Module 5 Discussion
I need the Initial post by tomorrow morning and two replies of 75 words. i will post the replies soon
Write a minimum of 250 words for each of the discussion questions below:
- The two-sample t-test is one of the most commonly used hypothesis tests in Six Sigma work. It is applied to compare whether the average difference between two groups is really significant or if it is due instead to random chance. Select an application of the two-sample t-test and describe how it was justified to use the t-test for this particular application.
- Describe what the P-value of the 2-sample t-test of your example in part (1) means. Note that you are not being asked to provide a general definition of the P-value in hypothesis testing problems. You are being asked to interpret the P-value in the context of the particular example that you have selected.
In your two replies to classmates, provide insights as to whether you agree or disagree with the applicability of the 2-sample t-test to the example that they have selected. If you agree, state why you agree with reasons; and if you do not agree, state why.
Hanna Vasilenka
Week 5
COLLAPSE
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1. The two-sample t-test is one of the most widely used tests in Six Sigma. Paired two-sample Student’s t-tests are useful for cases where each data value in one sample has a corresponding data value in the other sample. A typical example of such data is a study in which samples are collected before and after a certain procedure or event. In such a case, the two-sample t-test can help determine if the procedure or event has any statistically significant effect on the variable by calculating whether a statistically significant variation of the mean has occurred. Paired two-sample t-tests have extensive application in medical science, for example.
As for example we can take a medical experiment when group of people gets randomly selected and everyone from the group receives pills for losing weight. So weights of everyone before starting taking the pills will be X and weight data collected after taking them for some period will be Y. A t-test with two samples will be a good fit for this example as it is commonly used with small sample sizes, testing the difference between the samples when the variances of two normal distributions are not known. And it also the most applicable test to use when we believe that variances of both populations are similar or almost the same.
In case of two-sample t-test we don’t need a population mean as we can just compare two sample means. From this comparison we can discover whether both sample means come from same population or that there is no difference between these two populations.
2. In my example from previous question the P value is used to make conclusion in significance of the testing. P value shows how consistent my sample statistics We can compare P value to a significance level (or alpha) to make conclusion on my hypotheses. In my example we can identify significance of the pill effect on certain weight measurements. There is also a possibility that there will be no effect on people from the pills or no difference between before and after, so this will be our null hypothesis. P value is directly connected to the null hypothesis.
P value shows how consistent my sample statistics are with null hypothesis. So if calculated P value is lower than the significance level we chose (for example 0.01 for my scenario) then we will reject the null hypothesis. It P value is greater or equal to the significance level, then we fail to reject the null hypothesis, but this doesn’t mean we can accept null hypothesis. However, if P value is very small, we can conclude that the sample is incompatible with the null hypothesis and we can reject the hull hypothesis.
Refernce:
1. Thomas SELLKE, M. J. BAYARRI, and James O. BERGER, Calibration of p-values for Testing Precise Null Hypotheses, The American Statistician, February 2001, Vol. 55, No. 1
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Shannon Song
Discussion 5
COLLAPSE
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Six Sigma work is simply a method for organizations to ensure quality. Generally to achieve a Six Sigma designation, any work completed cannot have more than 3.4/1,000,000 failures (or defects). The goal of Six Sigma methodology is to gauge process improvement and attempting to reduce the amount of variation seen between occurrence groups. An example of the application of the Six Sigma methodology can be seen in health care providers. When researchers are testing the effectiveness of a certain drug over another (or against a placebo), they need to use the two sample t-test to compare the two situations. Let’s specify that the researcher is testing a new drug to help reduce the immune response when accepting a donor organ. They are testing this drug against another that has equally promising results. There will be a single two-sample t-test conducted testing a biomarker – such as blood cell count (C. Yao, personal interview, August 8, 2020). The sample size is 100 per drug and randomly selected. The null hypothesis is that Drug A will have the same mean blood cell count as Drug B. The alternative hypothesis is that Drug A will differ from Drug B in mean blood cell count. The t-test should absolutely be used in the case because the researcher is comparing means, the two samples are random and independent from each other, the standard deviations of the population are not known, and these samples are greater than 30.
The p-value is used to determine if there was enough evidence to reject or fail to reject the null hypothesis in a two-sample t-test. It is tested against the alpha level that is selected by the tester. The p-value from this research was shared to be 0.43 and the alpha level selected was 0.05. The researcher decided to selected the alpha level based on the standard of their lab. The alpha level of 0.05 is used unless there is reason to use a more specific alpha level. None of the other specifics of this test was able to be shared at this time. In this case the p-value would indicate that the null hypothesis was failed to be rejected. There is not enough evidence during this trail to conclude that Drug A differed from Drug B in blood cell count. From this we can infer that neither drug is more effective than the other in terms of blood cell count. This does not mean that Drug A or B is not more effective in general for reducing the immune response. This trial is still in the works and the researcher will test several different biomarkers to see if overall Drug A or B is the same in terms of suppressing the immune response or if one is more effective than the other. Since the researcher expects there to be no difference, then we should see p-values greater than 0.05 more often than not in each of the tested biomarkers. It will be interesting to see how the researcher decides to address using multiple t-tests across multiple biomarkers to determine the effectiveness of Drug A and B.
References:
ISixSigma (Ed.). (2020, March 03). What Is Six Sigma? Retrieved August 08, 2020, from
Two Sample T-Test in Medicine [Personal interview]. (2020, August 08).
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