Critical Value & P-Value Methods: Comparison & Relationships

In summary, the basic probability theory includes the concepts of mutually exclusive events and independent events, which are often prominent in discussions of probability. However, it is not possible for two events to be both mutually exclusive and independent at the same time. In regards to the relationship between the "Critical Value Method" and the "P-Value Method," the former is used for significance testing and the latter is a measure of evidence against or for the null hypothesis.
  • #1
jokerwild
4
0
1)
In the basic probability theory the concepts of mutually exclusive events and independent events share prominent roles, can two events be both mutually exclusive and independent at the same time?

2)
What are two vital concepts and the relationship between "Critical Value Method" and the "P-Value Method"?
 
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  • #2
Ooh, looks like homework...
 
  • #3
jokerwild said:
1)
In the basic probability theory the concepts of mutually exclusive events and independent events share prominent roles, can two events be both mutually exclusive and independent at the same time?
What is the DEFINITION of "mutually exclusive"?
What is the DEFINITION of "independent"?

2)
What are two vital concepts and the relationship between "Critical Value Method" and the "P-Value Method"?
Have you considered looking those up in your textbook
 
  • #4
For the second question I came up with this:

The critical value method is used for significance testing and is the value that a test must exceed in order for the null hypothesis to be rejected. The critical value would be the largest value of the test statistic that would end in the refusal of the null hypothesis. The p-value method is a measure of how much evidence you have against or for the null hypotheses.

Would this be a valid answer?
 

Related to Critical Value & P-Value Methods: Comparison & Relationships

1. What is the difference between a critical value and a p-value?

A critical value is a threshold used to determine if the results of a statistical test are statistically significant. It is compared to the test statistic, and if the test statistic is equal to or greater than the critical value, the results are considered significant. On the other hand, a p-value is a probability value that measures the strength of evidence against the null hypothesis. A smaller p-value indicates stronger evidence against the null hypothesis.

2. How are critical values and p-values related?

Critical values and p-values are related in that they both play a role in determining if the results of a statistical test are statistically significant. The critical value is compared to the test statistic, while the p-value is compared to a predetermined significance level. If the p-value is less than the significance level, the results are considered significant and the critical value is used to interpret the test statistic.

3. Can a critical value and a p-value have the same numerical value?

No, a critical value and a p-value cannot have the same numerical value. A critical value is a predetermined threshold used to determine the significance of a test statistic, while a p-value is a probability value that measures the strength of evidence against the null hypothesis. They are two different concepts and therefore cannot have the same numerical value.

4. How do critical value and p-value methods differ?

Critical value and p-value methods differ in their approach to determining if the results of a statistical test are statistically significant. Critical value method involves comparing the test statistic to a predetermined threshold, while p-value method involves comparing the p-value to a predetermined significance level. Additionally, critical value method is commonly used for hypothesis testing, while p-value method is used for both hypothesis testing and confidence intervals.

5. When should I use a critical value method versus a p-value method?

The choice between using a critical value method or a p-value method depends on the type of statistical test being conducted and the research question being addressed. In general, if the research question involves testing a specific hypothesis, the critical value method may be more appropriate. If the research question is more exploratory in nature and does not involve a specific hypothesis, the p-value method may be more suitable. It is also common for both methods to be used in conjunction with each other for a more comprehensive analysis.

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