turn things over to one of our first speakers. Felicia Barnett, who is
joining us from U.S. EPA and the office of research
and Feldman to provide opening remarks.
Felicia, whenever you are ready, please begin.
>> Thank you Jean. I just want to welcome everybody. This is the second
in our series of three seminars in the utilization of ProUCL software
tools. It has been introduced in those in the first seminar maybe
remember my name is Felicia Barnett.
I am the director of the EPA office of research and development site
characterization and technical support center. I am going to refer to it
as SCMTSC which is
provide support on hazardous waste issues to
the EPA program and resource offices created using ProUCL as part of
that function.
ProUCL is a statistical software packaged three on the EPA
website for the analysis of temperamental data sets with and without Logitech
observations but provide statistical methods and graphical
tools to address temperamental sampling and statistical issues.
It is not intended to be able to address every situation, and were
to be the only option for environmental statistical analysis. It was developed
to be an easy to use option for many standard statistical issues
encountered when evaluating data.
The second seminar in the series will focus on using ProUCL
for trend analysis. Has genes in the first seminar in the series
is always already available for viewing online.
If you were unable to attend went to view specific parts at your own
pace. We hope you find ProUCL to be a useful tool in these seminars
assist you with understanding both abilities and navigating its program.
We will be responding to all questions here and during the session or after
and documenting those sessions.
Additionally, SCMTSC provides internal and some limited external responses
to your those who use it. Does anyone have questions or issues with using
ProUCL? We did try to enter those as much as possible. On the ProUCL
website, you can find under the contact my name and my contact information.
I recommend contacting me via email with as much detail as possible,
including screenshots. We will try to respond to your questions quickly.
I am going to now turn it over to ProUCL over to Travis Lynn come
Hatfield to start the instruction on the data.
Thank you. Travis.
>> Yes, hello.
So, thank you guys and thanks everyone for joining us for our second part
of the ProUCL series.
As a Jean and Felicia mentioned, we will be focusing on the trend
analysis features in ProUCL today.
However, I am not going to be the one that is giving the majority
of the presentation. Alona Carson will be doing that but I figured
real quick I would give a nice recap of what we
talked about in our first one, just sent some of those aspects
we are going to be using today.
Really what we talked about for most of our last presentation
was really getting to look at exploratory data analysis inside ProUCL, looking
at summary statistics and different graphical methods, including box
plots and histograms and whatnot.
And then we also explored fit tests, as well as Q2 plots to
assess the normality of daytime, which is something that will definitely
be coming up today. We also looked at
layers and options for hypothesis testing in ProUCL. So while we
are going to be definitely using the goodness of fit test today again,
I hope everybody either
got to maybe watch it last time or watch it in between since it
was recorded but if not, hopefully we don't totally lose you. Other
than that, as Jean and Felicia mentioned,
it is definitely available online.
And so will this one be as soon as we are done.
But, with that in mind, I think I will turn it over to Polona
and we can get started talking about trend analysis.
>> Thank you Travis. Today, we will look at tools and features for
trend analysis. First, we will look at some exploratory tools
so time serials is a nice tool for that and then
we will continue with tests for trend analysis.
The first are Mann-Kendall and
Theil-Sen Line Test.
The second half of today's webinar will look at ordinary list square
regression. Some of you may know as linear regression.
So, now I just want to mention
like in previous sessions presented by Travis, I will try to keep the
statistical jargon as slow as possible and do my best to explain so the
practitioners in the audience can follow without hopefully too much
trouble. So, Felicia already mentioned
ProUCL software is intended for basic statistical calculation using
evaluation of contaminated sites.
So, today we will be touching a little bit more advanced
techniques. If you have questions, please ask them during
the session and Jean and Travis will monitor them and try to answer
as many as possible.
But, if we have more, the answers will be available at a later time.
So, at this point, I just want to
refresh our memory from previous time that ProUCL software is accompanied
by two valuable documents. These are user guides
and technical guides. You can find them both in document
folder of the ProUCL installation folder. So consult those when
you are working on your project if you don't know where to go exactly.
Really valuable resources but if you still have an issue where
to go, it is probably a time to consult a statistician for help
with your analysis.
So, at this point, if we can please share
my screen. So that I can start the demonstration
of ProUCL.
>> The other screen, not my screen Jean.
>> I have it here.
It is working.
So we should be good now I hope.
So we are good now. Just a few navigational remarks.
Here in this middle center is where we to auto analysis
so when we see the data on the left-hand side, we have
a navigation panel where ProUCL displays a list of
open data sets and generated outputs. ProUCL does
assign Suffolk splintering output but if you want to make them more
meaningful for your application, then you just go to
file and save. We don't have anything loaded so I can't show you that
but it would be file, save file, and rename it however
you want.
