# Comparing Learning Rates using Unit Curve in R

I have data for an experiment where 2 groups (Role) were tested over 3 consecutive trials for a task and time to complete task was recorded in sec.

I wanted to compare the learning curves of the two groups. The curves are not linear and do linearize after log or other transformations.

After searching long and hard, I came across this equation: Y_x = K x^{log_2 (b)}, which is the unit curve, where K= time to complete first trial, Y_x =Time to complete trial x, x=3, b= learning rate

Using this equation I can come up with a learning rate for each individual and than do a t-test to compare between the 2 groups.

My Question: is this equation and/or approach valid??

Here's a link to unit curve explanation

Here is my data and what I did in R

head(LR)
# ID    Trial1    Trial2  Trial3    Role
# N4        153     105     28.8    N
# N3        52.2    33      88.2    N
# NA1       360     52.8    118.8   N
# NA6       127.8   229.2   73.2    N
# F2        307.2   178.8   58.8    F
# F3        136.8   157.8   181.2   F
# F4        948     249 42  162     F
# F1        193.8   73.8    97.8    F

x=apply(LR,1, function(x) 2^log((x[4]/x[2]), base=3)) ##equation re-aranged to solve for b
t.test(x~LR\$Role)

• You would almost certainly do best to use a model that incorporates all of your data, rather than try to reduce your data somehow & then run a test. – gung Nov 27 '14 at 20:28
• Your suggested function linearizes (under log-log transformation), so either your data would be expected to approximately linearize with that transformation, or the data likely won't fit that function. – Glen_b Nov 27 '14 at 23:36