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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. All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/ Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening 5 PM as per Indian Standard Time. The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term.

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

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

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.

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.

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.

The control limits for Control charts are derived based on its own data, applying the statistical principles applicable for the distribution under which the data falls into. ‘c’ charts and ‘u’ charts are used for ‘count’ data, such as number of defects in as part / sample. The choice of ‘c’ or ‘u’ are made based on fixed or varying sample sizes. It goes without saying that, when these charts are used for monitoring count of defects, anyone will only want the defect count to be as low as possible. Hence the UCL for defect makes sense, but the question is “why do we require a lower control limit for defect count?” LCL - little significance: Some times when the limits are worked out, the lower control limit might assume a negative value; in such cases, the calculated LCL, being negative has no meaning and the LCL is taken as zero. Obviously, no point is going to fall below zero, and hence the LCL is of little significance here, except when the count is zero. However, if we are using the ‘run’ patterns for our study of stability as per its rules, then the 1sigma and 2sigma limits are also used, apart from the LCL. LCL - Could unearth important finding: Where we do have a positive LCL, and if some data points fall outside, it indicates a situation that may be “too good to be true”. It will be worthwhile to investigate the special cause(s) that could have resulted in this occurrence. 1. It could be measurement a error. For eg. a wrong gauge could have been used and it was failing to detect defects. 2. It could be a change of an inspector that added subjectivity in the defect identification, especially if the defect was to be visually identified. 3. Or it could be some genuinely favorable condition that brought down the defect count. These could be opportunities of unearthing some favorable factor that we have been missing or ignoring. One example from my experience is when we were using ‘u’ chart for plotting the count of character errors in captured data, processed from multiple sites. Few consecutive days we observed the count falling below the LCL. Upon investigation, we realized that one particular processing site was down during those days. Further probe revealed that this particular site was performing with an operating application, whose version was obsolete. Once the correct version was installed, we were able to sustain a reduced mean error count and the control limits could be narrowed. LCL - More important (than UCL?) 4. It is not necessary that c and u charts should always represent defects, which are always “lower the better”. For eg. a consumer goods company selling a popular brand of shaving cream, wants to do a study to see the number of individuals out of sample who use their product. They pick a sample of individuals in a city every day and find out how many of them are using their brand. In this case, since the sample varies every day and it is a count data, ‘u’ chart applies. However, this is a case where "higher the count, the better". Hence the LCL and the count falling below LCL is of utmost importance.

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.