Handling Outliers
An extreme value is either the most informative observation in your dataset or the one that ruins it, and the supplied deck takes both positions - along with two others. This page prints every characterisation and every instruction in the order they arrive, and leaves the reader holding the decision the source leaves them.
Four characterisations, in the order the deck gives them
An outlier decision is one of the few data-preparation choices that can move a headline finding on its own, so it matters that the material describing it is consistent. Here it is not, and the variation is not cosmetic: the four wordings pull towards two incompatible ideas, one about distance and one about error.
THE FOUR CHARACTERISATIONS, QUOTED AS THEY APPEAR
| Slide | Wording as given | What it makes an outlier |
|---|---|---|
| 4, key terms | "an outlying observation, or outlier, is one that appears to deviate markedly or is very distant from other members of the sample in which it occurs" | A distributional fact. Says nothing about correctness. |
| 8, outliers | "data that is different from the rest of your sample", then "an extreme value", then "Such an obviously erroneous figure" | Moves from difference to extremity to error in three sentences, treating them as one thing. |
| 9, outlier considerations | "an extreme value" | Extremity alone, in a sentence about which error is worse. |
| 18, reading a graphical display | "points which appear to be obviously different to the main pattern of the data" | A visual fact about a chart, and a signal "which could be quite valuable to understand". |
The key-terms definition and the treatment that follows it are not the same idea. Under the key-terms definition a genuine extreme observation is an outlier; under the following slide's treatment it is a candidate for deletion.
Three instructions, and the reversal at the end of the deck
The three positions arrive ten slides apart and are never set beside one another in the source. Setting them beside one another is most of what this page can usefully do.
WHAT THE DECK TELLS YOU TO DO, BY SLIDE
| Slide | Instruction, in the source's words | Direction it pushes |
|---|---|---|
| 8 | "Such an obviously erroneous figure will be removed from the data" - qualified immediately by the risk that "to ignore a genuine figure would also cause distortion" | Remove errors; then, on reflection, use judgement |
| 9 | "Wrongly including an extreme value is usually regarded as a more serious error than wrongly ignoring one" | Err towards exclusion |
| 18 | Outliers "often point to some set of special circumstances which could be quite valuable to understand" | Investigate; the value may be the finding |
The deck states no priority among the three and never refers any one of them to the others.
The two obviously-wrong values
The examples work because a reader already knows how old a year-one child is and how tall a man is. That is domain knowledge, not statistics, and it is the only detection method the week describes. It will find a data-entry slip in a variable you understand, and it will not find anything in a variable you are studying precisely because you do not yet understand it.
The one numerical illustration, and what it quietly demonstrates
Two things about this example repay attention. The first is that the person removed is presumably a genuine respondent rather than an error - which makes it an argument for care with genuine extremes, not for the asymmetry stated directly beneath it. The second is that the word "averaged" leaves it unstated which average is meant; the deck defines three of them four slides later.
No detection rule, anywhere in the week
This is the single most consequential absence on the topic. Every practical question a reader arrives with - how far from the centre is far enough, what to do with a value that is unusual but plausible, how to be consistent across variables - requires a rule, and the week contains none.
The deck's other route to spotting an extreme value is visual: its guidance on reading a chart asks whether any points appear obviously different from the main pattern. That is a real technique, and the week supplies no illustration of it - the two image slots in its presentation sequence are a production placeholder and an unlabelled picture with no recoverable content. See Reading a Graphical Display.
The six questions the deck asks before you enter data
Two slides carry questions to ask of a dataset. They are worth having: as a prompt list they are better than the deck's treatment of them. Read them as questions you now have to answer from somewhere else.
The six questions, quoted exactly and in order
- Does the data accurately reflect the responses made by the participants of my study?
- Is all the data in place and accounted for, or is some absent or missing?
- Is there a pattern to the missing data
- Are there any unusual or extreme responses present in the data set that may distort my understanding of the phenomena under study?
- Does the data meet the statistical assumptions that underlie the multivariate technique I will be using?
- What can I do if some of the statistical assumptions turn out to be violated?
Making an outlier decision you can defend
The source leaves the decision to your judgement and says so explicitly. That makes the record of the decision the only thing an examiner or a client can assess, which changes what you have to do about it.
A defensible record - guidance beyond the source, built on what the source does say
Decide the rule before you look at the results
A rule chosen after you have seen which way it moves your finding is not a rule. The source does not require this; nothing else protects you from the objection.