It is disbelieving and green color basically the log of the actions
you are performing. An orange color display and warning messages
and in red color, it displays the ever messages.
So, those two orange and red are something you
may want to pay attention if you don't think you are not accomplishing
what you want to do with the software.
Let's hope we won't have those today for the presentation. So,
we will be using two data sets today. They both
are available within the data folder in ProUCL. Sewn they are some of
the training data sets available.
You can also download them from the
link site for today's webinar.
To make it easier for the folder so
I can reach them quickly, let me these two files are
and W189.
We will use a little bit at the beginning of the demonstration and
then for most of the parts, we will use trend and W and
D to. Before we go further, I just wanted
to do a few remarks.
Two data set that we will be using today don't include non-detect.
So we won't be using them today in today's demonstration. But, as
many of you are facing that, I want to help
a little bit how to deal with them and trend analysis.
So, the first thing that I want to highlight is that the time
detect create problems and they should be removed before the analysis.
The reason for this really high non-detect and I mean
non-detect closest to the really high detect value,
the limitation of the laboratory to
perform analysis. They need to do to dilute the samples many times
and especially when they analyze simultaneously, they need to make
a compromise between the dilution and the possible
contamination of the analytical system. They can't always go back
if it's a high non-detect.
Can't always go back and read an alliance at the last
dilution because they may contaminate the system. Or it can also because
the interference with some other contaminants present in the
sample.
So, in this case, if you see the really high non-detect, a good practice
is to reach out
to the laboratory and get a little bit of insight how the samples were
analyzed. So, to rules of them how to treat the non-detect.
If they are greater than highest attempt, you are quite safe to reject
them. If you have non-detect
about 10 times higher than the lowest detected
value, use judgment and you may reach to the laboratory or just
do some investigation to get a feel for how those not
detect where obtained.
Then make a decision based on that if you want to reject. When you
have a data set with non-detect, you can use one of the
substitution method.
The two common substitution method you can substitute the value with
half report or have of the detection limit
but this makes sense to do only when you have
less than 10 or 15% of the non-detect.
When you are dealing with a lot of not detect in your dataset, I
strongly suggest that you work with statistician and consult
how you want to go about that kind of data set.
So, this is about non-detect. Let's go to time series
plot for our first data set. I am going to open
my data set
so and I will
use those the first two columns.
The index of the column is zero and one. Please see we have data
set for fuel as well as and here is the manganese value
concentration in groundwater. These data sets are really
nice to show you the capability of ProUCL to group
parameters. Many times you want to display like
several, you want to compare several wells. I am going
to do this how. The time series plot is found on the statistical
test trend analysis and here on the bottom
we have time series plot and I will select this time just data
so in measured data, we report our concentration of
the contaminant and here we have this grouping,
select group column. I will click at this little row here and
select well I.D.
Let's look under options.
We have event label here, those labels can be changed however
you want.
We can change that but one thing I
want to do at this point is I went to click this little box here, group
and okay. Okay.
Here we have this nice plot comparing three wells on the
same graph. Really nice feature, really easy to do
in UCL.
You may want to use this feature to compare contaminants
and if you want to do that, then you need to be aware of the
scaling may be an issue if you have contaminants in
foreign concentration ranges. You just need to play a little bit of
that option.
So now I want to open our main data set, the other one, that we
will use from now on for most of the presentation. So this is
trend MW real data. I have
a mark because I cheated a little bit for the demonstration. I'm
going to do the time series plot on time and
MW 28 variable. Just a quick
look at this time and date.
We have a few instances here. We have repeated measurement
of the same sampling event.
So, if you have those, make sure you put
in time: the same annotation.
Now statistical test, time analysis,
this time and will use the event so under events, it will
come with time and date and under measured data,
MW 28.
We don't have grouping parameter now.
The options can stay the same, we don't need to put up the graphs
now because we don't have at. Okay.
So this is our time series plot now.
So, before we jump in front of statistical analysis, I just
want to refresh some statistical
totems.
This is where many non-statistician specialist struggle. And trend analysis,
we always deal with two variables and our data are collected in
time intervals. So, our variable in interest, this is the contaminant
in most cases, is called a dependent variable.
To plot it is on the y-axis.
Here is contaminant, dependent variable. The other variable
entities normally set by the design.
So basically, beforehand, we determined time intervals
let's say when we would sample groundwater. These are variables
is displayed on the X axis and it is called independent or exploratory
variable.
Just so what we have those totems refreshed.
So and now let's go into our statistical test for trend analysis. The first
test that we will look at is a non-parametric
test.
So I will use this trend MW data statistical test
trend analysis, this is where
we will find it. The benefit of basically both
nonparametric tests Mann-Kendall and Theil-Sen Line Test if they
don't have any underlying assumptions
about the distribution of the data.
