Re: Error Bars and Interpretation

On Mar 21, 7:25 pm, "LindsE" <LindsEHill...@xxxxxxxxx> wrote:
On Mar 21, 4:54 pm, "Old Mac User" <chendrixst...@xxxxxxxxx> wrote:



On Mar 21, 10:11 am, "LindsE" <LindsEHill...@xxxxxxxxx> wrote:

Good day, everyone;

I'm plotting a best fit line to a timeseries of temperature data from
1885 to 1995, in an attempt to identify whether there has be a
significant change in temperature in the particular region. I am
attempting to determine whether the slope is significant at the 95%
level by plotting confidence limits. I am also trying to provide
statistical evidence, using error bars, as requested, to determine
whether there has been a significant change in temperature over this
time frame.

1) Can anyone tell me how to determine if the slope is significant?
2) I have error bars plotted, but they seem to increase as time goes
on. I can't seem to think why this might happen. Any suggestions?
3) How can I determine if the temperature change has been significant
using these bars?

I used the following commands in Matlab:
figure(1)
subplot(3,1,1);hold on
[pH1,sH] = polyfit(xx,HUseF,1);
[yH1,delta] = polyval(pH1,xx,sH);
plot(xx,HUseF,'.g','MarkerSize',5)
plot(xx,yH1,'k','LineWidth',2)
plot(xx,yH1+2*delta,'-.r','MarkerSize',1)
plot(xx,yH1-2*delta,'-.r','MarkerSize',1)
L=yH1+2*std(yH1);
errorbar(xx(1:50:end),yH1(1:50:end),L(1:50:end),'k')
ylabel('Temperature ({\circ}C)')
xlabel('Year')
set(gca,'XTick',x3(1:120:end))
set(gca,'XTickLabel',
{'1885','1895','1905','1915','1925','1935','1945','1955','1965','1975','1985','1995'})
title('Linear Fit to Deseasoned, Smoothed Time Series')

Sorry for the somewhat programming-based question, but I'm out of
practise in the
statistics department.

Thanks;
Lindsay

I think you are making it too complicated.

First, think in terms of fitting the data to a simple model and look
at the t-ratios for the model coefficients. (Ignore the t-ratio for
the intercept.) Is the t-ratio for the slope of the line large enough
to declare "significance" or is it trivial? As a quick approximation,
is that t-ratio larger than 2? That would suggest that the data
really did spawn from a trend and not from a "flat line". We can do
better than that, but it's a place to begin.

When I hear "error bars" my "uh oh antenna" goes up. You really don't
need error bars to answer your question re: is the temp change
significant. But my larger concern is this. Error bars on what? On
differences between observed and predicted values (residuals? Error
bars on predicted values? (The confidence interval on predicted values
will "fan out" at each end of a linear fit. OMU

Hi there, and thanks for your response.

I'll take the t-ratio into consideration, for sure. Thanks for the
suggestion.

This is actually an assignment for a course I'm taking, and I am
required to use the error bars. As I understand it, the bars are on
the bestfit line of the data. They seem to get larger in range from
start to finish. I have also plotted 95% confidence intervals.
Here's the precise question:
"Determine the confidence limits for the linear fit. Is the slope
significant at the 95% level? Has there been a significant increase
in temperature over the past 100 years? You need to provide some
statistical analysis to confirm this. Something with error bars.
Explain your approach and show the results for the different
stations."
What do you make of this?

Thanks;
Lindsay

Good morning, Lindsay

Well, the t-ratio for the slope should be sufficient to declare
"significance" or absence thereof. That should take care of the
matter of whether "there has been a temperature increase". Of course
this assumes linearity.

A confidence interval on the line of regression would be appropriate.

I have no clue to what to do about "error bars". I don't understand
why the lengths of those would increase with the passing of time if
you have fit a model of the form Temp = bo + b1*Years. If you fit a
model of the form Temp = b*Years (a bad choice) that would be another
matter. OMU

.

Relevant Pages

  • Re: Error Bars and Interpretation
    ... I'm plotting a best fit line to a timeseries of temperature data from ... I have error bars plotted, but they seem to increase as time goes ... Is the t-ratio for the slope of the line large enough ...
    (sci.stat.math)
  • Re: Error Bars and Interpretation
    ... significant change in temperature in the particular region. ... I have error bars plotted, but they seem to increase as time goes ... Is the t-ratio for the slope of the line large enough ...
    (sci.stat.math)
  • Error Bars and Interpretation
    ... I'm plotting a best fit line to a timeseries of temperature data from ... I have error bars plotted, but they seem to increase as time goes ...
    (sci.stat.math)
  • Error Bars and Interpretation
    ... I'm plotting a best fit line to a timeseries of temperature data from ... I have error bars plotted, but they seem to increase as time goes ...
    (comp.soft-sys.matlab)