Jump to content
  • 2

Type I Error, Type II Error


Go to solution Solved by Ronaaq,

Alternative Hypothesis

 

Null hypothesis (Ho) - It is a hypothesis that says there is no statistical significance between the two variables in the hypothesis.
It is a statement of “No Difference”. It is a statement we are testing in order to determine whether or not that statement is true. The observed difference is purely by chance and there is no special cause for the difference

Alternative Hypothesis (Ha) - Hypothesis which states that there is statistical significance between the two variables in the hypothesis. It is a statement of “Difference”. It states that there
is real effect and the observations are affected by the effect and some pure chance variations

Type I Error -
is rejec
tion of Null Hypothesis when it is true. In simpler words, Type I error occurs when we conclude that there is a statistical difference when there is actually no difference. This is also known as a false positive or producer's risk

Type II Error - is failing to reject a Null Hypothesis when it is false or rejection of Alternate Hypothesis when it is true. In simpler words, Type II error occurs when we conclude that there is no difference when there is actually a statistical difference. This is also known as false negative or consumer's risk

 

An application oriented question on the topic along with responses can be seen below. The best answer was provided by Ronaaq on 14th November 2017. 

 

 

Question

Q 44. Can Type 1 Error of one situation be considered as Type 2 Error in a different situation? In other words, can Null Hypothesis statement for one situation be the same as Alternative hypothesis for another situation?  

 

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

Link to post
Share on other sites

13 answers to this question

Recommended Posts

  • 1
  • Solution

Null hypothesis (Ho):- It is a hypothesis that says there is no statistical significance between the two variables in the hypothesis.

It is a statement of “No Difference”. It is a statement we are testing in order to determine whether or not that statement is true. The observed difference is purely by chance and there is no special cause for the difference.

 

Alternative Hypothesis (Ha):- Hypothesis which states that there is statistical significance between the two variables in the hyphothesis.

It is a statement of “difference”. It states that there is real effect and the observations are affected by the effect and some pure chance variations.

 

Example:-

A person reaching his office through a route 1, after some days he takes another route 2.

We have recorded time taken for a person to reach his office.

Ho:- there is no difference in time taken to reach the office from route 1 and route 2.

Ha:- There is statistical difference in the time taken to reach the office from route 1 and route 2.

 

There is no situation in which Ho becomes and Ha and vice versa.

Ho statement always has the words “No Difference”. While Ha statements will always have “statistical difference” words.

Link to post
Share on other sites
  • 1

Hypothesis testing helps an Organization:

 

1.      Determine if making a change to a process input (x) significantly changes the output (y) of the process

2.      Spastically determine if there are differences between two or more process outputs.

 

Hypothesis testing assists in using samples data to make decisions about population parameters such as average, standard deviations and proportions.

 

Testing a hypothesis using statistical methods is equivalent to making an educated guess based on the probabilities associated with being correct. When an organization makes a decision based on a statistical test of a hypothesis, it can never know for sure whether the decision is right or wrong, because of sampling variation.

 

Regardless how many times the same population is sampled, it will never result in the same sample mean, sample standard deviation, or sample proportion. The real question is whether the differences observed are the result of changes in the population, or the result of sampling variation.

 

Statistical tests are used because they have designed to minimize the number of times an organization can make the wrong decision.

 

There are two basic types of errors that can be made in a statistical test of a hypothesis:

 

1.       A conclusion that the population has changed when in fact it has not

2.      A conclusion that the population has not changed when in fact it has

 

The first error is referred to as a type I error. The second error is referred to as Type II error. The probability associated with making a type I error is called alpha (α) or the α risk. The probability of making a Type II error is called beta (β) or the β risk

 

Let’s consider the example of a prosecuting attorney trying a case in a court of law. The objective of the prosecuting attorney is to collect and present enough evidence to prove beyond a reasonable doubt that a defendant is guilty.

 

If the attorney has not done so, then the jury will assume that not enough evidence has been presented to prove guilty; therefore they will conclude the defendant is not guilty in the absence of enough evidence.