We don't need to think about distribution, we don't need to worry about transforming
the daytime but it is the first step in trend analysis to do those
tests. So, let's look now at the Mann-Kendall test.
Measured value MW 28.
One thing I want to highlight here is that the data you can them
in time and do need to pay attention that you
organize them that way when you and put them in the table. So that
they are ordered by time.
We don't have grouping parameter so you select
your confidence levels the standard confidence level is 95%.
We will disclaim graphics, we
can latest regression line is something that
helps visualize what is going on on the data. Click
okay. Okay. Here is our table with the results. We
have some general
information about the data and the test here in the general statistics
in the next section. And the bottom, we see the result of the Mann-Kendall
analysis. So here is the statistics, the
values were really small and we have this message
helping us to plot the results. So now let's
look at this trend test graphics.
Here is the plot.
It is again like the jacket to plot time
series plot and then I added this regression line, which helps to
visualize what is going on with the data and on the right-hand side,
we have the Mann-Kendall test table and
the interpretation. Statistical significant evidence
of decreasing trend in this data.
So the Mann-Kendall test only gives us an idea about the
modernist city of the trend. Basically what does that mean is if the trend
consistently decreases or increases.
It doesn't give us any information about slope of the trend. So, the
rate of the which the contaminant concentration is
increasing or decreasing.
So, one benefit of this test is that we can perform it with
as little as four data points. You need to know
that if you have a really small data set, the power of this test
is very low.
So the test may not detect the trend, even if the trend is present.
But let Satan groundwater analysis we keep disabling
kinetic points. Over time, we are gathering more and more evidence
and basically increasing the power of these tests whilst we are adding
the data. So, eventually the test will detect it.
So this is about the Mann-Kendall
test. Now we can go to the next step
in to do so we see here the decreasing trend, now we can go to the next
step, perform Theil-Sen Line Test. This gives us a little bit more
information. It does give us some idea about the
rate of the decay of the contaminant and the slope
of it. So, I am selecting again my data set,
going to statistical test, trend analysis,
Theil-Sen Line Test, we need to again
select variables, time under options
let's display Theil-Sen Line
Test. This is a nice feature. Previously I printed out
that the data set contains a few events when several
samples were obtained at the same interval.
Here we have 705 twice, 90 six twice.
1535 twice. It was also two samples
were taken.
When you click this box, the results will be average. And this is really
important the Theil-Sen test only can handle one
data point sampling event.
So let's see now. Analysis
so immediate advantage of this test is that
we can estimate slope as opposed to just
the identification of increasing or decreasing trend with Mann-Kendall
test. Since slope is negative,
let me just pull down the results, so here we have
the values. Slope is negative, the filter is really
small. That confirms the Mann-Kendall test.
One thing about this method it is robust against extreme values.
What it does is Theil-Sen test finds the medium,
medium slope and divides the points we have available
into two sections so half of them
will be above the line, half of them will be below the line.
Because of that, it is robust against a couple of those values.
Basically, it is the formative to ordinary square
regression. The intent of this test is it
can only handle one observation at sampling point.
So here is now the spot. This is the regression line on a median
slope. This divides the points into sections.
Half of them below, half of them about.
Another disadvantage of this test is that it does require a fair amount
of data to provide a reliable conclusion.
When it starts with the
Mann-Kendall test, we can use it to confirm the sign of the slopes
or do we have a decreasing or increasing trend
and gives us additional information about the rate of the change in
contaminant because it does give us that estimate of the slope.
So here is now time for a short break before we go to the ordinary
list square regression.
So, if we can have a couple of
quiz questions.
>> We will also be taking a couple of quick question and answer
session as well.
>> I will remind the audience there is still an opportunity to send
in questions using the Q&A window in the lower corner. We are going
to turn on a quiz in the proportion of the screen and test her knowledge
but there will be questions that will appear and you can click on
the answer that you think is correct then we will keep track of who
is is going well. Our first question is appearing now. Remember, just
click on the box you think is the correct answer.
The quiz score will keep track and let you know if you got that
right or wrong. The sooner you pick the right into, the sooner the higher
your score will be. It looks like we've got some people who know their
stuff. Moving on to our next question.
This one seems to be tripping few people up. A handful of you got
that one correct. Just reminding everybody,
with that, we will go ahead and go back to our split screen view
and take a quick break for questions.
I am going to start earlier. This first question comes in asking if
ProUCL can use J. Crew did values for trend analysis.
>> Yes, by j coded, I assume you mean not detect.
I totally understand but in ProUCL right now, there is not
a great way to have a directly handled you're not detect problems. Which
is why we kind of decided he would give some general rules of thumb
if you want to take a look at it basically really, if you are trying
to do trend analysis and you have interesting sets of not detect in
your data, you should probably consult
a statistician. On how your data is set up, how many detect in the
mood to have, what percent of your data are not detect, all those different
confounding factors, you are going to get different answers each time
and I think Jean, this also falls into the
second question wouldn't be substitution method
of doing half the deduction limit or whatnot artificially
alter the distribution of the data and
decreased the variance. The answer is yes, that totally could do that.
