Does a log transform always bring a distribution closer to normal?What is the reason the log transformation is used with right-skewed distributions?Confusion related to which transformation to useWhat distribution does this histogram look like?When should I perform transformation when analyzing skewed- data?How to log transform data with a large number of zerosTransforming extremely skewed distributionsDifference between log-normal distribution and logging variables, fitting normalOn log-normal distributionsHow to transform continuous data with extreme bimodal distributionTransforming a skewed data set to a Normal distributionHow to transform to normal distribution?log transform vs. resamplingTransform data used as response variable in mixed model to normal distributionLog of Ratio Results in Log-Normal Distribution?
Engineer refusing to file/disclose patents
Drawing ramified coverings with tikz
Has Darkwing Duck ever met Scrooge McDuck?
Why do IPv6 unique local addresses have to have a /48 prefix?
Divine apple island
Is camera lens focus an exact point or a range?
Does the Mind Blank spell prevent the target from being frightened?
Is it possible to use .desktop files to open local pdf files on specific pages with a browser?
Cell formatting and hiding code
Is XSS in canonical link possible?
Can I use my Chinese passport to enter China after I acquired another citizenship?
Drawing a topological "handle" with Tikz
How should I respond when I lied about my education and the company finds out through background check?
Do Legal Documents Require Signing In Standard Pen Colors?
Varistor? Purpose and principle
Greco-Roman egalitarianism
A social experiment. What is the worst that can happen?
anything or something to eat
How do I implement a file system driver driver in Linux?
Gibbs free energy in standard state vs. equilibrium
Is a model fitted to data or is data fitted to a model?
Visiting the UK as unmarried couple
How can "mimic phobia" be cured or prevented?
Did arcade monitors have same pixel aspect ratio as TV sets?
Does a log transform always bring a distribution closer to normal?
What is the reason the log transformation is used with right-skewed distributions?Confusion related to which transformation to useWhat distribution does this histogram look like?When should I perform transformation when analyzing skewed- data?How to log transform data with a large number of zerosTransforming extremely skewed distributionsDifference between log-normal distribution and logging variables, fitting normalOn log-normal distributionsHow to transform continuous data with extreme bimodal distributionTransforming a skewed data set to a Normal distributionHow to transform to normal distribution?log transform vs. resamplingTransform data used as response variable in mixed model to normal distributionLog of Ratio Results in Log-Normal Distribution?
$begingroup$
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 yesterday
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 yesterday
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♦
21 hours ago
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 yesterday
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 yesterday
Akaike's ChildrenAkaike's Children
254
asked yesterday
Akaike's ChildrenAkaike's Children
254
edited yesterday
Akaike's Children
asked yesterday
Akaike's ChildrenAkaike's Children
254
asked yesterday
Akaike's ChildrenAkaike's Children
254
asked yesterday
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♦
21 hours ago
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♦
21 hours ago
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♦
21 hours ago
$begingroup$
@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♦
21 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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 |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "65"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f398996%2fdoes-a-log-transform-always-bring-a-distribution-closer-to-normal%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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 |
Thanks for contributing an answer to Cross Validated!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f398996%2fdoes-a-log-transform-always-bring-a-distribution-closer-to-normal%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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♦
21 hours ago