 

 

 

H0 is true
 Truly not guilty

H1 is true
 Truly guilty

Accept null hypothesis
 Acquittal

Right decision (probability = 1 - α)

Wrong decision - fail to reject the null when it is false (probability = β)
 Type II Error

Reject null hypothesis
 Conviction

Wrong decision - rejecting the null when it is true (probability = α)
 Type I Error

Right decision (probability = 1 - β)

 

 

 

If the α risk is 0.05 ,any determination from a statistical test that the population has changed runs a 5% risk that it really has not changed. There is a 1 – α ,or 0.95 ,confidence that the right decision was made in stating the population has changed.

 

If the β risk is 0.10, any determination from a statistical test that there is no change in the population runs a 10% risk that there really may have been a change. There would be a 1- β or 0.90 , “Power of the test “ , which is the ability of the test to detect a change in population.

 

A 5% α risk and a 10 % β risk are typical thresholds for the risk one should be willing to take when making decisions utilizing statistical tests. Based upon the consequence of making a wrong decision, it is up to the decision maker to determine the risk he or she wants to establish for any given test, in particular the α risk. β risk ,on the other hand ,is usually determined by the following :

 

1.      δ : The difference the organization wants to detect between the two population parameters. Holding all other factors constant ,as the δ increases, the β decreases.

2.      σ : The average (pooled) standard deviation of the two populations. Holding all other factors constant, as the σ decreases, the β decreases.

3.      n: The number of samples in each data set. Holding all other factors constant ,as the n increases, the β decreases

4.      α : The alpha risk or decision criteria ,holding all other factors constant ,as the α decreases, , the β increases

 

p- Value

 

How does an organization know if a new population parameter is different from an old Population parameter? Conceptually, all hypothesis tests are the same in that a signal (δ) – to noise (σ) ratio is calculated (δ/ σ) based on the before and after data. The ratio is converted into a probability, called the P-Value, which is compared to the decision criteria, the α risk. Comparing the P value (which is actual α of the test) to decision criteria (the stated α risk) will help determine whether to state the system has or has not changed.

 

Unfortunately, a decision in a hypothesis testing is never conclusively be defined as a correct decision. All the hypothesis test can do is minimizing the risk of making a wrong decision.

 

Step to conduct Hypothesis Testing:

 

1.      Define the research hypothesis for the study.

2.      Explain how you are going to operationalize (that is, measure or operationally define) what you are studying and set out the variables to be studied.

3.      Set out the null and alternative hypothesis (or more than one hypothesis; in other words, a number of hypotheses).

4.      Set the significance level.

5.      Make a one- or two-tailed prediction.

6.      Determine whether the distribution that you are studying is normal (this has implications for the types of statistical tests that you can run on your data).

7.      Select an appropriate statistical test based on the variables you have defined and whether the distribution is normal or not.

8.      Run the statistical tests on your data and interpret the output.

9.      Reject or fail to reject the null hypothesis.

 

Rejecting or failing to reject the null hypothesis

Let's return finally to the question of whether we reject or fail to reject the null hypothesis.

If our statistical analysis shows that the p-value is less than or equal to the level of significance which is a cut-off point that we defined, and then we reject the null hypothesis and accept the alternative hypothesis.

Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis.

A common misconception is that statistical hypothesis tests are designed to select the more likely of two hypotheses. Instead, a test will remain with the null hypothesis until there is enough evidence (data) to support the alternative hypothesis.

 

Link to post
Share on other sites
  • 1

I understand, that a Type 1 / Type 2 error or the formulation of the Null / Alternative hypothesis depends on the perspective with which the research question is being pursued.

 

Typically:

  • Null Hypothesis denotes, “There is No Change” or Result After is same as Result Before a modification / change  ( any difference is by chance)
  • Alternative Hypothesis denotes, “There is A Change” or Result After is different from Result Before a modification / change. It is research question to be answered.

