Interpreting results of one-way bayesian ANOVA in JASP

Comments

• EJ

  March 2018

  Dear Vadim,

  1. You have BF10 = 0.175. This means that that BF01 = 1/0.175 = 5.71, meaning that the data are about 5.7 times more likely under H0 than under H1. This is support in favor of H0. I should not that BF10 = 0.99 would also have constituted evidence for H0 (but only a smidgen).
  2. Yes, that is correct.
  3. Weird. You can check with BayesFactor. I'll discuss this with Richard too. I doubt SPSS gives the correct result, because that BF is very small indeed.

  Cheers,
  E.J.
• richarddmorey

  March 2018

  SPSS is in error, almost surely. It would require a prior scale of almost two to get that low a Bayes factor.

  Here's my check. This isn't exactly right, because it appears you have slightly different numbers in each group, but this is the only way I can just use the F statistic. It should be very close.

  Fstat = .540
  N = 25
  J = 3
  
  df1 = J - 1
  df2 = (N - 1) * J
  
  1 - pf(.540, df1, df2 )
  ### [1] 0.5850897
  ### P value checks out against SPSS
  
  
  bf = BayesFactor::oneWayAOV.Fstat(Fstat, N, J, simple = TRUE)
  ###       B10 
  ### 0.1730758 
  ### Agrees with JASP
  
  ### Check for a range of prior scales
  rscale = exp(seq(log(.1), log(2), len = 50))
  bfs = sapply(rscale, function(r)
    BayesFactor::oneWayAOV.Fstat(Fstat, N, J, simple = TRUE, rscale = r))
  
  
  plot(rscale, bfs, ty='l', log = "xy", ylab = "Bayes factor", xlab = "Prior scale", las = 1)
  
  ## Blue line is default
  abline(h = bf, col = "blue")
  abline(v = 1/2, col = "blue")
  
  ## Red line is SPSS - way out there.
  abline(h = .022, col = "red")
  
  
• vadim

  March 2018

  Thank you very much for your answers and great software!
• Mila_Marinova

  April 2018

  Hello everyone,

  First, many thanks to the JASP team for the amazing job! I have the following naive question
  For a study we did 4 one-way Bayesian ANOVAs (for 4 different tasks) for both Reaction times and Accuracies. For the Acc the BF10 and 01 are easy to interpret (meaning that there is clear support either for BF10 or BF01), but for the RTs both the BF01 and BF10 are negligible (less than 1). So my question is: when both BFs are less than 1 would it be correct statement to say that the data (in this case the RT data) is not informative ( probably more evidence is needed) and thus no reliable conclusion can be provided by from this data? Or some other way to handle such small BF10 and BF01?
  Thank you in advance!
• EJ

  April 2018

  Hi Mila,

  BF10 = 1/BF01, so if BF10 < 1 then BF01 > 1. In other words, it is impossible that both BF10 and BF01 are lower than 1, unless you are referring to different tests. Maybe you have a concrete example? In general, BFs near 1 are not diagnostic, at least not as far as the hypotheses are concerned that you are testing.

  Cheers,
  E.J.
• Mila_Marinova

  April 2018

  Hi E.J.,
  Thanks for the response. Indeed, you are right I dis not express muself correctly. What I was wondering was wheter for cases like BF10 = 0.956 and BF01 = 1.046, for example, where both BFs are not diagnostic, as you said, would be sufficient to say that the data is not sensitive with respect to hypotheses tested and refrain from any conclusions?
  Thanks again!
• EJ

  April 2018

  Hi Mila,

  Yes. The correct conclusion is that the data do not provide information: the hypotheses under consideration predicted the data about equally well. Of course, the data may be informative in other ways; for instance, perhaps the posterior distribution is relatively peaked, or perhaps most posterior mass is on positive values of effect size, etc.

  Cheers,
  E.J.
• Mila_Marinova

  April 2018

  Many thanks!