Statistically removing erroneous values

Question

We have an application where users enter prices all day. These prices are recorded in a table with a timestamp and then used for producing charts of how the price has moved. Every now and then, the user enters a price wrongly (e.g. puts in a zero too many or too few) which somewhat ruins the chart (you get big spikes). We've even put in an extra confirmation dialog if the price moves by more than 20%, but this doesn't stop them entering wrong values.

What statistical method can I use to analyse the values before I chart them to exclude any values that are way different from the rest?

EDIT: To add some meat to the bone. Say the prices are share prices (they are not but they behave in the same way). You could see prices moving significantly up or down during the day. On an average day, we record about 150 prices and sometimes one or two are way wrong. Other times, they are all good.

Answer 1

For your specific question of plotting, and your specific scenario of an average of 1-2 errors per day out of 150, the simplest thing might be to plot trimmed means, or the range of the middle 95% of values, or something like that. It really depends on what value you want out of the plot.

If you are really concerned with the true max and true of a day's prices, then you have to deal with the outliers as outliers, and properly exclude them, probably using one of the outlier tests previously proposed ( data point is x% more than next point, or the last n points, or more than 5 standard deviations away from the daily mean). Another approach is to view what happens after the outlier. If it is an outlier, then it will have a sharp upturn followed by a sharp downturn.

If however you care about overall trend, plotting daily trimmed mean, median, 5% and 95% percentiles will portray history well.

Choose your display methods and how much outlier detection you need to do based on the analysis question. If you care about medians or percentiles, they're probably irrelevant.

Answer 2

That's a great question but may lead to quite a bit of discussion as the answers could be very varied. It depends on

• how much effort are you willing to put into this?

• could some answers genuinely differ by +/-20% or whatever test you invent? so will there always be need for some human intervention?

• and to invent a relevant test I'd need to know far more about the subject matter.

That being said the following are possible alternatives.

• A simple test against the previous value (or mean/mode of previous 10 or 20 values) would be straight forward to implement

• The next level of complexity would involve some statistical measurement of all values (or previous x values, or values of the last 3 months), a normal or Gaussian distribution would enable you to give each value a degree of certainty as to it being a mistake vs. accurate. This degree of certainty would typically be expressed as a percentage.

See http://en.wikipedia.org/wiki/Normal_distribution and http://en.wikipedia.org/wiki/Gaussian_function there are adequate links from these pages to help in programming these, also depending on the language you're using there are likely to be functions and/or plugins available to help with this

• A more advanced method could be to have some sort of learning algorithm that could take other parameters into account (on top of the last x values) a learning algorithm could take the product type or manufacturer into account, for instance. Or even monitor the time of day or the user that has entered the figure. This options seems way over the top for what you need however, it would require a lot of work to code it and also to train the learning algorithm.

I think the second option is the correct one for you. Using standard deviation (a lot of languages contain a function for this) may be a simpler alternative, this is simply a measure of how far the value has deviated from the mean of x previous values, I'd put the standard deviation option somewhere between option 1 and 2

Answer 3

Quoting from here:

Statisticians have devised several methods for detecting outliers. All the methods first quantify how far the outlier is from the other values. This can be the difference between the outlier and the mean of all points, the difference between the outlier and the mean of the remaining values, or the difference between the outlier and the next closest value. Next, standardize this value by dividing by some measure of scatter, such as the SD of all values, the SD of the remaining values, or the range of the data. Finally, compute a P value answering this question: If all the values were really sampled from a Gaussian population, what is the chance of randomly obtaining an outlier so far from the other values? If the P value is small, you conclude that the deviation of the outlier from the other values is statistically significant.

Google is your friend, you know. ;)

Answer 4

Or graph a moving average of prices instead of the actual prices.

Answer 5

You could measure the standard deviation in your existing population and exclude those that are greater than 1 or 2 standard deviations from the mean?

It's going to depend on what your data looks like to give a more precise answer...

Answer 6

Calculate and track the standard deviation for a while. After you have a decent backlog, you can disregard the outliers by seeing how many standard deviations away they are from the mean. Even better, if you've got the time, you could use the info to do some naive Bayesian classification.