Informative Hypotheses: Theory and Practice for Behavioral and Social Scientists

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Here we use two studies to illustrate how our principles demonstrate this gradation in scientific quality. We will introduce these datasets, evaluate informative hypotheses for every dataset and discuss what we have learned about the influence of effect size. Now that an intuitive definition of complexity and fit is established, we look at the formula for the Bayes factor in equation 9 again. Hoijtink, H. Dataset 1: Predicting Overconsumption from Eating Behavior The first research example stems from research on overconsumption by Van Strien et al.

The Bayes factor for every model against its unconstrained alternative is displayed. For every hypothesis a more detailed output file can be obtained where, among many other statistics, the fit, and complexity can be found. For H 1 — which stated that both predictors were positively related to overconsumption — we find a complexity of 0. This means that the hypothesis in equation 2 receives four times more support from the data than an unconstrained empty model does. H 2 — stating that emotional eating is more important for predicting overconsumption than restrained eating — has a complexity of 0.

This indicates that H 2 is still a better model for the data than its unconstrained alternative.


Informative Hypotheses: Theory and Practice for Behavioral and Social Scientists - CRC Press Book. Informative Hypotheses: Theory and Practice for Behavioral and Social Scientists : Herbert Hoijtink: Books -

This indicates that H 3 is eight times more likely than the empty model it was compared to. Recall that we were not merely interested in the hypotheses themselves; we wanted to compare them and select the most optimal hypothesis for the data. As discussed in the intermezzo we can obtain Bayes factors for the comparison of two hypotheses by dividing the Bayes factors of those hypotheses against an unconstrained alternative. For example, comparing the Bayes factor of H 3 with that of H 2 gives a Bayes factor of 8.

This indicates that H 3 receives most support from the data, either when it is being compared to an empty model or another informative hypothesis. To conclude, we would say that both emotional and restrained eating are related to overconsumption with emotional eating being the strongest predictor of the two.

For the second analysis — predicting work-family interference from contractual hours and overtime hours — we again prepared the data file and obtained Bayes factors for all three models. Recall our informative hypotheses from the introduction:. The Bayes factor for H 1 against the unconstrained hypothesis is 4.

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Although all informative hypotheses receive more support from the data than their unconstrained alternatives do, H 3 fits the data best. Our conclusion would be that contractual hours and overtime hours are both related to work-family interference, but the relation is stronger for overtime hours. A causal interpretation of the results remains complicated because this research project was not a controlled experiment. As mentioned earlier we also want to demonstrate how the Bayesian output is affected by differences in effect size.

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The purpose is to gather insight into the effect R 2 has on the Bayes factor a concept that will be discussed in the next section. This influence has never been studied before in regression models. Although our study is not extensive enough to serve as a full overview, it does give the reader a feeling of how effect size affects the statistical output. In contrast to the real-world datasets, the generated datasets consist of observations each.

What is Hypothesis? (Part 1 of 2) 13 Types of Hypothesis (Null & Alternative) - Research Methodology

This makes them more comparable to certain areas of psychological research where smaller datasets are common, such as experimental psychology. All variables are normally distributed with a mean of 0 and a standard deviation of 1 and the regression coefficients are uncorrelated. The sampling coefficients are identical to the population values. The hypotheses we want to evaluate for these seven datasets are a generalized form of the hypotheses outlined in the real-world examples:.

This helps us judge the performance of our Bayesian method. We evaluated the three informative hypotheses in equation 10 in the same way as the screenshots for the overconsumption data illustrate. Note that BIEMS estimates the complexity and due to the estimation process, the complexity for the three hypotheses will not be exactly the same in every analysis.

We know from the intermezzo that the complexity of H 1 should be exactly 0. The reason for estimation is that in more complex hypotheses it would not be possible to determine the complexity based on calculations Van de Schoot et al. Results corresponding to the generated datasets: Bayes factors for each informative hypothesis against its unconstrained alternative. Note that BF 12 denotes the Bayes factor for the comparison of H 1 versus H 2 and indicates the relative support for H 1 in this comparison.

Bayes factors for the comparison of the informative hypotheses with one another. Recall from the intermezzo that the complexity of an hypothesis is not influenced by the data. Here we see that the hypotheses indeed have the same complexity no matter for which dataset it was computed. We also observe that the complexity of H 1 is indeed 0. As for the fit values, we know from the intermezzo that they are influenced by the data.

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Indeed, we see that the fit increases as the effect size increases. For the computation of the Bayes factor this means that a larger and larger fit value is divided by a constant complexity, implying that the Bayes factor will increase as well. This indicates that there is about equal support for the informative hypotheses as there is for the unconstrained hypothesis.

Of course a researcher could still choose to prefer the informative hypothesis in this case, but his decision would be hard to sell. Instead we conclude that none of our hypotheses provides an accurate description of the data in dataset 1.

Note that this corresponds to the prediction we made when we introduced the generated datasets. Recall that the higher the Bayes factor is, the more support we have for our hypothesis versus an empty hypothesis.

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In datasets 2—4 we see a clear preference for H 1 and H 3. Note that the fit for H 3 is lower than that for H 1 , but because H 3 has a lower complexity it receives roughly the same Bayes factor as H 1 does. Thus, when H 1 is accurate, H 3 is at least partly accurate as well. The BF for this hypothesis remains stable around 1.

Note that the fit of H 2 is a bit higher than that of H 3 , but because H 2 imposes less constraints it has a higher complexity which results in lower Bayes factors. This is another example where the researcher is rewarded for having been specific when H 3 was formulated. Because in datasets 5—7 we receive support for all informative hypotheses versus the unconstrained model, it becomes especially interesting to see which of the three fits the data best. The generated datasets were designed to demonstrate how R 2 influences the results of Bayesian statistics.

After having seen these results we would say that even when effect size is zero or relatively low the Bayes factor helps us choose an accurate model for the data. We conclude that the Bayes factor can be used even when the researcher expects a small effect. In this paper we have illustrated how informative hypotheses can be evaluated by means of Bayesian statistics.

We applied the method to existing psychological research, where we showed the reader the process of formulating informative hypotheses, evaluating them in light of the data, and interpreting the outcomes. In addition to this application we generated and analyzed datasets with manipulated differences in effect size.

Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications

This endeavor demonstrated how the Bayes factor was or was not affected by the magnitude of an effect. We now review our findings and discuss the practical value of Bayesian hypothesis evaluation for psychological researchers. In the introduction we claimed that the null hypothesis is often not the expectation that a psychological researcher wishes to evaluate. Instead we argued that researchers often have very specific prior expectations about parameter values.