With not detect, you are making
the best of a bad situation.
How to do that again is going to come down to a case-by-case basis.
Not to beat a dead horse here if you're going to want to consult
a statistician if there isn't something that is immediately solvable to
you. And, in the case of lots of not detect, multiple detect limit,
that is not easily solvable situation I would say.
So, sorry to kind of breeze over all of those not detect questions
with basically the answer is consult a statistician.
>> Okay.
Going to bounce back to some questions about dates and times in the data
set you have been working with.
One of the attendees noted that the data set didn't appear to have
a column for the date of the sampling event and we were wondering if ProUCL
automatically convert the date to a corresponding event number or
is it calculating the number of days in between these event?
>> I believe Polona mentioned earlier but just in case it got messed,
ProUCL needs to have numbers in the date
column. Because of if you want to put in the March third 2020.
like that is not going to work, to were going to need to convert
it to a numeric representation of date or time or sampling event.
You can either do that by just saying a set number of weeks after an
initial sampling event or days or months or if you are coming back
and forth from maybe different software, you can convert things to a
set up where is it is cutting a number of seconds from
a given starting point. That is going to give you a
couple of weird x-axis but it might play a little better if you are
bobbing back and forth between our or Python or what have you.
But in ProUCL, door time variable does
need to be numeric not a character or data string.
>> If I can just hear that it is really easy and Excel
to convert the date into a number of dates, number of days between
the events.
>> Okay. I did just want to comment.
I see a lot of the dialogue and comments that are coming in from
what I believe are statisticians about how to handle
J coded values and whether they are estimates or documents that
something is there, we just can't be certain of what the value is
as we can to zero it out so I want to thank everyone that has been
coming in with comments and input on how to
handle J coded values. I will certainly work to take the speculative. This
could be a topic for a future webinar in itself. Thanks for everyone present
in the methods but think of the interest of time, we have about
50 minutes left, but we transitioned back to the presentation. People
pause again for Q&A and will encourage
those parts bins to get this questions incomes coming on input if you haven't
to join us late, if we don't get your question live, we will be looking
to get a written response to what the questions that were submitted
that we may not have addressed live during the webinar. With that, I
will turn it back to Travis and Fran eight.
>> So, yes, I will speak up from here again. So, the third option
for trend analysis in ProUCL is ordinary list square aggression.
This is the most advanced method of three but gives the most information.
So, without getting in-depth on the mass of ordinary list square
regression, what is really trying to do is to fit
a line between the data point that maximizes the square distance
between the points and the line.
So, since this is a little bit more and then
advanced analysis, I am first providing you the steps to do about it.
So, first you select dependent and independent variables.
Then, fit the regression. Then you need to evaluate the
regression model that you get.
First to go to the steps, then you need to
check the assumptions that they were met. There are three assumptions,
we will explain them a little bit later but you need to check
them, and then based on the evaluation of the model and assumptions, you
interpret your results. Okay, let's go ahead and
analyze our data set with ordinary list square regression features.
I am selecting this trend MW real data set going
to do a statistical test and ordinary list square regression
is just about trend analysis option. Now
here we have this dependent variable, remember, dependent variable is
our variable of concern. The contaminant MW
28. Then we have independent variable, which is our time and date.
Under options, to
select the confidence level. You want to
apply the regression people with regression results. We will display
a diagnostic as well. Just take a look at it.
You want to display a regression plot. On
regression plot, we also want confidence prediction interval for this demonstration.
So, okay. Okay.
Here we display the results. Let first pop up the regression.
This is now the regression line.
The gray dotted line in the middle is and were fitted regression line.
The two green lines on at this point are confidence intervals of
the mean and the two plants are protection
intervals. Let me explain the meaning of the confidence and protection
interval in a plain language as I can do that. So, 95 confidence
interval if we take a bunch of samples
of time, let's say here we have a
point of 160. if we would take several samples of that time and then
average them, we expect the meaning of those samples to be within the
green lines 95% of the time.
So, but then on the other hand, if we only take one random sample
the same time, we expect
the value of that sample to be 95% of the time
between the redlines. We are 95% confident that its value will be
within the redline.
So, here on this plot, we have also the results of the regression
analysis. At this point, I will move back to the table because we
have a little bit more information there. So, let's look.
Here in the middle, we have regression
estimates and interference table.
So, in regression, we are estimating two parameters. Intercept
and slope of the regression line.
These are the values for the estimates
and on the slide, to hear see the table
that is a regression model, regression equation. Our contaminant is equal
to intercept, 2164 minus
a decreasing trend is negative slope minus one point 637.