 

(While formulating the Alternative hypothesis care should be taken to clearly identify what the researcher is trying to prove regarding the “results before” and “results after” i.e. whether the two results are Not equal or Greater or Lesser than one another)

 

So, I feel, that the Null /Alternative Hypothesis statements or Type 1/Type 2 error would switch if the research question /perspective changes.

 

Example:

 

A medicine manufacturer must create a capsule with 50 mg dosage of an ingredient Z. So, it should be ensured that the machine calibration is correct and accurate.

 

Research Question 1: Is the machine calibration inaccurate and the mean dosage of ingredient Z (in the population data) is different than 50 mg?

  • Null Hypothesis: Machine Calibration is accurate and the average dosage of ingredient Z is 50 mg. (population mean dosage = 50 mg).
  • Alternative Hypothesis: Machine Calibration is inaccurate and the average dosage of ingredient Z is not 50 mg (population mean dosage ≠ 50 mg).

 

Research Question 2: Is the machine calibration accurate and the mean dosage of ingredient Z (in the population data) is equal to 50 mg?

  • Null Hypothesis: Machine Calibration is inaccurate and the average dosage of ingredient Z is not 50 mg (population mean dosage ≠ 50 mg).
  • Alternative Hypothesis: Machine Calibration is accurate and the average dosage of ingredient Z is 50 mg. (population mean dosage = 50 mg).

So, in my opinion, the research question perspective is very important to formulate the Null / Alternative hypothesis or determine Type 1/Type 2 error.

Link to post
Share on other sites
  • 0

Giving a try to Visualize where the Confidence Interval varies between 90%/95%/99% !! In a highly critical operation, the Confidence Interval of 99% is used and vice versa(a 90% Confidence Interval is used)

The corresponding P values are : 0.10 / 0.05 / 0.01

For Example, for a Confidence Interval of 95%, after performing the Hypothesis Testing, if the calculated P Value is 0.06, rejecting the Null Hypothesis will be a Type I error. 

The same scenario, with a Confidence Interval of 90%, rejecting Null Hypothesis will be considered a "Right" Decision.

Apologies, couldn't identify a scenario as stated in the question !!

Same situation being 1) Right or Type I Error 2) Right or Type II Error could be visualized.

Link to post
Share on other sites
  • 0

Every hypothesis test uses samples to interfere properties of a population on the basis of an analysis of the sampling information. Therefore,  there is some chance that although the analysis is flawless,  the conclusion may be incorrect.  These sampling errors are not errors in usual sense,  because they can't be corrected.  There are two types of error Type 1 and type 2 Error.  When we reject null hypothesis when it is true that's is type 1 Error and it is producer risk.  When we fail to reject null hypothesis when it is false,  then type 2 Error occurs and it is consumers risk. 

To ensure that hypothesis tests are carried out portered,  it is useful to have a well defined process for conducting them. 

1specify the parameters to be used. 

2.state the null and alternate hypothesis. 

3.state alpha value

4determone test statistic

5. Define Rejection criteria

6.compute critical values and test statistics 

7.state conclusion for the test. 

 

Null hypothesis for one situation can be same as alternate hypothesis of another situation.  It depends how we are considering the situations. If null statement of one situation is used as alternative of another situation it will also reverse the definition of type 1 and type 2 Error. 

We need to think more carefully about which hypothesis is more appropriate and situation before finalise the statement for null and alternate hypothesis. 

The null and alternate both are mutually exclusive so wee need to take care while finalise the statement according to situation 

For example

We are saying when we are standing o earth our eyes are able to see that earth is flat surface so in this case null hypothesis is that earth is flat when we are seeing while standing on a surface and alternate hypothesis is that earth is not flat when we are seeing while standing on a surface. 

Now another situation that we are saying earth is not flat when we are seeing from space. In this case null hypothesis is while seeing from space earth is not flat and alternate hypothesis is while seeing from space earth is flat. 

 

Another example of the same that sun is revolving round the earth as day change to night.  In this example null is sun revolvs around earth as day change to night. 

