Her question was, what's the difference between a monitoring well and a man?

Do you remember her reply?

DAVE ADAMSON: I don't, but I think you do.

CHUCK NEWELL: She said, at some point, they're both going to lie to you, OK?

But it's just her humorous way to sort of suggest

that we do have this instrument that does give this variability,

and we need statistical methods like the Mann-Kendall to breakthrough

and do this.

DAVE ADAMSON: OK, well that's a good analogy.

Let's go into the nuts and bolts of the Mann-Kendall trend analysis.

Just to back up a second, though, a lot of people

do, in terms of establishing trends, rely a lot on linear regression.

And that has a lot of utility, but one thing to remember

is that's a parametric test, and so it does

sort of build in assumptions about how it works

and how the underlying data are.

It really has this assumption that the data are normally distributed,

and that really isn't always applicable with environmental data.

So a lot of times we want to switch to something

that we call a non-parametric test, and that's what the Mann-Kendall test is.

It's a test that by definition makes no assumptions about the underlying

distribution of that data.

CHUCK NEWELL: Has less statistical power,

but it's more flexible and sort of more reliable in some ways.

DAVE ADAMSON: Yeah, and so it gets used a lot in these cases.

And other things to remember then about Mann-Kendall

is it really only cares about the relative magnitudes of concentrations.

It's really this ordering system that it goes through,

and so you're really just sort of ranking things.

Like Chuck mentioned, it's a little bit easier to establish a trend.

The thresholds are maybe a little bit lower, on the other hand,

it handles non-detects a lot better than something like linear regression.

And then the most important thing for a lot of people

is it's pretty simple to use, and we're going to go through some examples

here as we go through this lecture, right?

CHUCK NEWELL: OK, well let's dive in, and basically you're

going to look at some of these different variables,

and combine them, and then put these different data sets--

what we call temporal records-- concentration versus time

in the different buckets, but what are some of the key factors here?

DAVE ADAMSON: Yeah, so this is a statistical method.

So you're basically calculating a test statistic, and for the Mann-Kendall,

we call it the S statistic, and that's shown here on this first row.

It's basically indicating if the trend is increasing, in which case

that S statistic would be positive, or decreasing it would be negative.

CHUCK NEWELL: Now, if you actually look at the Mann-Kendall in a statistics

book, this is really what they're talking about.

It's just that statistic.

DAVE ADAMSON: Yeah, that's the key metric in this case.

CHUCK NEWELL: But for this particular method we're going to talk about today,

there's these added elements to it to come up with this the system.

So tell us about the other two factors.

DAVE ADAMSON: The second one that's listed there

on that table is this confidence factor, CF.

So you can think about that as 90% confident, 95% confidence,

or related to that p value that you see for a lot of statistical tests.

So it reflects the degree of confidence in that particular result.

Then third there is the coefficient of variation, COV.

So this is the variability and concentration versus time data,

and in this case, for our purposes, we're

using that to determine whether there's a difference

between a stable or no trend at all.

CHUCK NEWELL: OK, and so a lot of statistics here.

I guess just a quick question is that, do I have to do all this on my phone

or on my slide rule, or is there a tool that people can use?

DAVE ADAMSON: Well, I hope they don't have to rely on a slide rule,

because that might be hard to come across,

but yes, the answer is there's tools out there that are available to do this.

One we're citing here basically down there.

What's that, Chuck?

CHUCK NEWELL: That's the Mann-Kendall tool kit actually

from GSI Environmental.

It's a spreadsheet.

You can download it at the web page there.

So Dave, these are the input data.

What do you get from all this?

DAVE ADAMSON: Well, the goal here, remember, is establish a trend,

and so you can use those combination of those metrics basically

to sort of assign a trend, and we like to call

these bins that you might fall in.

And so here's your S statistic and your particular confidence and trend,

but quickly you want this to then determine

which of these bins that you fall in.

And so for example, let's take a look.

If I had an S statistic that was greater than 0

with a CF, a confidence factor, greater than 90%,

that would actually put me then on that right hand side

into an increasing trend.

CHUCK NEWELL: Slam dunk.

Your data's going up.

That's it, but if you have a little more murky,

let's say you've got a Mann-Kendall S statistic that's less than 0

like the second to bottom row there.

DAVE ADAMSON: True.

CHUCK NEWELL: And you've sort of got this confidence between 90% and 95%,

so it's still pretty confident, but maybe it's

a little more variable than the other one.

We put that in this bucket probably decreasing,

and that's the second to bottom row.

DAVE ADAMSON: So at the end of the day, you're

going to run the Mann-Kendall test.

It's going to tell you which one of these categories that you fall in.

CHUCK NEWELL: And six different buckets.

There's increasing, probably increasing, stable, probably decreasing,

decreasing, and the last one?

DAVE ADAMSON: No trend-- basically that you

don't have enough data to establish any sort of trend

with any statistical power.