Ordinary list square regression gives us more information then the
Theil-Sen. It gives us the estimate of the
ever of those parameters. Parameter estimates. Here is the estimate
of the error and then it performs the t-test for significant of those
parameters.
Basically, the value is how strong is the relationship between
observed valuables. With the really care about
is the P-Value
of the slope. This is a measure of
how good is the model. How strong is the relationship between two
parameters. P-Value is really small in this case. We have a strong relationship
between the two variables. If P-Value is large, what does
this mean?
It means slope is zero so basically the slope
is constant, there is no relationship between the variables.
So slope is negative.
That is nice, but is agreement between the previous two tests, which we
hope that will be the outcome. And we can move on from this point down
to the next table.
So, in the second table, we have another table put we have
sources of variation looking down in regression,
which means how much of the variability
is explained with the model that we just don't. So, with the equation
we just informed it the ever totem is explained variation.
And then this total is basically the sum of two. It is the total
variation. Here on the right-hand side we have a test for regression
and here I want to mention this is
basically the only part really and regression analysis
that is sensitive to non-normality of the residuals. I
will explain what residuals are in a moment I
want to highlight there is really no requirement for normality of
our data. But all assumptions are about the residuals.
So, P-Value is a small, which again confirms that
our model shows a strong relationship between the
two variables. Here on the bottom, we have our
square and probably most of you are very familiar bull
with that. Statisticians are making the decisions based on the our square.
Adjusted our square is a little bit more conservative.
That is why I am suggesting you to basically use
adjusting our square as a measure, another measure
to evaluate the model.
What it means, this number is basically 83.3%
in this case of variation is explained by this regression model. Basically,
the meaning is present variability explained by the regression
model.
It is not the best measure. We still need to look into the assumptions
but it gives us some ideas about how good is the model.
So, main advantages of the ordinary list
square regression arm is a pretty standard approach
so most of the users are familiar with it.
It provides more information than either
of the nonparametric tests. Besides the estimate for slope and intercept,
we also get our information about the uncertainty
of both parameters. Regression analysis also provides us confidence
Benz. There's confidence bends can be used to determine compliance
with the extent of cleanup levels, even with the trend is apparent.
Even when concentration of the pollutant is changing, we
can still use those confidence bands to compare
with standards and make conclusions.
So, the downside of the regression analysis is that it is really sensitive
to extreme outliers.
And underlying assumptions. There are three assumptions for residuals
that we need to check to make the final conclusion about the result
of the regression model. So, in the next step, I will
show you how to go about the the residual analysis.
First, let's explain what residuals are. If we
take our regression equation that we talked about a little bit ago
and Clark in time and date,
the results that we get our cold fitted values were model outcomes.
Because our model doesn't perfectly fit the data, we
said before this model for our training data
explained that 83% of variation.
So the fitted values are different from
the observations.
So, the residuals are actually the difference between the two.
Observed values minus fitted values gives us residuals.
Regression analysis give us this bottom table, regression
table, where we have the
fitted values and residuals.
It calculates that for us.
There are three assumptions that we need to
check.
First, they are all related to residuals. The first one is constant
variance, or total elasticity
of residuals. We need to confirm the residuals are independent into
that the residuals are normally distributed.
So, remember there is no requirement for data itself to be normally distributed
but this requirement needs to hold for the residuals.
Many times, checking these assumptions is overlooked.
We do need to check then. So, I will
so you know how to do that. We need to do little bit of extra work.
We need to copy this part of the
regression table. The easiest way to copy and paste it in Excel and
open it again in Excel. When you do that, sometimes
when you paste the data in the XL, you have
leading blank spaces that they don't like
to do the analysis because that makes the values not numerical.
So we provided you on the slide help with how to remove
those leading spices. They are listed there but I am not going
to for the six of them, I am not going to demonstrate it.
I did that before so we can just move on with ProUCL
features. So I am opening now the file, which
is residuals.
>> You will need to switch it to XL.
>> Thank you Travis. It is the
XLS file.
Residual analysis, this one, right?
Here we have the same table that we put into
the ProUCL. What we do now, we will basically use of the time
series plot to make some plots of those residuals.
The first plot that I will create is
the residuals for fitted value. I am selecting
this data set, statistical test, trend analysis, time series plot.
We will need the event data now plodding
on the event so under X axis, I am plodding fitted values.
There by axis, I am plotting our residuals.
And okay.
So now I will do this plot a little bit nicer so that
we are not too distracted. I am going into properties,
series, I want this to be scatterplot
and I am going to make bullets a little bit bigger so it will be
easier to see. Okay, this is now our plot.
I can just show you real quickly how to change
the title.
You right-click and this little menu pops up and
you can have it
residuals, fitted values.
Okay.
So we want this picture to be, the scatter of the plot, to
be as random as possible.