State the rule you used and where you took it from
The supplied material contains no detection rule, so any rule you apply comes from elsewhere and should be cited to the text it came from.
Separate errors from genuine extremes in your write-up
The deck's own distinction is between a figure that is erroneous and one that is genuine, with different consequences stated for each. Report how many of each you found.
Report the analysis both ways when it matters
If dropping the value changes the finding, the reader needs to know. The source does not ask for this; the cruise-ship example is the argument for it.
Say what an unusual case might mean
The deck's last word is that outliers often point to special circumstances that could be valuable to understand. A sentence about what the extreme case was is often worth more than the mean it disturbed.
What to carry forward
- Four characterisations across four slides, and the distributional one on the key-terms slide is not the same idea as the error-focused one that follows it.
- Three instructions, ending with the opposite of where the deck began. Both ends stand; the source resolves neither.
- No detection rule of any kind is supplied. Whatever rule you use comes from outside this material and should be cited there.
- The cruise-ship figures are an illustration of one respondent's effect on a reported average. They are not a threshold, a benchmark or a worked calculation - no arithmetic is shown.
- "Statistical assumptions" is invoked twice and never defined, and the question about what to do when they are violated is asked and abandoned.
Frequently asked questions
What counts as an outlier according to this material?
It gives four answers. One slide defines it distributionally, as an observation that appears to deviate markedly or is very distant from other members of the sample. Another treats it as data different from the rest of the sample, then as an extreme value, then as an obviously erroneous figure. A third calls it an extreme value; a fourth calls it a point obviously different from the main pattern of the data. The source does not reconcile them and neither does this page.
Should I delete outliers?
The supplied material takes three positions: that an obviously erroneous figure will be removed, that wrongly including an extreme value is usually regarded as the more serious error, and that outliers often point to special circumstances that could be valuable to understand. Its own resolution is that the final decision is left to the researcher's judgement and depends on individual circumstances - so what you can defend is your reasoning and your record of it, not an appeal to the material.
How far from the mean does a value have to be before it is an outlier?
The supplied material states no distance, threshold or cut-off anywhere. It gives no rule expressed in standard deviations or in any other measure, and no measure of spread is defined anywhere in the week. Any numeric rule you use will come from a text outside this material and should be cited to it.
What are the statistical assumptions the deck asks about?
It never says. The phrase appears twice on one slide, in the question of whether your data meet the assumptions underlying the multivariate technique you will use, and no assumption is named, defined or exemplified anywhere in the week. No multivariate technique is named either, and the follow-up question about what to do when assumptions are violated is never answered.
Does removing one respondent really change an average that much?
The deck's cruise-ship illustration says a survey average of $10,000 becomes a maximum of $1,000 once one wealthy respondent is taken out. It shows no arithmetic and states no sample size, so the figures illustrate the direction of the effect rather than its size. Treat them as an example of what can happen, never as a benchmark.
Is an outlier always an error?
Not on the material's own key-terms definition, which is about distance from the rest of the sample and says nothing about correctness. The slide that follows nevertheless moves from difference to extremity to obvious error in three sentences. Its own worked case - a wealthy cruise passenger - is a genuine respondent rather than a mistake, which is the clearest evidence in the deck that the two ideas are not the same.
References and source attribution
- Veal, A. J. 2005, Business Research Methods: A Managerial Approach, Longman - the one work with complete bibliographic data cited in the supplied quantitative week.
- Bryman, A. 2016, Social Research Methods, 5th ed., Oxford University Press, Oxford - cited elsewhere in the supplied source; a place to obtain the outlier detection rules this week does not supply.
- O'Leary, Z. 2017, The Essential Guide to Doing Your Research Project, 3rd ed., Sage Publications, London.
- Naoum, S. G. 2013, Dissertation Research & Writing for Construction Students, 3rd ed., Routledge.
- The supplied teaching source: the quantitative analysis and presentation slide deck, slides 4, 8, 9, 10 and 18. The week's study notes are listed in the upload manifest and are not present in the supplied files.
Suggested questions for Ask KEVOS
- Give me a cited outlier detection rule suitable for a survey with about sixty responses.
- How should I report an analysis that changes when one extreme respondent is removed?
- What are the usual assumptions behind common multivariate techniques, since this material names none?
- Draft the outlier paragraph of a methods chapter that is honest about where the rule came from.
- Help me decide whether an unusually long project duration in my dataset is an error or a finding.