Alternate hypothesis is that sun does not revolve round earth. 

If we say as day change to night it means earth is revolving around its own axis. In this null is as earth revolvs around duty own axis that's why day change to night. Alternatee is earth does revolves around its own axis. 

 

Another  example of student passing an exam >=40. Null hypothesis is passing exam with 40
Alternate is it should be greater than 40 to excel in exam.

Null says no difference before and after in terms of grades calculated on the other hand Alternate says there is a difference.Now in this case, passing exam is acceptable but greater than Benchmark set is also acceptable. Null can be used as alternate in this situation If we have to consider that null is equal to and alternate is less than or not equal to or greater than. 

 

Another example is of average salary of an engineer in a company is =>50000 per month. 

 

So there are various situation where we can use null of one situation  as alternate hypothesis of another situation but wee need to think carefully while deciding the statement. 

Link to post
Share on other sites
  • 0

Type I error is rejecting a Null Hypothesis that is a true (should have been accepted).

Type 2 error is accepting a Null Hypothesis that is false (should have been rejected)

 

Let us discuss this question with an example.

 

Machine A and Machine B are producing certain part, and the weight of the part is a characteristic of interest. The weights of samples taken from these machines are as follows:

A – 10.8, 10.3. 10.7, 10.9, 10.4, 10.7, 11.0, 10.3, 10.8, 10.7.

B – 11.2, 11.3, 11.1, 11.6, 11.0, 11.6, 10.8, 11.4, 11.4, 11.6.

Mean weight for Machine A = 10.6

Mean weight for Machine B = 11.3

 

Situation - 1

Assume that in reality there is a significant weight difference on the output from Machine A and B. But we are trying to prove using a Hypothesis test.

Hypothesis statements:

H0 : Mean weight from Machine A  =   Mean weight from Machine B

H1 : Mean weight from Machine A    Mean weight from Machine B

The true conclusion would have been to reject the Null Hypothesis, in this situation.

However, as a result of the test, if H0 gets retained, it is an incorrect acceptance of null hypothesis and is a Type-2 error

 

Situation - 2

Now let’s examine another situation. Here we want to test the effectiveness of an improvement action taken, which is expected to bring down the differences on the weight of their outputs. Our aim is to improve the process to reduce the difference. Assume that the difference between the machines continues to exist. The Hypothesis statements may be as follows:

H0 : (Mean weight from M/c B ) – (Mean weight from M/c A) = 0.7

H1 : (Mean weight from M/c B ) – (Mean weight of M/c A) ≤ 0.7

The true conclusion would be to accept the null hypothesis, in this situation and accept the difference is equal to 0.7

However, conducting the Hypothesis test, if H0 gets incorrectly rejected, it means that the means are having difference which is less than 0.7. This amounts to Type-1 error.

 

Thus, the null hypothesis in the situation in situation-2 is the alternate hypothesis in situation-1

Link to post
Share on other sites
  • 0

Type 1 error is when Null is true but gets rejected, type 2 error is when null is false but gets accepted. When a producer becomes a consumer then type 1 and 2 error contexts will change. In case if competent candidate is rejected then type 1 error occur, where as if the incompetent candidate is hired then type 2 error.

Link to post
Share on other sites
  • 0

An old proverb goes, “One man’s candy is another man’s poison”. This is true in the case of Hypothesis testing also. The following situations could be examples for a Type 1 error in one situation being a Type 2 error in another situation, which includes Conditions, Environment, Organization, Point of Time etc.

 

Improved Technology

In a factory, a process is presently being run using Technology A. The organization is upgrading this process to Technology B. By this, all products that were produced through Technology A would be produced through Technology B. This progress is being tracked by a KPI which is the proportion of product volumes which is produced through Technology B. When this progressing to completion, there is another wonder technology, Technology C that is doing the rounds. The organizational Management decides to bite the Technology C bullet. This progress of this upgrade is also tracked using the same KPI, “proportion of product volumes which is produced through Technology B”. While earlier, the objective was to maximise the proportion of product volumes which is produced through Technology B, now the objective is to minimize the same KPI. In this case, a Type 1 error in A to B upgrade would be a Type 2 error in B to C upgrade.

