I want to create a nomogram using least squares polynomial regression. The data to be analyzed contains at least five outliers that considerably skews the data positively (4.5). Removal of the outliers reduces the skewness to 2.2. A log transformation with the outliers gives a positive skew of 1.9 while the same log transformation without the outliers give a near zero skewness of -0.2. Is it advisable to analyze the data keeping or removing the outliers. Warm regards
This is a problem we all face at some point. If you do enough experiments you will find outliers in some of them. I know professionals that systematically go through their data and remove all outliers before they even start any other analysis. On the other hand, I favor the other extreme, where you never delete an outlier unless there is a good reason to suspect that a particular observation is somehow biased. Some things to consider:
1) If all or most of the outliers come from one "treatment" then their removal may lead to the erroneous discovery of significant or non-significant differences.
2) What causes the outliers? Are these valid data, or mistakes? This could be nothing more that noting that all the outliers are with data gathered by Jim, and Jim is always a problem.
3) Not everything is normally distributed despite the Central Limit Theorem.
4) What is your sample size? What does it mean to have an outlier if you only have 4 replicates? This also work the other way .... if I have 1000 replicates does one outlier really matter?
5) Is polynomial regression the best choice?
There is an old saying "Lies, damn lies and statistics" (http://www.york.ac.uk/depts/maths/histstat/lies.htm). Removing outliers just because the result is in better agreement with how you think the outcome should be is an excellent example of how a researcher can lie using statistics. If you don't put enough information in your methods, no one will catch you. So what kind of scientist do you want to be?
If excluding the outliers now results in the wrong conclusion, how will you deal with this? It might be that you will discover your mistake, or that someone else will. Now what?
If it can be done simply, you could add a column to a table (or add a figure) and present the result (in brief) from taking the other path. That way people know what was done, and can decide for themselves. Then this becomes a game of "I have a theory, the data can be analyzed in a way that it agrees with the theory and we choose to present that option. However, my opponents could take the same data and come to a slightly different conclusion."
The data intensive approach would be to run the regression on all the data, all data less one outlier, ... the data with all outliers removed. You now have several different models and you can present this as a range in possible outcomes (much like a confidence interval). The idea here is that readers can now decide if I remove one of the 20 outliers I am left with models that are nearly identical to the one that you want (in which case I am inclined to accept your interpretation), versus I have to remove at least 18 outliers before I get something even close to the result that you want me to believe (in which case I will be less inclined to believe you, though I might still have to consider your interpretation as a possible outcome).
This is a problem we all face at some point. If you do enough experiments you will find outliers in some of them. I know professionals that systematically go through their data and remove all outliers before they even start any other analysis. On the other hand, I favor the other extreme, where you never delete an outlier unless there is a good reason to suspect that a particular observation is somehow biased. Some things to consider:
1) If all or most of the outliers come from one "treatment" then their removal may lead to the erroneous discovery of significant or non-significant differences.
2) What causes the outliers? Are these valid data, or mistakes? This could be nothing more that noting that all the outliers are with data gathered by Jim, and Jim is always a problem.
3) Not everything is normally distributed despite the Central Limit Theorem.
4) What is your sample size? What does it mean to have an outlier if you only have 4 replicates? This also work the other way .... if I have 1000 replicates does one outlier really matter?
5) Is polynomial regression the best choice?
There is an old saying "Lies, damn lies and statistics" (http://www.york.ac.uk/depts/maths/histstat/lies.htm). Removing outliers just because the result is in better agreement with how you think the outcome should be is an excellent example of how a researcher can lie using statistics. If you don't put enough information in your methods, no one will catch you. So what kind of scientist do you want to be?
If excluding the outliers now results in the wrong conclusion, how will you deal with this? It might be that you will discover your mistake, or that someone else will. Now what?
If it can be done simply, you could add a column to a table (or add a figure) and present the result (in brief) from taking the other path. That way people know what was done, and can decide for themselves. Then this becomes a game of "I have a theory, the data can be analyzed in a way that it agrees with the theory and we choose to present that option. However, my opponents could take the same data and come to a slightly different conclusion."
The data intensive approach would be to run the regression on all the data, all data less one outlier, ... the data with all outliers removed. You now have several different models and you can present this as a range in possible outcomes (much like a confidence interval). The idea here is that readers can now decide if I remove one of the 20 outliers I am left with models that are nearly identical to the one that you want (in which case I am inclined to accept your interpretation), versus I have to remove at least 18 outliers before I get something even close to the result that you want me to believe (in which case I will be less inclined to believe you, though I might still have to consider your interpretation as a possible outcome).
I would just like to agree with the whole of Timothy's reply.
Also, if you do remove outliers because Jim gives problems then you should remove all of Jim's results, not just the outliers.
Explaining outliers can be very useful to the Client, who might not know about Jim or about the malfunctioning machine, or whatever. Don't think of them as being necessarily bad.
But don't remove them just to make the data look neater or to make your analysis easier.
Another option is to include Jim (and Joe, and Gloria, and Sam) as a new variable in your model. Removing all of Jim's results should certainly be considered, but it depends on why I think Jim's results are bad.
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