This is not completely random but it is not the worst I have seen.
In this case, I am going to do what I would say
variance is roughly constant. This plot tells us about the
first assumption, the variance residuals constant.
We will say okay, assumption is
satisfied.
The second plot is to check the second assumption
for the independent. I will again create a timeseries plot of residuals
and this time I will plot them against the consecutive event number.
Basically, let me Paul the data.
Timeseries plot again.
This time, event is our observation.
This column that tells us the number of the observation.
Observation and residuals.
Again, we will create, sorry for that.
Observations, residuals. Okay.
Where is the plot?
Try again.
Let me just explain to you. We will play the same plot. Is on the
slide. Similar plot, we want scatterplot to be random and we
don't want to see any unusual patterns. If you
see on the slide that we presented, you seem the
second half of this life if maybe Travis you can
get the green arrow or it is some kind of curvature. We
don't want those curvatures in the plot. That is
an indication that we have what is called black feet. In
this case, the second assumption is not
completely satisfied. So we can move on to the third
assumption. The third assumption is about the normality
of the residuals. So prove for sprints at the normality of the
residuals, we will do the goodness of fit test. So,
I will again pull the staple, go to statistical test, goodness
of fit, we want the one for normality. And we want
to perform this test on residuals. Okay. Let's
cross our fingers that this will work.
So, here we see this point. They are very close to
the line. This is not perfect but it is a reasonable line.
If we look at the results of the normality
test here on the right-hand side, we see here
in the middle part where I am circling now it says
data appears normal. So this test confirms that our residuals are
normally distributed, so the third assumption is also
confirmed.
So, to summarize, if any of the assumptions are
substantially violated and a list square
regression has a little bit of variance. If the assumption
is violated, that might indicate that the trend is either
nonlinear or the magnitude independent, the main concentration
level. We have what we call a lack of fit.
What does it mean is that the model we have built is not perfect. We
can improve it but there is an opportunity to improve
it but when this really matters, when we want to improve the model
but this really matters when we are interested for predictions.
If you just want to evaluate whether you have a friend to present, a
downward or upward trend on your data then
not a perfect model will show you that. If you want to predict or
if you want to make conclusions about the rate of decay,
in that case, you want to improve the model.
ProUCL is a very limited in what kind of improvements
it can make. Basically the only improvement in the model
we can handle and ProUCL is transforming the data. Even
that is not really encouraged. We need to make some
extra steps with the data. The other options are like adding
the variables or adding polynomial toward hymns but these are
more advanced techniques when I strongly recommend you
go to statistician and work with a statistician if you want to protect
so before we jump into transforming the data,
I will demonstrate how you can do it. I want to give you some additional
guidelines when you can kind of
get an information from the site if transformation of the data as
the right way to go.
So, if you have a visible exponential decay express the next financial
trend on the timeseries plot and let me be a consequence of
the first order reaction. In this case, the
rate of decay of the contaminant is proportional to
the amount of contaminant present.
More contaminant present that you are observing faster is the decay.
Practical example of this is the
solution of contaminated groundwater, which no absorption of it from
the soil.
In this case, when we know these kinds of reactions
can be present on the site and receive the exponential pattern
on the data, the data makes sense.
Another case may be that we have zero order reaction, which is expressed
as a linear decay rate.
It is basically the decay rate is limited by a limiting factor.
It is constant instead of exponential.
So some examples of zero order reaction so that maybe
in the media are bio
dictation limiting the toxicity of contaminant or nutrient limited
biodegradation or we have maybe absorbed contaminant that is distorting
groundwater pollutes contaminant concentration. So, in this case,
transformation of data won't help.
But if we see that the model is not perfect, we need
to take some other approach. So, options are non-linear fit so
polynomial regression or adding more exploratory variables
but these are advanced techniques that need assistance of a
study to Titian into some better software with more capabilities.
So, okay. Now let's show how you can
do transformations.
For transformation, you will need to go to XL and and
an additional column to your data whether you are
in XL or some other spreadsheet software.
So, here in my spreadsheet, I have already done that. Just
so you want to take a note, I used the natural logarithm. You can do
the logarithm as well but I used the natural logarithm so that you
can replicate what I am working on here. So and
now we can repeat the regression analysis
with this log transformed variable. There
are some downsides of the regression with log transformed data
so it is really probably this is the time to go to a statistician.
But for some of you, let me be a little bit more
advanced. Demonstrate how you can do that in ProUCL. So, I
will, instead of the variable
in the original skill, I will use now the log transformed as a dependent
variable and then the time and date of independent variable. Okay?
Before, we will first looked at the regression plot.
So regression plot here with the confidence and protection intervals,
we see a little bit in those
points around the regression plot but it
is not too bad.
Now let's look at the results of the regression. Again, I will
switch to the spreadsheet because it has more information. So, in
the regression estimate table, we have intercept
and slope.
