Learning Bayesian Analysis, Request Peer comments and Guidance for the Bayesian Binomial Test Shared

drravikch

Proportion of Dengue and Malaria Children in a Cohort of Febrile Children.pdf

Dmartin427

To put it plainly:

1. The purpose of the Bayesian Binomial Test is to assess the probability that two independent nominal variables have counts that are either different from an expected value (BF10), or the same as an expected value (BF01). In other words, this test evaluated if the counts in your sample were different from the expectation that Dengue Fever and Malaria were evenly split at 50/50 in your sample.
2. Prior to conducting the analysis, we establish a Prior Probability, which is a statement of the strength of our belief in our hypothesis prior to collecting our data. When we don't have any specific prior information to provide prior to the analysis, we often default to what is called an "uninformed prior". For binomial tests, this means that we could assume that both nominal variables are present in the data at a 50/50 split, which is the case for this analysis.
3. The Binomial Test will take the counts of two nominal variables and provide a proportion figure for each, which are percentages of how much that variable accounts for the whole sample. In this case, counts for Dengue Fever are 55.8% of the 224 sample; Malaria is 44.2% of the 224 sample. These proportions are compared to the expectation that we set as our prior probability, which is that both Dengue Fever and Malaria were evenly split at 50/50 in your sample (50% for each one).
4. The Bayesian Binomial analysis produced a Bayes Factor (BF10) of 0.376, which are the odds that your output supports H1 (the alternative hypothesis; the counts are different) over H0 (the null hypothesis; the counts are the same). To interpret the value, use this table.
5. A BF10 of 0.376 implies that the odds for supporting H1 is 37.6% as likely as H0; in other words, there is ~2.660 times (1/0.376) greater odds of support for H0 over H1, which implies a moderate level of evidence for the null hypothesis that there is no difference between the observed counts of Dengue Fever and Malaria in your sample and a 50/50 split.
6. A Bayesian credible interval is a range of values within which we believe our counts lie, based on the data and prior probability. 
7. With these results, we can reasonably conclude that there is no difference between the counts for Dengue Fever and Malaria, given the evidence we now have for the null hypothesis.

drravikch

Thank you very much Dmartin for explaining the Bayesian concepts in plain language.

I request further clarification to make me further understand as I am a non-statistician.

 

1.   In the example analysis shared, there is only one categorical variable - ‘Diagnostic category’ which has dichotomous or two values: Dengue & Malaria.

Is it right to understand that a Bayesian Binomial test is essentially testing:

·      Whether the proportions of dichotomous or two values (Dengue and malaria) of a variable (Diagnostic Category) are significantly different from previously known-informed population proportions or if previous population proportions are not known whether proportions of the two values are significantly different from a test value (assumed prior: here 0.5 or 50.0% each)? This is H1.

·      Whether the proportions of two values of a variable are not significantly different from informed prior population proportions or assumed/uninformed prior proportion)? This is H0.

 

2.   Bayesian Binomial test is a descriptive statistic of dichotomous categorical variables but is not testing association between two categorical variables.

 

3.   You mentioned point 5:

 “A BF10 of 0.376 implies that the odds for supporting H1 is 37.6% as likely as H0; in other words, there is ~2.660 times (1/0.376) greater odds of support for H0 over H1…”.

May I understand this way too: A BF10 of 0.376 implies that the likely support for H0 is 100-37.6%=62.4% as likely as H1. In other words, odds wise or likely percentage wise there is support for H0 over H1.

Hence neither the proportion of Dengue nor the proportion of Malaria is significantly different from the assumed prior proportion of 50%. Therefore, the proportions of Dengue and Malaria are similar in the sample studied.