OK, so let's take a look at an example, a bird's eye

view then here of maybe a plume with all these monitoring wells here.

In a lot of cases for MNA, we're interested really

what's going on in that toe end in the plume, right?

And then let's take a look at data from one of those wells.

So there's MW-1 one is listed right there, that like green

towards the down gradient end.

And then we've got some data shown here, and we've got concentration

on the y-axis and micrograms per liter.

So think of it as maybe TCE or something like that, and then we've

got the sampling date on the x-axis, so each of those individual points

is a concentration data point that you have for that particular well.

CHUCK NEWELL: OK, about four years of data.

It looks like it goes down, but then it goes back up.

DAVE ADAMSON: Well, I'm going to ask you, Chuck.

We have a chance to see your knowledge on this.

What do you think the trend will be for this particular well?

CHUCK NEWELL: Well, looking at that, I'm tormented.

I'm torn.

It goes down.

It goes down from what, the eight?

Down to almost two micrograms per liter.

Things are looking good, but there's this little kick at the end.

I just don't know.

So you know what I think we should do?

DAVE ADAMSON: Tell me, please.

CHUCK NEWELL: We got to ask the Mann.

What does the Mann-Kendall method say?

What bucket does it put this in, and how do we do this?

DAVE ADAMSON: Well, we're going to download the tool

kit-- you can do the GSI one, or there's other online calculators

if you want to do this, but basically in these sorts of cases,

you've got this spreadsheet set up to easily enter your data.

So that's what you're going to do.

You're going to take that data that we showed,

and you're going to put an individual data point on each row.

It's associated with a particular sampling date and a concentration

measurement on there.

CHUCK NEWELL: So it's just a calendar date,

and then here's the concentration.

Now, this is a non-parametric method, so it's

sort of comparing not the absolute values of the numbers, but sort of it

ranks them and then does this sort of sorting based on that,

but just copy and paste these in there from your data set?

DAVE ADAMSON: Yeah, it's a pretty straightforward case in this,

and we've got the chance then to see what the trend is.

It's plotted the data again here, but you're basically

on automatic calculation of your trend.

So what do you think?

Do you think you're right, Chuck?

CHUCK NEWELL: I think it's decreasing.

I think I'm just going to look at the overall weight of evidence

and just eyeball it.

What does Mann-Kendall say?

DAVE ADAMSON: It says it's decreasing, and so it'll

actually output in this case your coefficient of variation,

your Mann-Kendall test statistic, you confidence factor,

as well as the overall trend in here.

So we've got a decreasing trend based on this data set.

CHUCK NEWELL: OK, here's a question.

Let's say I got two years of data.

I put it in here, and it says it's probably decreasing,

and then I get over the next two, three, four years more data.

Can that trend change?

DAVE ADAMSON: Yeah, that trend can absolutely change,

and so you're just amending these with the future data in these cases.

CHUCK NEWELL: But based on the last lecture, once you

get to maybe seven years of data-- very rough rule of thumb-- maybe

you'd start really seeing that thing stabilized,

and you'd be more firm on it.

DAVE ADAMSON: Yeah, maybe less event to event sort

of change in the overall trend.

CHUCK NEWELL: That's right.

DAVE ADAMSON: So there's one example.

We put another example up here then.

This is sort of the red dots on the concentration versus time there.

And so here's an example of maybe in a source

area where you've got higher concentrations,

but you've got a longer record.

So you've got data from much earlier than you did for that MW-1.

So MW-2 started in what, about 2006 where you have data,

but then you have a long gap in here.

And so that can be really problematic when

you're doing things with linear regression

and not very good at handling those gaps.

So in this case, Mann-Kendall, not a big problem, right?

CHUCK NEWELL: No, not a problem.

It just sort of ranks through.

You're going to rank these data and tell us what that trend is.

DAVE ADAMSON: OK, so not sensitive.

What do you think in this case?

What are we going to get out of this, Chuck?

CHUCK NEWELL: Probably decreasing.

DAVE ADAMSON: I think we're going to have decreasing.

CHUCK NEWELL: It's still decreasing.

OK.

DAVE ADAMSON: Yeah, so in this case, we still

are able to establish a trend with that data.

CHUCK NEWELL: OK, well the Mann is a lot smarter than me,

so I'll believe the toolkit.

DAVE ADAMSON: OK, well, that's good.

All right, well let's look at the key points then from this lecture.

Statistical methods like Mann-Kendall provide a great way

to establish long term concentration trends

in data that exhibit significant short term variability.

CHUCK NEWELL: OK, and Mann-Kendall-- it's a non-parametric test,

and it makes it suitable for MNA data that

can range over several orders of magnitude

and may not be collected at regular frequencies.

DAVE ADAMSON: And then this trend analysis-- pretty easy to perform.

There's a lot of free software tools available to do it.