 

As an example of the above, the manufacture of plates for chains could be considered. The traditional method would be of blanking sheets first and piercing the blanks next. This is Technology A. The first improvement is to improve the blank layout, which uses sheets better and there is less of material wastage leading to cost reduction. Improved blank layout is Technology B. The next improvement is to have a progressive tool, which pierces the sheet and then blanks plates in a pierced condition. This is Technology C.

 

Salvage and repair section of a factory

 

In a typical “Stockholm Syndrome” case, the extent to which the Salvage and repair section in a manufacturing unit is utilized is also a measure of the overall quality of production in the factory. If the Salvage team is kept busy, it would mean that the factory produces too many out of specification products. If there were any improvements being implemented in the Salvage section, then if a hypothesis test were to be conducted, the Type 1 error on a Salvage section parameter would be close to being a Type 2 error for the overall organization.

 

Supplier – Customer contradictions

There could be some processes or components or services outsourced as an exception only if the customer organisation is facing a problem. This will mean that more the outsourcing of that particular service, process or component, more the problems the organization is facing. While for the vendor, volume produced is a positive KPI, for the customer organization it is negative. In this situation also, a Type 1 error for the vendor would be a Type 2 error for the customer.

 

Public Service Vs Private Enterprise

As part of a service spirit driven, health-driven and value driven campaign, a state or local government implements various measures to supply clean, drinking water to all its residents. This it does by maintaining its natural water resources well, implementing rain water harvesting, strictly controlling effluent disposal into water bodies, purifying water supplied through traditional and modern methods and various other administrative and legal measures. This results in all residents getting good quality drinking water. This also results in a decrease in the cases of patients suffering from water-borne diseases. But the success of the same campaign has also resulted in a reduction in the sales of bottled water and also various types of water purification equipment. If the government’s campaign is tracked using (say) people not getting drinking water, a Type 1 error here could actually be a Type 2 error for those organizations, who are impacted adversely by this success.

 

Others

In addition to the above, whenever there is a fundamental difference in the motives of two different entities, this “phenomenon” can be observed.

Link to post
Share on other sites
  • 0

Null hypothesis

It states that the assumption that there is no difference in parameters for two or more populations and that any observed difference in samples is due to chance or a sampling error.

 

Alternate Hypothesis:

An alternate hypothesis is any hypothesis that differs from the given null hypothesis

Type 1 Error:
This occurs when null hypothesis is actually true, but it is rejected. This is also known as Alpha Error.

 

Type 2 Error:
This occurs when null hypothesis is actually false, but it is failed to be rejected. This is also known as Beta Error.


As we perform the hypothesis testing, there are 4 possible outcomes which can be put in a truth table format.

Let us put the truth table for this

 

Decision

 

True

 

False

 

Fail to Reject Null Hypothesis

Correct Decision

Type II Error

Reject the null hypothesis

Type I Error

Correct Decision

 

Let us see a hypothetical situation

A person (Person1) was seen with a gun on a place where a murder had happened. He was arrested on suspicion of murdering that person (Person2) who was lying down. He is taken to a high court.

 

Now,
Null Hypothesis (h0) states that “Person1 is not guilty”
Alternate Hypothesis (ha) states that “Person1 is guilty”

 

Then the possible outcomes for the above scenario would be

 

Decision

 

Innocent

 

Guilty

 

Set the person free

True

Type II Error

Jail the person

Type 1 Error

True

 

Now, with circumstances and other evidences, the innocent person(Person1) is charged with murder and a Type 1 Error has occurred now.  The innocent is jailed. Now, Person1’s lawyer takes the case to the highest court of the land (Supreme Court).  With his oratory skill and with valid arguments and showing evidences that his client did not do the murder, the lawyer convinces the judge that his client (Person1) did not do the murder and hence is innocent.  The judge accepts this and makes the decision of letting person1 free. 

