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# Bayes analysis for a linear trend.

edited June 2016

Hi,
I'm trying to figure out the best way to test for a linear trend in a data-set I have.
the data consists of four variables, each represent an object size, and the dependent variables are reaction times for each object size.

My hypothesis is actually a null-hypothesis. I predict that reaction times will not increase as the object size increases (a linear trend). I could do a simple RM-ANOVA and test for a linear trend by using a comparison with linear weights (i.e. -3, -1, 1, 3) and see that the linear comparison is insignificant, but of course that is not a suitable way to support a null hypothesis, so a Bayesian analysis seems to me like a proper solution, by calculating the probability of receiving my data given that the null is correct.

Please advise me with a possible way to test for such a hypothesis using Bayes analysis in JASP, if there is one.

Thank you.

• edited 8:30PM

Hi Zennie,

JASP does not do contrasts yet, but I think you should be able to compute what you want using Richard's BF package. I recall Richard also wrote a blogpost on this. Richard may be able to provide the details.

Cheers,
E.J.

• edited 8:30PM

"I predict that reaction times will not increase as the object size increases (a linear trend)"

Is the alternative really a linear increase? The first part of your hypothesis suggests an unstructured alternative (and do you mean average RT?), but you've couched it as a question about a linear trend. Are you sure that the linear trend is what you want to test, and not an ordinal hypothesis (eg, X1>X2>X3)?

• edited 8:30PM

Thank you both.
Yes, I am sure that I want to test for a linear trend. As H1 states that the data should act linearly, H0 should be the lack of such trend.

Secondly, I am thinking that I can get away with a Bayesian linear regression. Can I use the RT data as the dependent variable, and the object size as the predictor and calculate the Bayes factor for the linear regression? A high BF(01) should indicate a high probability that the data does not align linearly. If not, why is it different from calculating a linear trend using contrasts?

Thank you again.

• edited 8:30PM

You can create the contrasts you want and define them as predictors, then use lmBF to test them.