Remember now that these are log transformed data
so the values may not be straightforward to interpret.
In terms of the rate of decay, let's say. P-Value's appeared
here are the errors. Let's look at the P-Value
for slope.
P-Value is a small, which indicate that there
is a relationship between the statistical significant relationship between
the dependent and independent variable.
During the contaminant and time.
And another table, we have ever
terms and here is the statistical test for aggression. Statistical
test indicates that regression is statistically significant and if
we look at adjusted R Square as
one of the indicators for regression, adjusted R square we set is more
conservative, it is a little bit higher now. 0.874. which, many
people would quickly say, okay, we have a better model. But remember,
we really can't make final conclusions before we look
at the residuals.
Here on the bottom, we have again the residual table.
So, you will take the same steps as before, take
this table in XL and bring it in
ProUCL.
I prepared a data table in excel already
so I will open it now.
It should be XLS again.
I think I have and it in. Longoria
longer correction. These are my residuals for
log regression. I am opening now this table. You see here
log transformed data. These are fitted values and residuals.
We will again repeat the same plot as we did before for diagnostic
the regression model.
So, first I am going to plot residuals
versus fitted values.
I am going to the data
table. Statistical test, trend analysis, we both use time
series plot and tweak it a little bit, just the same as before.
Residuals as measured data, why is event. On
X axis, okay, here is our plot now.
I am tweaking it, going to properties, series
scatterplot, making bullets a
little bit bigger so it is easier to see. Okay.
So with
that before checking the first assumption, we want this scatter
to be as random as possible. It's assumption is that the residuals
are not having a constant variance.
This picture is not too bad. I would say first assumption is approved.
That the variance is reasonably constant. Now, let's create the
second plot to check the second assumption that residuals
so, I am taking residuals into measured value
and observation as event on X part. Okay.
Oh, this time it worked. Nice. I am tweaking it again.
Series scatterplot.
It is always better to look at scatterplot so we are not distracted
with the line.
So, this time we see this curvature may be even
more pronounced. It is going the other direction upwards
but it is maybe even more pronounced, so
this definitely indicates there is a lack of fit.
So, the residuals are not completely independent.
Now, the third assumption, we need to do another
goodness of fit test for log transformed data.
So, let me do that.
I am going to log regressions, statistical test, goodness
of fit. We want to check for normality. Taking residuals, okay.
So, this plot doesn't look at that nice now. Let me just make
those bullets a little bit bigger so that we see better.
We see this around
the plot and if we look at the outcome
of the goodness of fit test, here in the middle
it says that they are not normal.
So the third assumption definitely is not confirmed.
So, no, what did we learn from all this?
So, you really can't rely on R square.
R square was a little bit better but it really didn't
contribute to the problem with residuals. You need to look at residuals,
need to take the assumptions. To give us a lot of information about
the regression model. So, plotting residuals will actually read the
lack of a fit of the model. What we haven't seen in our example but
will also show on residual pots extreme value outliers.
That is another reason why to take time and analyze.
The point to remember is that when you can't confirm the assumptions
for the residuals, and you
do have a need to improve the model to can do some
predictions, then that is definitely the time to work with statisticians
and find a way to best analyze your data. This brings us almost to the
end of the first session. Next slide we will see
on the screen is the comparison of three trend
tests we explored today. So, at the beginning we looked at the two
nonparametric tests that are both nice starting point when we are
looking for trends in the data.
So Mann-Kendall will tell us if we have a consistent or monotone
trend, statically increasing or study decreasing.
The nice thing about this test is that it will give us a reasonable
outcomes with as little as four points. Remember the power of the
test when we have a small Beta test low.
Even if the trend is present, it may not
show because of the low power of the test. So, the next task nonparametric
test is Theil-Sen. It identifies the transit
confirms the trend observed with Mann-Kendall. It also gives a slope
estimate.
But, for the contrast of the Mann-Kendall test requires a fair amount of
data and it only works when we have one observation per time interval.
However, it averages repeated measurements of the same sampling
event. So, if you have repeated measurements, remember
to check that box.
And the third metric we looked at in ProUCL is
OLS Regression. This is the most advanced of the three methods.
Because of that, it also gives us the most information. It evaluates
slope and intercept. It gives us estimate for both parameters
and there are three assumptions for
residuals that need to be confirmed.
So, it does require a little bit more work but it really gives
us the residual analysis can reveal a lot about
the data. Another downside of the ordinary square regression
is it also requires a fair amount of
data to obtain reliable perimeter estimates.
So, this is a more or less everything we wanted to cover today. It is
time for a second quiz. If we can show that on the screen now.
And then Travis will make a short recap and if he has something
to add.
>> Okay. We are going to stick that second quiz questions. Travis or
Polona, we have had people ask if you could read questions out
loud because some are following along on the phones. Going to start
that quiz now. Feel free to read them out to them.
