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moonman239
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I don't know much algebra (I kind of skipped it and went to geometry), but I do sort of understand statistics. I can certainly perform a z-test or a t-test and know when they should or shouldn't be used.
moonman239 said:I don't know much algebra (I kind of skipped it and went to geometry), but I do sort of understand statistics. I can certainly perform a z-test or a t-test and know when they should or shouldn't be used.
moonman239 said:I can certainly perform a z-test or a t-test and know when they should or shouldn't be used.
Stephen Tashi said:What does a t-test tell you? ... Does it tell you the probability the null hypothesis is true given the observed data? No. And it doesn't tell you the probability that the null hypothesis is false given the observed data. There is a difference between "the probability A given B" and the "probability of B given A".
haruspex said:Quite. Nor does it usually tell you the probability of the data given that the null hypothesis is false. That's because the null hypothesis is often a single point (the effectiveness of a drug, say) on a continuum.
No, that's not what I was trying to say. An example will help:chiro said:If you are talking about single-points in terms of a continuum, this is out of context for the discussion since you will always get zero-probabilities for any single point for continuous random variables which results in having to supply an interval.
Bayesian statistics is a mathematical framework for updating beliefs and making decisions based on new evidence. It allows for the incorporation of prior knowledge or beliefs into the analysis, making it a powerful tool for decision-making in uncertain situations.
Traditional statistics relies on frequentist methods, which use a single fixed value for unknown parameters and do not incorporate prior beliefs. In contrast, Bayesian statistics allows for the use of prior knowledge and updates beliefs based on new evidence, resulting in more flexible and accurate conclusions.
In Bayesian statistics, probabilities are calculated using Bayes' theorem, which is a mathematical formula that describes the relationship between prior beliefs, new evidence, and updated beliefs. This involves multiplying the prior probability by the likelihood of the new evidence, and then normalizing the result to get the posterior probability.
Some of the main advantages of Bayesian statistics include its ability to incorporate prior knowledge, its flexibility in handling complex and uncertain data, and its ability to update beliefs as new evidence is obtained. It also allows for the use of intuitive and interpretable probability statements, making it useful for decision-making.
One potential limitation of Bayesian statistics is the need for prior knowledge or beliefs, which may be difficult to obtain or may introduce bias into the analysis. Additionally, the calculation of probabilities can become complex and computationally intensive in more complex models. However, with appropriate methods and techniques, these limitations can be mitigated.