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The first thing is to make a decision on using a one-tail or two-tail test. If you want to compare some product between two companies, then you can go for the two-tail test. If you want to test the performance of a product, then you can go for the one-tail test. The next thing is to identify whether the collected data are one sample, or two sample or more than two samples and you should check the nature of the data: whether it is discrete or continuous. Finally, by selecting the population parameter whether it is the mean, median or the standard deviation. Depending on the population parameter, the statistical test can be performed to find a valid inference. Common practice in every statistical analysis is that if the sample size is small (usually observations less than or equal to 30) then one can use t-test (independent sample, two-sample), fisher’s exact test, etc., depending on the nature of the data. If the sample size is larger, then one may go for z-test, chi-square test, etc.

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Hello Ransingh

 

Both Type I (alpha) and Type II (Beta) errors may be critical. However, mostly we are interested in knowing whether the process has changed or not. Hence we look at the p-value and then compare it with alpha. Reason is because alpha error is the threshold for deciding whether the sample data is coming from the same population or from a different population. If the p-value (calculated) is more than alpha, we go conservative and conclude that the sample data is coming from the same population, whereas whenever p-value is less than alpha, we conclude that there is reasonable confidence that the sample is from a different population. 

Type II (Beta) error plays a significant role in deciding the sample size for hypothesis testing. And therefore, we first decide the minimum sample size and then carry out the hypothesis testing.

 

The above is the traditional knowledge, however there are instances where we are interested in process not changing at all. In such cases, the Null and Alternate hypothesis are interchanged (a word of caution - not the usual practice except for in some industries). With the Null and Alternate hypothesis changed, alpha effectively becomes beta error and vice versa. E.g. Checking for bio-equivalence in pharma industry.

 

Refer the below links for more clarity

 

1. https://www.benchmarksixsigma.com/forum/topic/34918-type-i-error-type-ii-error/

 

2. https://www.benchmarksixsigma.com/forum/topic/35850-test-of-equivalence/

 

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