>> I don't see them if you can with them Travis.
>> The R square and adjusted R square
values tell us what?
Proportion of the variation that is explained by the cut off but
his post as a model at the end there and see, the estimate of our
OLS slope.
All right. Non-normality of our OLS residuals indicate a lack of
fit, be our model is
not optimal, see, the confident in our predicament is not relabeled,
or the, all of the above.
>> Okay.
It looks like the right answer for that one was the. Job everybody.
>> Just. Real quick. I think we will just make a couple final remarks
and answer a few more questions at the end. Just to recap everything
that Polona sat there.
When you are looking to do trend analysis, really make
sure you spend time exploring your data before you start doing your
tests. And, want to have to figure out, especially with OLS, don't
totally rely on your R square and adjusted R square
values because they might not be revealing the problems that your
underlying assumptions need to have validated.
Also, if you are thinking, transforming your data, take time to think about
the processes that might be underlining that need,
such as the first order or zero order reactions that we discussed
for a moment there.
And, really as always, when in doubt consult
a statistician. I know that was brought up a bunch with the nondetectable
stuff and I can't say it enough there that
that one is a tricky subject and you are not totally sure on what,
you need to talk to people who might know better. That doesn't
even mean just one. Maybe a fuel.
People will have different opinions on how to handle non-detect in different
situations.
As always, similar to the outliers with last time,
make sure you are really documenting all the steps in your analysis and
the decisions that you decide to make. Yeah, real quick, if we want
to jump into a shoe questions that we had, Jean, did you want to be
the one I had highlighted there?
>> One of the participants is asked what should you do if your data
appear to exhibit a seasonal trend?
>> So, I picked that one because it can apply to all of them.
If you are doing ordinary least squares regression
and when you view your data you don't see a linear trend whether
that be a seasonal trend or when we look at it initially there looked
like there was be a quadratic print to it, something nonlinear that
you want to figure out if there are any transformations
that work best for your situation, so far as we had happened to look
at the lognormal transformation because it is something
that is effective for fixing a quadratic curve. For seasonal things, you
might want to look at aggregating your data in some way to get rid
of that seasonality but again, really any of those are going to
beat this dead horse that you should talk to a statistician. The answer
isn't clear to you as to how you want to
handle it, you need to make sure to talk to someone but it is clear
to them. And then so there were some other questions in their
but individuals had asked and I got a little ahead of myself and
at entered directly to them. I realize some of them might be helpful for
you all.
Some one had asked the question that, in a previous
webinar of how do you save all of the work that you have done inside
of ProUCL.
>> I can show.
>> You are just going to highlight.
>> I highlighted here on the navigation
panel the name of the item that you want to save. Go to file, save
as and to save it.
>> Yes. Cool.
Someone else had asked as far as ProUCL's need to have a numeric
value for the time estimates, could you also have a text column in their.
The answer is to cut but
if you need it for some sort of presentations at the, feel free
to throw it in there. You are not going to be able to use it for any
of the data analysis. When you are selecting your independent and dependent
variable, you just going to want to make sure you don't select that
character: and in fact select the numeric one.
>> And another remark here is that it is especially important
because if you don't capture that your events are unevenly
placed, let's say five days followed by
10 days in between the event and something like that, you may miss
the shape of your trend.
>> I think that was, also I am aware there were a lot
of questions asking for a ProUCL session just on dealing with non-detect
and trend analysis. Agreed.
I think that would be a great one to do. The main focus on the
three part webinar with just getting people
comfortable with all of the available tools that we have in ProUCL at
the moment. Since that is such a large
topic, it deserves release on webinar and not be shoved in five
minutes of trying to explain it. That is why we pushed
it off a bit on this one. It is a tricky topic that we couldn't
recover and cover everything else that we
did today as well. Just wanted to let everyone know that their concerns
are noted. Yes. Jean, anything else?
>> I think we have a couple of other reminders in terms of the sessions.
Coming up to our scheduled time and a few
more remotest walk-through. Preface or Polona, can you take the audience
through a few final reminders?
>> Next session, which I believe is on March 9th, correct Jean? Is
going to be discussing background site comparisons as well as
UCL's. We finally get
to the UCL part of ProUCL.
As always, our contact information is going to be available at the
end if you want to get hold of us.
Yes, I think that is most of the housekeeping staff.
>> Okay. All right. With that, let me walk through a few final reminder
before we officially close out today's session. What to think the nearly
500 people who joined us for today's live broadcast. We will walk-through
just a couple of things. We often get questions about how you can
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Hopefully, will be on for our third and final webinar this weekend please
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With that, I will formally conclude today's broadcast. Thank you so
much for joining us.
>> Thank you everybody. Thank you Gene.
>> Thanks everyone.