## Fitting a log2 curve to 4 related within subjects variables

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packard
Posts: 1
Joined: Fri Dec 15, 2017 12:31 pm

### Fitting a log2 curve to 4 related within subjects variables

Hi everyone,

This is my first post here. I basically want to replicate Burrows and Okada (1975, Memory Retrieval from short and long lists) in which they plot Reaction Time (dependent variable) vs Word List length (independent variable) and find that

Reaction Time = A + B*log 2 (Word List length)

In my case, I have 20 subjects and each subject has 4 different reaction time means for Word List length (20, 40, 60 and 80). So I have a table with 1 row for each subject and 4 columns with different Reaction Time values (1 for each word list length).

I would like to test whether there is a difference between these 4 related variables (Word List length (20, 40, 60, and 80)) and whether this follows a log2 function. Ideally, I could contrast it with a linear function and show that it fits the log2 function better.

So far I have tried looking at the 'within-subjects contrasts' table in the ANOVA output but the problem with that is that there is no logarithmic contrast, only linear or quadratic.

I have also tried calculating the means for each word list length to create a table with one column with mean Reaction Times and another with the Word List length, and then doing a curve fit, but the problem here is that I only have the option for a logarithmic fit of log 10.

I want to fit a log 2 curve, and possibly compare with a log 10 curve or a linear fit.

How can I do that?

Should I just transform my word list lengths to log2(word list length) and then do a linear regression on the mean Reaction Times?

I am using SPSS 22 on a OS X Yosemite in case that matters.