Hi,
I plotted my data in a bar chart (I used GraphPad) showing the average values, the standard deviation error bar and the single point values. I can't understand if the points that are plotted outside beyond the error bars can be coinsidered outliers or not. And if not, why are they not inside the error bars? Could this happen?I attached an example of picture.
Thank you very much.
Silvia
Outlier detection is dependent on the context of the data, and with small samples like this there's no real objective way to do it. But looking at those graphs, if they were my data set I wouldn't consider them outliers. The data points seem pretty evenly scattered around the mean. I would expect histogram/box plots of the data would show symmetric, somewhat bell-shaped, distribution. If the population you're sampling from is assumed to be normally distributed, then according to the empirical rule, only 68% of observations will be within 1 standard deviation of the mean, 95% within 2 standard deviations, 99.8% within 3 standard deviations. Even in the middle one, those furthest points would be within 2 standard deviations of the mean.
Error bars can indicate different things. They may show the whole range of the data, they may show some inter-quantile range (e.g. IQR is the central range containing 50% of the values), they may show some summary statistic for the variability of the data (like the MAD or, as in your case, the SD), or a summary statistic for the variability of the estimated mean (SEM).
Only when error bars indicate the whole range of the data, all individual values must be inside. In all other cases, values can be outside, particularily for larger sample sizes. The IQR, by definition, will leave 25% of the value below and another 25% above. The SD is practically interpretable under the assumption of a normal distribution. It was nicely explained by Joe Stanek that then about 70% of the values are expected to be withing the range of one SD, what means that it is expected than about 30% of the values will be outside this range. The size of the SEM will decrease with increasing sample size. So for large samples, it may be that the range of one SEM does not contain even a single value.
So there are two things:
- you need to understand what the error bars show
- you need to understand your distributional assumptions
I further agree with Joe that the normal distribution seems a plausible assumption for your data, so the SD is interpretable: the range of one SD around the mean is expected to contain about 70% of the values. Your data fits well to this assumption.
Generally I would not judge "outlyingness" relative to some error bars. I would rather look at only the points in a scatterplot (without error bars or anything else - only the points). If here one or two points are really really and obviousely far away from the rest of the data, then I would consider these points as "outlying". This means that I would go and check the validity of these values (go back to the lab book, have a look at the transcripts, check the circumstances) to identify a possible mistake in the experiment or recording. If I can't find anything, these values have to be taken as serious as all the other values.
If I would see more "outlying" points, I would rather become sceptical if the experiment worked at all or if my assumptions about how the data "should look like" are inadequate. Something has to be refined here (and sometimes, this "something" may even be the research question!). Such cases are not very convenient, but they can really push us towards a better understanding and to get really new insights. Things start becoming really interesting when they are unexpected!
you can verify the outliers with Grubbs' test
https://www.graphpad.com/quickcalcs/Grubbs1.cfm
Grubbs' test gives the probability to get values further in the tails of a normal distribution than the value under investigation (the suspected outlier). This doe not mean that the value is "verified" as an outlier. It just means: assuming the distribution of the values is normal, it is relatively unlikely to get values that are further in the tails of that distribution.
If you don't have an automated process of data collection and unless you know quite well how the distribution of the data should look like, outlier tests are of no use. It's far easier and more instructive to actually look at the data and if there are outlying values, you anyway have to go to the details and see if the value is (im-)plausible and if there is some (possible, plausible) explanation for this value to be outlying.
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