 

Now the outcome is

Decision

 

Innocent

 

Guilty

 

Set the person free

True

 

Type II Error

Jail the person

Type 1 Error

True

 

While accepting the judge’s decision, the prosecutor interrupted that there has to be another case on Person1.  The root cause for this suspicion on murder was due to Person1 carrying a gun.  The prosecutor said that it is illegal to carry a gun without license and Person1 was carrying it without a license and hence he should be jailed.  The Judge agreed to this valid argument but decided not to punish Person1 , because he (Person1) had spend some time in jail for a sin that he did commit and had mental agony. However the judge warned Person1 to be careful going forward.  So in nutshell, even though Person1 was guilty, he was freed.

 

Decision

 

Innocent

 

Guilty

 

Set the person free

True

 

Type II Error

 

Jail the person

Type 1 Error

True

 

Conclusion:

There are cases where type 1 error can be considered as type 2 error.  In the above mentioned example, the null hypothesis states that the person is not guilty. But the Person is jailed when he is actually not guilty, when he is tried for the murdering case. So a type 1 Error happens. But on appeal on the next higher court, the person is set free. But he is found guilty on illegal possession of a gun. But considering that the person has already served sentence ,the judge decides to set free with a caution remark. So this becomes a type 2 error (person set free inspite of being guilty).

 

 

 

Link to post
Share on other sites
  • 0

Q 44. Can Type 1 Error of one situation be considered as Type 2 Error in a different situation? In other words, can Null Hypothesis statement for one situation be the same as Alternative hypothesis for another situation?  

 

Null Hypothesis:

It is commonly denoted as Hsub0.  This is typically a standard observation made by the researcher to say that there is no interaction between these variables. It is called null hypothesis.

 

Alternate Hypothesis:

It is denoted as Hsub1. Opposite of null hypothesis is alternative hypothesis, also called as researcher hypothesis, which is their prediction and measured for existence of relationship between these variables.

 

Significance:

Statistical tests are done to determine the relationship is significant. It also means that the difference in the results are not by random chance.

 

Type 1 & Type II errors:

No hypothesis is 100% certain for decision making. Because it is based on the probability value, there is chance of making a wrong decision as well. There are two types of errors possible in hypothesis. Type I and type II errors.

 

Type I errors are when the null hypothesis is true and you reject the null. This is denoted by level of significance.

 

Type II errors are when the null hypothesis is false and you fail to reject the null and accept alternative. This is denoted by Power test.

 


Truth about the population

 

Decision based on sample

H0 is true

H0 is false

Fail to reject H0

Correct Decision (probability = 1 - α)

Type II Error - fail to reject H0 when it is false (probability = β)

Reject H0

Type I Error - rejecting H0 when it is true (probability = α)

Correct Decision (probability = 1 - β)

 

Negations:

There are certain negations before making any hypothetical statements.

  • Null hypothesis: “x is equal to y.” Alternative hypothesis “x is not equal to y.”
  • Null hypothesis: “x is at least y.” Alternative hypothesis “x is less than y.”
  • Null hypothesis: “x is at most y.” Alternative hypothesis “x is greater than y.”

Example of Null and alternative hypothesis with 2 types of errors.

·         Null hypothesis (H0): μ1= μ2

The two medications are equally effective.

·         Alternative hypothesis (H1): μ1≠ μ2

The two medications are not equally effective.

In the above example, the errors would be defined as

Type I error – if the physician rejects the null hypothesis and concludes that the 2 medications are different when actually it is not.

Type II error – If the physician fails to reject the null and concludes that the 2 medications are same when actually it is not same. Type II error is sometimes serious or life threatening.

Having considered the consequences of the risk or seriousness of commiting one type of error, the decision is taken accordingly.

 

Refernce: http://support.minitab.com/en-us/minitab-express/1/help-and-how-to/basic-statistics/inference/supporting-topics/basics/type-i-and-type-ii-error/

 

Another Example

Null hypothesis - Earth is not at the center of universe.

