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I have chemical A concentration measured at various locations from 1993-2010. I have broken the time into 2 periods 1993-2004 and 2005-2010.

How can I test whether the trend line between the two periods significantly differ?

Someone told me to use the t-test. However, I thought that the t-test is for testing differences in means between 2 population and that it does not involve trend lines. But I might be wrong.

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Just curious, what defines the trend line? is it the relationship between time and concentration? – Jeromy Anglim Jun 29 '12 at 5:40
Yes. It is the relationship between year and concentration. I want to see if the regression line for 1993-2004 significantly different from regression line for 2005-2010. If both lines show decreasing trend, is the trend coefficient from 1993-2004 different from coefficient for 2005-2010 – Amateur Jun 29 '12 at 8:22

1 Answer

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You could estimate a model with the following specification:

$y_t=(\alpha_1+\delta_1d_t)+(\alpha_2+\delta_2d_t)t+\varepsilon_t$

where $d_t$ is a dummy variable with value 0 for one period and 1 - for other. In this way your trend coefficients are $\alpha_1$ and $\alpha_2$ for one time period as well as $\alpha_1+\delta_1$ and $\alpha_2+\delta_2$ for the other. Testing significance of $\delta_1$ and $\delta_2$ (using F or Wald test) will answer your question.

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How would you code this is R using mixed model nlme package? – Amateur Jun 29 '12 at 23:42
Do not know, never used this package. But I think in your case lm function is sufficient. – danas.zuokas Jul 2 '12 at 6:06

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