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I am about to commence data analysis, but am slightly unsure about which test to use.

My experiment concerns persuasion where participants view figures on screen making speeches. Thus must choose which figure won the argument. My design is 2 x 2 (left vs right) x (first vs second). All participants view the same arguments and must choose left vs right (as most persuasive), but in one condition, the right figure goes first and in the second condition the left figure goes first. Participants are either in group 1 or group 2.

Participants view firstly a text on screen - explaining a scenario, they are then presented with figure that give an argument for and against. All arguments are the same across all participants, however condition 1 - figure 1 always goes first - condition 2 - figure 2 goes first. Hypotheses tested are 1) that figures positioned on the left will be more convincing and 2) order may influence decision (i.e., arguments presented first = greater persuasion).

Would a binary logistic regression be the best test here? Step by step would be most helpful.

Thank you

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    $\begingroup$ Are participants measured/tested more than once ? Also, are the same figures viewed by more than one participant, or does each participant see unique figures ? $\endgroup$ Commented Aug 21, 2021 at 18:32
  • $\begingroup$ You don't seem to mention any hypotheses that you want to test. $\endgroup$
    – Glen_b
    Commented Aug 22, 2021 at 3:12
  • $\begingroup$ Hello both! Many apologies for the lack of detail. Participants view firstly a text on screen - explaining a scenario, they are then presented with figure that give an argument for and against. All arguments are the same across all participants, however condition 1 - figure 1 always goes first - condition 2 - figure 2 goes first. Hypotheses tested are 1) that figures positioned on the left will be more convincing and 2) order may influence decision (i.e., arguments presented first = greater persuasion). $\endgroup$
    – user332893
    Commented Aug 22, 2021 at 17:24
  • $\begingroup$ Please add new information as an edit to the post, and not only as a comment. Comments get often unread! $\endgroup$ Commented Aug 22, 2021 at 20:04
  • $\begingroup$ Thank you, halvorsen. :) $\endgroup$
    – user332893
    Commented Aug 24, 2021 at 15:51

2 Answers 2

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I don't think you need a logistic regression. The outcome is binary (Left/Right is Most Persuasive) if I have understood correctly. The hypothesis is about the order in which arguments are presented.

We can organize the results into a 2x2 table

Left First Left Second
Left Most Persuasive a b
Right Most Persuasive c d

Here, $a$ people who observed left make arguments first thought left was the most persuasive. $c$ people in that same group thought right was most persuasive.

To test if the order in which arguments are presented affects the proportion of people who think left is most persuasive, we can use any number of tests in this answer though I would be preferential to a test of proportions + a Wilson Confidence Interval.

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  • $\begingroup$ Would Clopper-pearson be appropriate too? (I'm more familiar with, than Wilson). :) $\endgroup$
    – user332893
    Commented Aug 24, 2021 at 17:59
  • $\begingroup$ @user332893 Yea that's fine. There are a bunch of binomial confidence intervals. $\endgroup$ Commented Aug 24, 2021 at 18:01
  • $\begingroup$ Great! Thank you for your guidance. Much appreciated! :) $\endgroup$
    – user332893
    Commented Aug 25, 2021 at 15:08
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Use a nonparametric method! They're robust and make very few assumptions about your data. They're also weak, but better to err on the side of caution.

For your case, you can run a simple permutation test to obtain a p-value.

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  • $\begingroup$ Your answer doesn't address OP's hypothesis. What nonparametric method? Permutation test of what? $\endgroup$ Commented Aug 24, 2021 at 16:12
  • $\begingroup$ Randomly resample the data into a table of the proper shape to approximate the null. Count how many times we observe a difference larger than the experimental results. Another benefit of doing it this way is that it's really obvious what null you're actually testing, because you're constructing it manually. $\endgroup$ Commented Aug 24, 2021 at 16:14
  • $\begingroup$ No, I understand what a permutation test is and how it works. I'm saying it might be better to perhaps show OP how this test might work for their problem. Maybe you could do a simulation and perform the test for OP. $\endgroup$ Commented Aug 24, 2021 at 16:17

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