Alternative hypothesis - The Earth IS at the center of the Universe.

In such statements, instead of proving one of the favorable conditions only, you have to first disprove that the theory of rejecting the null is equally important to accept the alternate. It is to just prove that the study or experiment conducted is flawless. If you only prove the alternate to be effective and not proving null to be rejected would set a system failure.

Type I Error :

In this example, the astronaut concludes by watching the sky over nights and conclude that the all other planets revolve around the earth. Hence the earth is at the centre of universe. So, alternate is proven. And the null is rejected.

Type II Error –

Here the astronaut concludes that the planet is not revolving around the earth. In fact the earth is revolving aroudnd the planets. Hence the earth is not at the center, because it keeps moving. Here he fails to reject the null and accept it, when actually it is not.

 

Conclusion:

So,  to conclude the hypothesis statements depends on the situations we study and it is equally important to disprove the one with accepting the other hypothesis.

Typically the null hypothesis says that there is nothing new happened either before and after or after the solution implemented. The difference is equal to 0. Generally, the people’s claims are always true until proven otherwise. If we have to prove, show evidences to reject the null hypothesis.

To conclude the 2nd part, a null hypothesis can never be a alternate hypothesis in any type of situations, since the null hypothesis is generally a work done to nullify the statements or claims by people. Whereas the alternative hypothesis is a opposite nature of null hypothesis. It is not a equalized statements. It can be greater or lesser of the effect studied.

 

Thanks

Kavitha

Link to post
Share on other sites
  • 0

Type 1 & Type 2 error:

Type 1 error is one that happens when we reject a true null hypothesis

Type 2 error happens when we fail to reject a false null hypothesis.

Now what is true null Hypothesis: A true null Hypothesis is the one which hypothesize the true nature/facts of an issue or a thing..

For example:-

Decision to go out based on whether it rains outside or not.  

We want to go outside: this is our requirement, but the decision will be based on Hypothesis testing.

Risk that can be taken say is 5%, meaning if the chances that it rains up to 5%, then we shift to Alternate hypothesis, meaning we go outside.

If the chance is more than 5%, we remain inside, meaning we remain in Null.

From the above example:- if we have to say that the error:-

Actual status -- The chances of raining is more than 5%:

Type 1 error :

The chances of raining is more than 5%: But we go out.

Actual Status – The chances of raining is not more than 5%: But we assume it will be more & remain inside, this is false null Hypothesis.

 Type 2 error:

The chances of raining is not more than 5%, but we don’t go outside. Meaning we missed to meet our requirement : Type 2 error, we could not reject the false null Hypothesis.

Can Type 1 error be considered as Type 2 error in a different situation ?

Could be considered but I feel if the requirement changes.

in above case, if we want to go outside for a rain dance, meaning we can only go if it rains.

In that case the errors could be considered vice versa.

Basically it all depends on what we require. the perspective will only change based on the requirement.

For example:-

we accept the lot if the length of the fabric is not less than 45 cms. :

We do not accept the lot if the length of the fabric is less than 45 cms

Different situation leads to different requirement. hence said.

Link to post
Share on other sites
  • 0

This was a tricky question and the answer is that exact reversal of the same statement is not possible. Hence, one situation's null hypothesis, in the same form, cannot be alternate hypothesis in another situation.

 

Keeping this in consideration, Ronaaq's answer has been chosen as the best answer - owing to the fact that this is the only answer that says so. Close second is Venugopal's answer in which he has indicated so with the help of an example.

 

A big applause to everyone who attempted this question as it undoubtedly was a tough one.

Link to post
Share on other sites
Guest
This topic is now closed to further replies.
  • Who's Online (See full list)

    There are no registered users currently online

  • Forum Statistics

    • Total Topics
      2,864
    • Total Posts
      14,505
  • Member Statistics

    • Total Members
      55,043
    • Most Online
      888

    Newest Member
    Dan Weigel
    Joined
×
×
  • Create New...