horizontal magnitude scale with low values on the left.
$endgroup$
– Nick Cox
yesterday
2
$begingroup$
I always naively assumed that the log transform works well if your data can be thought of as some constant, times many (more or less) independent factors close to 1. E.g. A guy's salary is 10% above the mean if he has a degree, 5% higher if he's living in a large town, 5% lower if he has health issues... A log transform turns that into a sum of independent small numbers, so you get a normal distribution.
$endgroup$
– nikie
yesterday
$begingroup$
@Akaikes See here, here and particularly here & here which indicate that the log-transform won't always make even a right-skewed variate less skew (in absolute terms) than it was. A simple counterexample is the Maxwell(-Boltzmann) distribution, which is mildly right skew but the log of a Maxwell-variate is more strongly (left) skew.
$endgroup$
– Glen_b♦
yesterday
add a comment |
$begingroup$
I have a highly right skewed data set with a large range of values (from 1 ~ 10^6) (can't share the actual data for work related reasons).
When I plot the log of the data instead, the distribution looks a lot more like a normal distribution.
Have I stumbled on a meaningful insight in the data set, or is just a general property of the log transform that it brings the distribution closer to normal?
distributions normal-distribution data-transformation skewness
asked 2 days ago
Akaike's ChildrenAkaike's Children
254
$endgroup$
I have a highly right skewed data set with a large range of values (from 1 ~ 10^6) (can't share the actual data for work related reasons).
When I plot the log of the data instead, the distribution looks a lot more like a normal distribution.
Have I stumbled on a meaningful insight in the data set, or is just a general property of the log transform that it brings the distribution closer to normal?
distributions normal-distribution data-transformation skewness
distributions normal-distribution data-transformation skewness
asked 2 days ago
Akaike's ChildrenAkaike's Children
254
asked 2 days ago
Akaike's ChildrenAkaike's Children
254
edited yesterday
Akaike's Children
asked 2 days ago
Akaike's ChildrenAkaike's Children
254
asked 2 days ago
Akaike's ChildrenAkaike's Children
254
asked 2 days ago
Akaike's ChildrenAkaike's Children
254
254
1
$begingroup$
I have to guess that you mean right-skewed. Left or right indicates which tail is longer; the terminology implies a horizontal magnitude scale with low values on the left.
$endgroup$
– Nick Cox
yesterday
2
$begingroup$
I always naively assumed that the log transform works well if your data can be thought of as some constant, times many (more or less) independent factors close to 1. E.g. A guy's salary is 10% above the mean if he has a degree, 5% higher if he's living in a large town, 5% lower if he has health issues... A log transform turns that into a sum of independent small numbers, so you get a normal distribution.
$endgroup$
– nikie
yesterday
$begingroup$
@Akaikes See here, here and particularly here & here which indicate that the log-transform won't always make even a right-skewed variate less skew (in absolute terms) than it was. A simple counterexample is the Maxwell(-Boltzmann) distribution, which is mildly right skew but the log of a Maxwell-variate is more strongly (left) skew.
$endgroup$
– Glen_b♦
yesterday
add a comment |
1
$begingroup$
I have to guess that you mean right-skewed. Left or right indicates which tail is longer; the terminology implies a horizontal magnitude scale with low values on the left.
$endgroup$
– Nick Cox
yesterday
2
$begingroup$
I always naively assumed that the log transform works well if your data can be thought of as some constant, times many (more or less) independent factors close to 1. E.g. A guy's salary is 10% above the mean if he has a degree, 5% higher if he's living in a large town, 5% lower if he has health issues... A log transform turns that into a sum of independent small numbers, so you get a normal distribution.
$endgroup$
– nikie
yesterday
$begingroup$
@Akaikes See here, here and particularly here & here which indicate that the log-transform won't always make even a right-skewed variate less skew (in absolute terms) than it was. A simple counterexample is the Maxwell(-Boltzmann) distribution, which is mildly right skew but the log of a Maxwell-variate is more strongly (left) skew.
