- Thread starter ulrika
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- Tags chemistry comparing slopes reaction rate

I have been running a reaction where two reactants form one product. I have been using 3 different reactants in combination with 2 different substrates of the other reactant. And for all of these I have done two replications so in total 12 reactions. For all of these I have measured the consumption of one of the substrates and plotted the consumption vs time in a scatter plot. From this I am assuming that the starting material is consumed linearly for the first 14 samples and therefore I have done a linear regression giving me the equation telling me how fast my starting material is consumed over time. What I first want to do is comparing the slopes of the curves for the replicas of the same reaction to say that all values come from the same population. Afterwards, I would like to compare the slopes of the curves in between different measurements for different starting materials to see of there is a significant difference in consumption rate between substrates.

I wanted to use an ANOVA table but then I'm only comparing the means of all the data points and different sets of data could give the same mean. Or have I gotten it wrong? What I find problematic is that I just want to compare one value to another and not the whole set of data.

Hope this was clearer!

I would like to compare the slopes of the curves

z = (beta1 – beta2)/sqrt(stderr1^2 +stderr2^2)

where beta1 is the estimated regression coefficient in the first regression and stderr1 is the estimated standard error in the first regression, etc. (And it could even be considered as a t-test as the stderr^2 seems to be chi-squared distributed (and divided by its degrees of freedom).)

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On a more principled point, this seems to be a quite common situation in chemistry and biology. They do some kind of regression (linear or non-linear) of their favourite model in a first step. Then they take that regression coefficient and use it as an observation and insert it in data table and run a second model (and do various comparisons).

This seems to me as a multilevel model and I guess that more efficient estimates could be achieved (than using the two-stage method from above).

So why don't you compare the slopes? You have the estimated slope and the standards error for that slope. You could do a z-test.

z = (beta1 – beta2)/sqrt(stderr1^2 +stderr2^2)

where beta1 is the estimated regression coefficient in the first regression and stderr1 is the estimated standard error in the first regression, etc. (And it could even be considered as a t-test as the stderr^2 seems to be chi-squared distributed (and divided by its degrees of freedom).)

z = (beta1 – beta2)/sqrt(stderr1^2 +stderr2^2)

where beta1 is the estimated regression coefficient in the first regression and stderr1 is the estimated standard error in the first regression, etc. (And it could even be considered as a t-test as the stderr^2 seems to be chi-squared distributed (and divided by its degrees of freedom).)

So for the comparison of slopes, you should actually use the t-distribution. Not that it changes things much, as the t-statistic rapidly converges to the normal at about df = 300 but for small sample-sizes the t should be best.

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