# Baysian statistical test

#### javedbtk

##### New Member
Hi, how can we perform a baysian test which is alternative of Wilcox test.? My data is not normalized so can't do baysian t tests.

#### GretaGarbo

##### Human
Step one. What is the distribution of the data, i.e. what is the likelihood?

(Btw Bayesian)

#### javedbtk

##### New Member
Step one. What is the distribution of the data, i.e. what is the likelihood?

(Btw Bayesian)
Thanks for the reply. Data is continuous. Let's say, algorithm A has data like, 0.01, 0.15, 0.03, - 0.21 etc and algorithm B : 0.12,0.002, 0.13, 0.4 etc. The number of samples could be more than 100 like this.

#### GretaGarbo

##### Human
If you intended to use Bayes theorem you would need to have the likelihood and a prior distribution. And by that I mean the densities from a distribution, like e.g. the gamma distribution.

Let's say, algorithm A has data like, 0.01, 0.15, 0.03, - 0.21
I guess that the data are non-negative, are close to zero and that the data are skewed. I would look at distributions like the gamma distribution or the log-normal distribution. Then you could do maximum likelihood estimate of that and test if the means are equal.

What is the sample size?

#### javedbtk

##### New Member
If you intended to use Bayes theorem you would need to have the likelihood and a prior distribution. And by that I mean the densities from a distribution, like e.g. the gamma distribution.

I guess that the data are non-negative, are close to zero and that the data are skewed. I would look at distributions like the gamma distribution or the log-normal distribution. Then you could do maximum likelihood estimate of that and test if the means are equal.

What is the sample size?
Sample size is more than 500

#### GretaGarbo

##### Human
What does the histogram of the the data look like (for each of the two groups)?

If you take the log of the data (for each of the two groups) what does the histogram like then? Does it look like the normaldistribution (i.e. bell shaped)?

Are the data such that it must be larger than zero? (i.e. non-negative)

Are the data resticted to be between zero and one (between 0 and 1)?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Can you post these histograms? Also, do you believe these histogram are representative of the overall population. Because if we are just basing priors on your current data, we being biased by the empirical data. What is your theory on the over all distribution, if you don't have any, perhaps a flat prior is needed.

What is your familiarity with Bayesian analyses?

#### javedbtk

##### New Member
What does the histogram of the the data look like (for each of the two groups)?

If you take the log of the data (for each of the two groups) what does the histogram like then? Does it look like the normaldistribution (i.e. bell shaped)?

Are the data such that it must be larger than zero? (i.e. non-negative)

Are the data resticted to be between zero and one (between 0 and 1)?
The data is between - 1 and 1. It can be 0.3,0.002, or - 0.01

#### GretaGarbo

##### Human
Why don't you tell us what your data is about? As the guidelines sayes, your little investigation is not a state secret (If it is, you should not reveal it here.)

So the data is between -1 and +1. (Is it correlations?)
What does the historgam look like?

if the sample size is about n=500 in each group, why not just rely on the central limit theorem and compare the means and do a z-test? What are the means, standard deviation and n1 and n2?

#### javedbtk

##### New Member
Why don't you tell us what your data is about? As the guidelines sayes, your little investigation is not a state secret (If it is, you should not reveal it here.)

So the data is between -1 and +1. (Is it correlations?)
What does the historgam look like?

if the sample size is about n=500 in each group, why not just rely on the central limit theorem and compare the means and do a z-test? What are the means, standard deviation and n1 and n2?
My data is about the error (absolute residuals) of two algorithms like linear regression and support vector regression. The dataset is about school results where the actual values are contnous from 0 to 1 and the predicted values are also like that. For example, students spend time in lab is a feature of the dataset and its value is 0.9 but the linear regression predict it as 0.1 and support vector regression predicts it - 0.3. All the data is distributed like this. Now I need a statistical test which is not frequentist because I read that frequentist tests are biased.

#### Dason

Now I need a statistical test which is not frequentist because I read that frequentist tests are biased.
... So naturally instead of explaining what your goal is and why you decided that you made the decision that Bayesian methods (which from a frequentist perspective are almost always biased) was the definite route to go?

Don't get me wrong... I love Bayesian methods but this seems silly.

#### GretaGarbo

##### Human
Don't get me wrong... I love Bayesian methods but this seems silly.
@Dason, I think that you need to explain to the user @javedbtk what it is that you find "silly". The user tried a conventional way of analysing the data. In the useres view, it did not work. The user might be confused about what to do.

I am also interested in why @javedbtk wanted to go the Bayesian way. And I want to hear her/his answer.