# Which critical region is best?

## Which critical region is best?

The “best” critical region is one that minimizes the probability of making a Type I or a Type II error. In other words, the UMPCR is the region that gives the smallest chance of making a Type I or II error. It is also the region that gives a UMP test the largest (or equally largest) power function.

## Who invented p value?

Sir Ronald A. Fisher
Although the p value was introduced by Karl Pearson in 1900 with his chi square test [17], it was the Englishman Sir Ronald A. Fisher, considered by many as the father of modern statistics, who in 1925 first gave the means to calculate the p value in a wide variety of situations [3].

Why is Neyman Pearson lemma the most powerful test?

The Neyman-Pearson lemma shows that the likelihood ratio test is the most powerful test of H0 against H1: Theorem 6.1 (Neyman-Pearson lemma). Let H0 and H1 be simple hypotheses (in which the data distributions are either both discrete or both continuous).

What is the difference between Neyman Pearson’s approach and Fisher’s P value approach for hypothesis testing?

My understanding is: p-value is to tell us what to believe (verifying a theory with sufficient data) while Neyman-Pearson approach is to tell us what to do (making best possible decisions even with limited data).

### What is the region of rejection?

A critical region, also known as the rejection region, is a set of values for the test statistic for which the null hypothesis is rejected. i.e. if the observed test statistic is in the critical region then we reject the null hypothesis and accept the alternative hypothesis.

### What is the most powerful statistical test?

A very important result, known as the Neyman Pearson Lemma, will reassure us that each of the tests we learned in Section 7 is the most powerful test for testing statistical hypotheses about the parameter under the assumed probability distribution.

Who founded the hypothesis testing?

In the 1920s, Ronald Fisher developed the theory behind the p value and Jerzy Neyman and Egon Pearson developed the theory of hypothesis testing.

Who is known as the father of null hypothesis?

Gosset and R. A. Fisher.

#### Is UMP test unique?

Suppose that X is a sample of size 1, 乡0 = {P0}, and 乡1 = {P1}, where P0 is N(0,1) and P1 is the double exponential distribution DE(0,2) with the p.d.f. 4−1e−|x|/2. Since P(f1(X) = cf0(X)) = 0, there is a unique nonrandomized UMP test. α = E0[T∗(X)] = P0(|X| > t)+P0(|X| < 1−t).

#### Who made the t test?

William Sealy Gosset
In 1908 William Sealy Gosset, an Englishman publishing under the pseudonym Student, developed the t-test and t distribution. (Gosset worked at the Guinness brewery in Dublin and found that existing statistical techniques using large samples were not useful for the small sample sizes that he encountered in his work.)

What is Neyman Pearson inference?

The Neyman-Pearson Lemma is a way to find out if the hypothesis test you are using is the one with the greatest statistical power. The power of a hypothesis test is the probability that test correctly rejects the null hypothesis when the alternate hypothesis is true.

What is the fisherian significance test?

Fisher proposed tests of significance as a tool for identifying research results of interest, defined as those with a low probability of occurring as mere random variation of a null hypothesis.

## What is left tailed?

A left-tailed test is used when the alternative hypothesis states that the true value of the parameter specified in the null hypothesis is less than the null hypothesis claims.

## How do I find my ump?

To find a UMP test via the Neyman Pearson lemma, you need to check that the cutoff value k does not depend on θ1 ∈ Θ1 and usually need to transform the NP test statistic to put the test in useful form. With exponential families, the transformed test statistic is often T. Example 7.2.

Who is the father of null hypothesis?

Ronald Fisher

Sir Ronald Fisher FRS
Born Ronald Aylmer Fisher17 February 1890 London, England, UK
Died 29 July 1962 (aged 72) Adelaide, SA, Australia
Nationality British
Education Harrow School

What are the 7 steps in hypothesis testing?

1.2 – The 7 Step Process of Statistical Hypothesis Testing

• Step 1: State the Null Hypothesis.
• Step 2: State the Alternative Hypothesis.
• Step 3: Set.
• Step 4: Collect Data.
• Step 5: Calculate a test statistic.
• Step 6: Construct Acceptance / Rejection regions.
• Step 7: Based on steps 5 and 6, draw a conclusion about.

### Who is father of statistics in world?

For his work in statistics, he has been described as “a genius who almost single-handedly created the foundations for modern statistical science” and “the single most important figure in 20th century statistics”….Ronald Fisher.

Sir Ronald Fisher FRS
Scientific career
Fields Statistics, genetics, and evolutionary biology

### Who invented statistics?

John Graunt
The birth of statistics is often dated to 1662, when John Graunt, along with William Petty, developed early human statistical and census methods that provided a framework for modern demography. He produced the first life table, giving probabilities of survival to each age.