$endgroup$
– Glen_b♦
yesterday
1
1
$begingroup$
I have to guess that you mean right-skewed. Left or right indicates which tail is longer; the terminology implies a horizontal magnitude scale with low values on the left.
$endgroup$
– Nick Cox
yesterday
$begingroup$
I have to guess that you mean right-skewed. Left or right indicates which tail is longer; the terminology implies a horizontal magnitude scale with low values on the left.
$endgroup$
– Nick Cox
yesterday
2
2
$begingroup$
I always naively assumed that the log transform works well if your data can be thought of as some constant, times many (more or less) independent factors close to 1. E.g. A guy's salary is 10% above the mean if he has a degree, 5% higher if he's living in a large town, 5% lower if he has health issues... A log transform turns that into a sum of independent small numbers, so you get a normal distribution.
$endgroup$
– nikie
yesterday
$begingroup$
I always naively assumed that the log transform works well if your data can be thought of as some constant, times many (more or less) independent factors close to 1. E.g. A guy's salary is 10% above the mean if he has a degree, 5% higher if he's living in a large town, 5% lower if he has health issues... A log transform turns that into a sum of independent small numbers, so you get a normal distribution.
$endgroup$
– nikie
yesterday
$begingroup$
@Akaikes See here, here and particularly here & here which indicate that the log-transform won't always make even a right-skewed variate less skew (in absolute terms) than it was. A simple counterexample is the Maxwell(-Boltzmann) distribution, which is mildly right skew but the log of a Maxwell-variate is more strongly (left) skew.
$endgroup$
– Glen_b♦
yesterday
$begingroup$
@Akaikes See here, here and particularly here & here which indicate that the log-transform won't always make even a right-skewed variate less skew (in absolute terms) than it was. A simple counterexample is the Maxwell(-Boltzmann) distribution, which is mildly right skew but the log of a Maxwell-variate is more strongly (left) skew.
$endgroup$
– Glen_b♦
yesterday
add a comment |
1 Answer
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For purely positive quantities a log-transformation is indeed the standard first transformation to try and is very frequently used. It is also done if for regression you want a multiplicative interpretation of coefficients (e.g. doubling/ halving of blood cholesterol).
Of course it will not always make a distribution more normal, e.g. take samples from a N(1000, 1) distribution: any transformation can only make it less normal.
edited yesterday
Nick Cox
39k587131
answered yesterday
BjörnBjörn
11.5k11142
$endgroup$
4
$begingroup$
Similarly a distribution that is symmetric or left skewed will have its skewness made worse by logarithmic transformation. Consider the not very magnificent seven 1 2 3 4 5 6 7; then their square roots are left skewed and in the logarithms of those are even more left-skewed.
$endgroup$
– Nick Cox
yesterday
add a comment |
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1 Answer
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1 Answer
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$begingroup$
For purely positive quantities a log-transformation is indeed the standard first transformation to try and is very frequently used. It is also done if for regression you want a multiplicative interpretation of coefficients (e.g. doubling/ halving of blood cholesterol).
Of course it will not always make a distribution more normal, e.g. take samples from a N(1000, 1) distribution: any transformation can only make it less normal.
edited yesterday
Nick Cox
39k587131
answered yesterday
BjörnBjörn
11.5k11142
$endgroup$
4
$begingroup$
Similarly a distribution that is symmetric or left skewed will have its skewness made worse by logarithmic transformation. Consider the not very magnificent seven 1 2 3 4 5 6 7; then their square roots are left skewed and in the logarithms of those are even more left-skewed.
$endgroup$
– Nick Cox
yesterday
add a comment |
$begingroup$
For purely positive quantities a log-transformation is indeed the standard first transformation to try and is very frequently used. It is also done if for regression you want a multiplicative interpretation of coefficients (e.g. doubling/ halving of blood cholesterol).
