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# Alpha and Beta

Go to solution Solved by aritradasgupta187,

Alpha (or Significance Level) is the maximum allowed probability of committing Type I error in hypothesis.

Beta is the maximum allowed probability of committing Type II error in hypothesis.

An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Aritra Das Gupta on 8th Oct 2020.

Applause for all the respondents - Nilesh Akre, Aritra Das Gupta, Sanat Kumar

## Question

Q 303. In hypothesis testing, the permissible probabilities for errors are Alpha and Beta. The commonly used probabilities are 5% and 10-20% respectively.

Provide examples where unusual values for Alpha and Beta are needed.

Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.

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• Solution

In any hypothesis testing we have to decide on the level of significance which is denoted by alpha. This is important as failure to choose correctly null hypothesis can cause Type 1 error.

IF α is small - There is lass chance of incorrectly rejecting a Null hypothesis (H0)

Since the power is low this decreases the chance of detecting an effect if one exists

IF α is Large - There is a higher chance of incorrectly rejecting the Null hypothesis (H0)

Since the power is high there is high chance of detecting the effect

To Select α for a Hypothesis test we need to understand which mistake will be worse ,finding an effect which does not really exist or not finding an effect that does exists .

Examples where α is Small

1. Buying an expensive machine as the cost might be very high and we might set a very low α so that we are able to determine if there is any effect on productivity post buying the new machine

2. Fitting a new car model with a new engine Vs a old one

3. Changing the breaking system in an elevator with a new mechanism which is more economical. This can have serious impact on safety if the machine fails to work

4. Changing a bearing in a jet plane with new ones which are less expensive

5. Using cheaper building material for construction to bring down overall cost of the project. In order to save money if the company replaces the material there can be serious implication to the lives of people

6. New Iron & steel used in a dam construction project from a different vendor who is offering a discount

7. New material used for GAS pipeline Vs the old one which can reduce the cost. If the company does not test this adequately then there can be major catastrophe and company can be answerable to government & public

Examples where α is Large-

1. Checking the effectiveness of a new delivery model for a chain of restaurant which is already getting customer complaints due to delivery delays

2.A new Sales strategy for a firm which is making losses due to low sales

3. A decision for Digital strategy implementation for a company which is on verge of bankruptcy

4.A new repair allocation process for a Insurance company which is loosing customer base due to the high claims life cycle time

The above are some examples which will help to decide whether to take a higher or lower α value.

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Alpha value: Is the probability of making mistake of rejecting good lot i.e. rejecting null hypothesis when it is true

Beta value: Is the probability of making mistake of accepting defective lot i.e. accepting null hypothesis when it is false

Alpha value is producer's risk whereas Beta is Consumer's risk.

When Alpha decreases Beta value increases and vice versa.

Deciding Alpha and Beta value depends on circumstances. Generally alpha value is kept at 5% and Beta value at 20%

When to keep Alpha below 5% and beta above 20%

• When cost is the focus
• When margin is low in case of cheap items like nails manufacturing

When to keep Alpha above 5% and beta below 20%

• When it relates with the human safety and mistake may result into big disaster
• When it relates with competency and skill

Examples

1.In case of costly item alpha can be kept as low as possible as the rejecting good lot can not be affordable

2.In low cost items alpha can be kept low as defective nails not going to affect consumer too much

3.In manufacturing of airways assembly and spare parts where defective parts may result into disaster ,alpha value should be kept as large as possible so as to reduce the type 2 error i.e beta value

4.While selecting top management candidate alpha value should me more than 5% to reduce the beta value as selection of wrong candidate will not be affordable to organization whereas in low skill job case is reverse ,alpha can be kept more than 5%  as low skill candidate can be trained .

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In inferential statistics, Null and Alternate Hypothesis are defined (Ho- Null and Ha- Alternate) to conduct hypothesis testing.

Null Hypothesis – states population parameters or commonly known facts

Alternate Hypothesis – is the statement that one wants to prove using statistics (normally one defines alternate hypothesis first)

Post defining hypothesis a sample is selected from population for the test and based on the p value either Null is accepted or Fail to accept Null Hypothesis

P value < significance value (α) –Fail to accept Null hypothesis

P value >= significance value (α) –Accept Null hypothesis

At time due to selection of wrong samples result get impacted which is classified as Type 1 and Type 2 error

So Type 1 error is normally termed as α error and Type 2 as β error

In normal circumstance probabilities (significance level) are 5% and 10-20% but at time these % are altered

Examples when probabilities (significance level) are very less even than 1%

1)      Depends on the type of industry where one want to reduce the error –where high precision are required:

a.       Pharma industry

b.      Aviation industry

c.       Metro-logy products

d.      Ophthalmic lenses

e.      Hospitals  etc

2)      When population data is easy to collect

Reducing the significance levels requires high effort (in collecting large sample) and high cost.

Hence low significance level is not advisable for businesses where high precision are not required

Decreasing significance level increases the chances of type 2 errors. Hence if significance levels are selected ensure that there sample size is very large to avoid errors (high sample size increase the power that is 1-β)

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Aritra Das Gupta has given the best answer to this question for correctly explaining the effects of a higher and a smaller alpha along with many relevant examples.

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