Comparing Continuous Probability Distributions: Finding Significance

In summary, the conversation discusses a method for comparing continuous probability distributions by using two variables, X(t) and Y(t), and running a regression test to determine if the joint hypothesis of "a=0 and b=1" is statistically significant. The question is raised about how to account for values that are close to 0 and 1, and the answer is suggested to be a two-tailed hypothesis test.
  • #1
jjstuart79
7
0
Hi,
I was searching the forum about comparing continuous probability distributions and came across this post back in 2005.

"You could make two variables X(t) = value of the "true" disrtibution (expensive simulation) at point t and Y(t) = value of the alternative dist. (practical simulation) at point t. Then run the regression Y(t) = a + b X(t) for as many t's as you can (or like), then show that the joint hypothesis "(a = 0) AND (b = 1)" is highly statistically significant."

My question is about the last sentence. What would be the best way to check to see if a = 0 and b =1? I know I could count how many times that is exactly true, but what if a = close to 0 and b = close to 1? I would like a way for that to count for some significance as well.

I appreciate any help.
 
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  • #2
I think I found the answer. A two-tailed hypothesis test should work.
 

1. What is the purpose of comparing continuous probability distributions?

The purpose of comparing continuous probability distributions is to determine if there is a statistically significant difference between two or more sets of data. This can help researchers understand the relationship between variables and make informed decisions about their findings.

2. How do you determine significance when comparing continuous probability distributions?

Significance can be determined by conducting a statistical test, such as a t-test or ANOVA, to compare the means of the distributions. The results of the test will provide a p-value, which indicates the likelihood of obtaining the observed difference between the distributions by chance. A p-value of less than 0.05 is typically considered significant.

3. What is the difference between a parametric and non-parametric test when comparing continuous probability distributions?

A parametric test assumes that the data follows a specific distribution, such as a normal distribution. Non-parametric tests do not make any assumptions about the underlying distribution of the data. Parametric tests have more statistical power but may not be appropriate if the data does not meet the assumptions. Non-parametric tests are more robust but may have less power in detecting differences.

4. Can you compare more than two continuous probability distributions at once?

Yes, it is possible to compare more than two continuous probability distributions at once using an ANOVA or a non-parametric equivalent. These tests will determine if there is a significant difference between any of the distributions. If the overall test is significant, post-hoc tests can be conducted to determine which specific distributions differ from each other.

5. What are some common mistakes to avoid when comparing continuous probability distributions?

One common mistake is assuming that a significant difference between two distributions means that one is better or more important than the other. It is important to consider the context and relevance of the data being compared. Another mistake is not properly checking the assumptions of the chosen statistical test, which could lead to incorrect conclusions. Additionally, it is important to consider the sample size and variability of the data when interpreting the results of the test.

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