Of course it will not always make a distribution more normal, e.g. take samples from a N(1000, 1) distribution: any transformation can only make it less normal.
edited yesterday
Nick Cox
39k587131
answered yesterday
BjörnBjörn
11.5k11142
$endgroup$
4
$begingroup$
Similarly a distribution that is symmetric or left skewed will have its skewness made worse by logarithmic transformation. Consider the not very magnificent seven 1 2 3 4 5 6 7; then their square roots are left skewed and in the logarithms of those are even more left-skewed.
$endgroup$
– Nick Cox
yesterday
add a comment |
$begingroup$
For purely positive quantities a log-transformation is indeed the standard first transformation to try and is very frequently used. It is also done if for regression you want a multiplicative interpretation of coefficients (e.g. doubling/ halving of blood cholesterol).
Of course it will not always make a distribution more normal, e.g. take samples from a N(1000, 1) distribution: any transformation can only make it less normal.
edited yesterday
Nick Cox
39k587131
answered yesterday
BjörnBjörn
11.5k11142
$endgroup$
For purely positive quantities a log-transformation is indeed the standard first transformation to try and is very frequently used. It is also done if for regression you want a multiplicative interpretation of coefficients (e.g. doubling/ halving of blood cholesterol).
Of course it will not always make a distribution more normal, e.g. take samples from a N(1000, 1) distribution: any transformation can only make it less normal.
edited yesterday
Nick Cox
39k587131
answered yesterday
BjörnBjörn
11.5k11142
edited yesterday
Nick Cox
39k587131
edited yesterday
Nick Cox
39k587131
edited yesterday
Nick Cox
39k587131
39k587131
answered yesterday
BjörnBjörn
11.5k11142
answered yesterday
BjörnBjörn
11.5k11142
answered yesterday
BjörnBjörn
11.5k11142
11.5k11142
4
$begingroup$
Similarly a distribution that is symmetric or left skewed will have its skewness made worse by logarithmic transformation. Consider the not very magnificent seven 1 2 3 4 5 6 7; then their square roots are left skewed and in the logarithms of those are even more left-skewed.
$endgroup$
– Nick Cox
yesterday
add a comment |
4
$begingroup$
Similarly a distribution that is symmetric or left skewed will have its skewness made worse by logarithmic transformation. Consider the not very magnificent seven 1 2 3 4 5 6 7; then their square roots are left skewed and in the logarithms of those are even more left-skewed.
$endgroup$
– Nick Cox
yesterday
4
4
$begingroup$
Similarly a distribution that is symmetric or left skewed will have its skewness made worse by logarithmic transformation. Consider the not very magnificent seven 1 2 3 4 5 6 7; then their square roots are left skewed and in the logarithms of those are even more left-skewed.
$endgroup$
– Nick Cox
yesterday
$begingroup$
Similarly a distribution that is symmetric or left skewed will have its skewness made worse by logarithmic transformation. Consider the not very magnificent seven 1 2 3 4 5 6 7; then their square roots are left skewed and in the logarithms of those are even more left-skewed.
$endgroup$
– Nick Cox
yesterday
add a comment |
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1
$begingroup$
I have to guess that you mean right-skewed. Left or right indicates which tail is longer; the terminology implies a horizontal magnitude scale with low values on the left.
$endgroup$
– Nick Cox
yesterday
2
$begingroup$
I always naively assumed that the log transform works well if your data can be thought of as some constant, times many (more or less) independent factors close to 1. E.g. A guy's salary is 10% above the mean if he has a degree, 5% higher if he's living in a large town, 5% lower if he has health issues... A log transform turns that into a sum of independent small numbers, so you get a normal distribution.
$endgroup$
– nikie
yesterday
$begingroup$
@Akaikes See here, here and particularly here & here which indicate that the log-transform won't always make even a right-skewed variate less skew (in absolute terms) than it was. A simple counterexample is the Maxwell(-Boltzmann) distribution, which is mildly right skew but the log of a Maxwell-variate is more strongly (left) skew.
$endgroup$
– Glen_b♦
yesterday