Type i and ii errors, Applied Statistics

Assignment Help:

TYPE I AND II Errors

If a statistical hypothesis is tested, we may get the following four possible cases:

  1. The null hypothesis is true and it is accepted;

  2. The null hypothesis is false and it is rejected;

  3. The null hypothesis is true, but it is rejected;

  4. The null hypothesis is false, but it is accepted.

Clearly, the last two cases lead to errors which are called errors of sampling. The error made in (c) is called Type I Error. The error committed in (d) is called Type II Error. In either case a wrong decision is taken.

P(Committing a Type I Error)

=       P (The Null Hypothesis is true but is rejected)\

=       P (The Null Hypothesis is true but sample statistic falls in the rejection region)

=    α, the level of significance

P(Committing a Type II Error)

=       P (The Null Hypothesis is false but sample statistic falls in the acceptance 
         region)

=        β (say)

The level of significance,   α , is known. This was fixed before testing started.   β is known only if the true value of the parameter is known. Of course, if it is known, there was no point in testing for the parameter.


Related Discussions:- Type i and ii errors

Compute the roughness of several parametric densities, An approximation to ...

An approximation to the error of a Riemannian sum: where V g (a; b) is the total variation of g on [a, b] de ned by the sup over all partitions on [a, b], including (a; b

Principal components analysis, In the context of multivariate data analysis...

In the context of multivariate data analysis, one might be faced with a large number of v&iables that are correlated with each other, eventually acting as proxy of each other. This

Admixture in human populations, Admixture in human populations The inte...

Admixture in human populations The inter-breeding amongst the two or more populations which were previously isolated from each other for the geographical or the cultural reason

Correlation - cause and effect, Cause and Effect Even a highly signifi...

Cause and Effect Even a highly significant correlation does not necessarily mean that a cause and effect relationship exists between the two variables. Thus, correlation does

Applied, Question 1 Suppose that you have 150 observations on production (...

Question 1 Suppose that you have 150 observations on production (yt) and investment (it), and you have estimated the following ADL(3,2) model: (1 – 0.5L – 0.1L2 – 0.05L3)yt = 0.7

Systematic sampling, Systematic Sampling In Systematic Sampling ...

Systematic Sampling In Systematic Sampling each element has an equal chance of being selected, but each sample does not have the same chance of being selected. Here,

Analysis of variance (anova), Analysis of variance allows us to test whethe...

Analysis of variance allows us to test whether the differences among more than two sample means are significant or not. This technique overcomes the drawback of the method used in

Index number, give a elementary example for characterstics of index number

give a elementary example for characterstics of index number

Regression analysis and experimental design, For many decades, there has be...

For many decades, there has been considerable attention paid to identifying various factors that help to reduce the number of fatalities on Australian roads. In 1964 Victoria and S

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd