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I performed an ANCOVA on final height (height4) with initial height as a covariate.

Dependent variables:

ipc.gm = initial % cover of garlic mustard

fence = factor with 2 levels: Fence, Open

There was a significant interaction effect: ipc.gm*fence

An interaction plot shows that height4, corrected for initial height, increases with increasing ipc.gm, but only in Fence plots.

enter image description here

I used emtrends() to get the slope of each line:

> emtrends(model3, pairwise ~ fence, var = "ipc.gm")
NOTE: Results may be misleading due to involvement in interactions
$`emtrends`
 fence ipc.gm.trend         SE df    lower.CL   upper.CL
 Fence   0.06585603 0.02670941 92  0.01280884 0.11890322
 Open   -0.02830168 0.03487092 92 -0.09755835 0.04095498

Results are averaged over the levels of: gm 
Degrees-of-freedom method: containment 
Confidence level used: 0.95 

$contrasts
 contrast       estimate         SE df t.ratio p.value
 Fence - Open 0.09415771 0.04201853 92   2.241  0.0274

Results are averaged over the levels of: gm 

The "ipc.gm.trend" for Fence gives a positive slope of 0.0659, with a lower confidence limit of 0.0128 and an upper confidence limit of 0.1189.

The "ipc.gm.trend" for Open gives a negative slope of -0.0283, with a lower confidence limit of -0.0976 and an upper confidence limit of 0.0410.

Questions

  1. When writing my paper, I will say that height4, corrected for initial height, increased with increasing ipc.gm at the Fence level. Do I back this up by reporting the positive slope, or confidence limits, or both?

  2. For the Open level, the slope is negative but the confidence limits contain zero. Should I say that height4, corrected for initial height, decreased with increasing ipc.gm and back this up by reporting the slope? Or should I say that height4, corrected for initial height, was not affected by ipc.gm and back this up by reporting the confidence limits?

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1 Answer 1

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Confidence limits are not hard limits but randomly vary with the data. With a method that generates confidence limits that cover an unknown constant with some probability, you can make a reasonable assertion that the particular limits generated from your particular sample contain the unknown constant.

Now that brief review is out of the way, your limits for Fence do not contain 0, so asserting the limits contain the true slope is equivalent to asserting the slope is greater than 0. On the other hand, asserting your limits for Open contain the true value neither confirms or refutes the possibility that the slope is 0. You may report that the slope computed from your sample was negative, but you should also report that your confidence limits contain 0.

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