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Background I am comparing data on how ATPase activity from flight and leg muscle from locusts reacts to different concentrations of calcium. I plotted a scatter graph of each data set on the same graph (ATPase activity on the Y axis, calcium concentration on the X axis) and have a trend line for each. The trend line for leg muscle has a steeper gradient, suggesting it is more responsive to changes in calcium.

I carried out 9 repeats for each muscle type at each concentration of calcium.

Question How do I test if there is a statistically significant difference between the trends of each data set?

I am a novice user of R and excel, though any general pointers would be appreciated.

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    $\begingroup$ Hi D Greenwood, welcome. These three posts from the site could be helpful: First, second, third. Since you have repeated measurements, you'll probabily need to fit a linear mixed effect model (e.g. with lme in R). $\endgroup$
    – COOLSerdash
    Commented May 23, 2013 at 18:53
  • $\begingroup$ Thanks CoolSerdash for the links. However the trends are not linear and the data collected at each calcium concentration does not follow a normal distribution. I was thinking of carrying out a Mann-Whitney u test between the two data sets for each Calcium value individually but this seemed a bit long winded. $\endgroup$
    – D Greenwood
    Commented May 23, 2013 at 19:06
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    $\begingroup$ Could you maybe post your models (and scatterplots)? You say that the trends are not linear. How did you fit the trends? Are they polynomial (e.g. quadratic)? $\endgroup$
    – COOLSerdash
    Commented May 23, 2013 at 19:42

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you can try log transforming the data on either of both axis to get a normal distribution. Then do linear regression and compare the slopes to see if they are significantly different (calculate Z and then look up p-value in statistics table).

Alternatively you can calculate area under the curve (AUC) using the trapezoidal rule, for each rep, this should give a normal distribution and then do a standard Student's t-test. You can do this for different sections of your curve.

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