Yesterday I found a copy of one of the first manuscripts I ever submitted. It was never published, so it is time for it to be made available. Ideas discussed are nowadays common place. The manuscript, I think, is still mostly valid almost 30 years after I wrote it… I should have tried harder to get it published then.
A small set observations with a few extreme observations plus subjective splitting of a data set into two subsets to be fitted separately to a linear regression model resulted in very clear cut conclusions and striking figures. However, none of this is solid evidence, or evidence at all supporting the paper’s conclusions. This series of articles, not only discusses the problems in the paper, but more importantly, it traces the review process that allowed it to be published in Nature.
A new analysis of the data appears in an article at “Ask a Swiss” but still based on model fitting. They detect a significant change in slope, but still we do not have confidence bands available.
This is a very clear-cut example of a case of not being aware of the limitations of the data. The same problem affects the interpretation of data from any survey or experiment and any statistical method, machine learning to linear regression or t-tests. The design of the survey or experiment limits the range of validity of possible conclusions and the nature of such conclusions. No sophisticated analysis can correct for biased data unless the bias is measured. We cannot extract information that is not already in the data. We need to make assumptions, but this imposes limitations to what can be concluded. Less dangerous, but equally wrong interpretations of data analyses are a lot more frequent in the scientific literature than we usually realize. Look for parallels between this example and your own research or what you read. What are the data representative of? and meaningful for?