(1) For the first research question, we want to see if there is a difference in confidence for those who were correct, and who were incorrect. These two groups are different participants, so this is a between-subjects question. For the second question, we want to know whether peoples' judgment was higher for alcoholic or non-alcoholic beer. This is measured within-subjects, so calls for a paired samples t-test.
(3) The descriptives are below. We see that the average confidence rating for the incorrect participants was 64.733, and for the correct participants it was 77. The standard deviations are pretty large (24 and 20), so we need some inferential statistics to see if this difference in means is meaningful
(4) The one-sided, negative Bayes factor (BF-0) equals 2.52, so we have "anecdotal" evidence in favor of the alternative hypothesis.
(5) There is some minor evidence in favor of the alternative hypothesis (that correct people were more confident in their answers), but it is not very convincing.
Bayesian Independent Samples T-Test
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|---|---|---|---|---|---|
| BF₋₀ | error % | ||||
| ConfidenceRating | 2.520 | ~ 7.758e-4 | |||
| Note. For all tests, the alternative hypothesis specifies that the location of group 0 is smaller than the location of group 1 . | |||||
Descriptives
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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 95% Credible Interval | |||||||||||||||
| Group | N | Mean | SD | SE | Lower | Upper | |||||||||
| ConfidenceRating | 0 | 15 | 64.733 | 23.963 | 6.187 | 51.463 | 78.003 | ||||||||
| 1 | 42 | 77.000 | 19.967 | 3.081 | 70.778 | 83.222 | |||||||||
Next, we analyze whether participants had a preference for the alcoholic beer or the non-alcoholic beer. Here, we look at the difference between the ratings they gave for the two beers.
(7) The Bayes factor in favor of the one-sided alternative hypothesis (BF+0) is 22208. This is extremely strong evidence in favor of this hypothesis, compared to the null hypothesis.
(8) The two means are 56.6 (alcoholic beer) and 36.33 (non-alcoholic beer). The difference is therefore 56.6 - 36.33 = 20.27.
(9) Based on this analysis, we can conclude that participants prefered the taste of the alcoholic beer. Whether this finding generalizes to other beers (and not only Weihestephan Hefeweissbeer) requires some more experiments..
(bonus) Based on the descriptives, we see that the average rating for the alcoholic beer is 56 (out of 100), which is also not very high. We could conclude that participants did generally not really like the taste of these beers.
Bayesian Paired Samples T-Test
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|---|---|---|---|---|---|---|---|---|---|
| Measure 1 | Measure 2 | BF₊₀ | error % | ||||||
| AlcRating | - | NonAlcRating | 22208.762 | NaN | ᵃ | ||||
| Note. For all tests, the alternative hypothesis specifies that AlcRating is greater than NonAlcRating. | |||||||||
| ᵃ t-value is large. A Savage-Dickey approximation was used to compute the Bayes factor but no error estimate can be given. | |||||||||
Descriptives
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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 95% Credible Interval | |||||||||||||
| N | Mean | SD | SE | Lower | Upper | ||||||||
| AlcRating | 57 | 56.605 | 20.255 | 2.683 | 51.231 | 61.980 | |||||||
| NonAlcRating | 57 | 36.333 | 22.122 | 2.930 | 30.463 | 42.203 | |||||||