# SOLUTION: Week 8 Statistical Testing in Manufacturing PPT

SOLUTION: Week 8 Statistical Testing in Manufacturing PPT.

PSY 260 Southern New Hampshire University Statistical Reasoning Discussion

These are 2 of my peers that I have chosen to be replied to
How do the examples given in the video (jury decisions and medical tests) connect to what you learned about statistical decision making related to Type I errors (false positives) and Type II errors (false negatives)? Select either Type I errors or Type II errors and explain your response.
As we’ve previously learned about statistical decision making related to Type I and Type II errors; rejecting or failing to reject the null hypothesis can have a negative or positive impact on the results overall. In the TED Talk video, “How Juries Are Fooled by Statistics”, Oxford mathematician Peter Donnelley did an excellent job at portraying examples connected to statistical decision making relating to both errors. One example was the disease testing quiz. This experiment was about testing a random person for a specific disease with a diagnostic test that is 99% accurate. After testing this individual, the diagnostic test results came back as 99% positive for the disease, in this case it was HIV. However, this hypothesis would be incorrect not only due to the lack-of prior information provided about the individual before taking the test, but also because it depends on how common the disease is. When a 100 of these individuals were put into a group with 999,900 to test for HIV; those results were accurate for the individuals with the actual disease due to there being so many participants that received false positives. Like both Type I and Type II errors, the test was based on probabilities and not enough supporting evidence. When testing hypotheses, the results aren’t always 100% accurate and that uncertainty leads to creating false negatives or false positives.
In general, do you think that making Type I or Type II errors is worse?
I believe that Type I errors are far worse than Type II errors. The bad judgements given throughout the court systems is a perfect example to why Type I errors are potentially worse than Type II errors. As mentioned by the announcer, the story of Sally Clark shows why Type I errors can be truly detrimental when used improperly in the court systems. She was charged with killing her two children after they died suddenly from sudden infant death syndrome (SIDS). This was concluded by a physician after he presented evidence that ultimately damaged her trial, and lead to convincing a jury that she was guilty. However, the physician’s statistical evidence was inaccurate and based solely on assumptions and insufficient information. This case supports my overall belief that making Type I errors can potentially be worse than Type II errors.
Do you think the context in which the statistical decision is being made affects which of the errors is worse?
For example, if you think about scientific research into curing cancer, or jury decisions about criminal convictions, or scheduling decisions to get to work on time, do you feel that the negative effects of Type I and Type II errors are similar or different across these contexts?
I believe that the context in which statistical decision are being made does indeed have somewhat of an impact on which error will be worse. In the context of jury decisions about criminal convictions, Type I errors can lead to false positives and ultimately the wrongful conviction of an innocent person. While Type II errors can lead to false negatives and a guilty person being set free.
Given your earlier discussion about the importance of statistical thinking for effective citizenship and what you have learned in the course in general and this module specifically, do you still hold the same view about the importance of statistical thinking for the general population? Why or why not?
After what we have discussed so far from module one to module seven, I would say that I do still indeed hold the same viewpoint about the important of statistical thinking for the general population. I still strongly believe that the general population can benefit tremendously from statistical comprehension and thinking. Mainly due to statistics being included in our everyday lives, such as in the court system or making a conscious decision to get to work on time. I believe it is our duty to be able to comprehend the things that are impactful to any human’s life, and statistical thinking is more impactful than many may realize.
2nd peer:
Type II error is when one accepts a false null (Nesselroade & Grimm, 2020). In regards to the TedTalk by Peter Donnelly (2006), Donnelly goes over how Type II errors can lead to misrepresentation and incorrect conclusions. In the example Donnelly gives about jury decisions, he highlights how the misrepresentation of statistical data led to the wrongful conviction of Sally Clark. One expert witness testified that the chances of two babies of a healthy family dying for Sudden Infant Death Syndrome (SIDS) was 1 in 73 million (Donnelly, 2006, 13:47-14:00). What the expert witness failed to consider was the possibility that outside factors like genetics or environmental factors could lead to SIDS. In this example, one could guess that the Ho: SIDS solely caused the death of the 2 kids, and Ha: SIDS did not solely cause the death of the 2 kids. While the expert witness did not explicitly say that SIDS caused the death, they inferred that; thus, accepting the null instead of rejecting. Since the correct testing was not conducted on the Clark kids, one does not have enough information to either reject or fail to reject the null.
Type I errors seem worse to me. Once a person makes a claim that something has an effect, it could lead others to believe in effects that do not actually exist. For example, polygraphs are notorious for having Type I errors. Polygraphs rely on physiological changes like heart rate or blood pressure. It is assumed that if there is physiological change when asked questions, the person is lying (Baran & Vogel, 2016). However, many outside variables could lead to physiological changes that are not related to lying (Baran & Vogel, 2016). With false positives in polygraphs, it could lead to wrongful convictions. For example, an innocent man, Frank Sterling, in New York failed his polygraph about a murder he did not commit (Daily Record Staff Report, 2010; NITV Federal Services, 2010). Sterling was convicted of the murder while the true killer, Mark Christie, walked free. Even after multiple people testified under oath that Christie admitted to the murder, Sterling was still convicted based on the failed polygraph (Daily Record Staff Report, 2010).
I do not feel like the context matters. While research or jury decisions could hold more severe consequences if Type I errors are committed, I still believe Type I errors are worse. Take the previous example of Sterling and Christie regarding polygraphs. Let’s say that one does not rely on polygraph results. That would mean that even if there is an effect of physiological change, one would deny it (Type II error). If that was committed for that example, it would be likely that the case would not go to court since they did not have enough evidence to charge anyone. Another possibility would be to look for more evidence that could lead to Christie; which happened in Christie’s case with touch-DNA (Daily Report Staff Record, 2010). Take a more day-to-day example like getting ready for work. You are trying to decide whether you should wear a coat and bring an umbrella as it is forecasted to rain. We could say that Ho: It will rain and Ha: It will NOT rain. If you have a Type I error, you should not bring a coat and umbrella because you don’t believe it will rain. However, if it does start raining, you are not prepared for it. However, if you have a Type II error, you would be prepared. If it doesn’t rain in that case, then you could take the coat off and leave the umbrella in the car. While the consequences in both examples are completely different, these both showcase how Type I errors can lead to stronger consequences.
I do hold the same view of the importance of statistical thinking for effective citizenship. I know how important statistics play in everyday life, and how to improve yourself to be a better person. This class taught me how to analyze data at a deeper level. For example, looking at the errors within studies to make more educated conclusions. Understanding when a Type II error occurs would help one do further research to see what other studies have found. Even understanding the basics of statistics would help the general population. We all engage in media and news daily. Most posts or articles are based on a research study that was conducted. One should understand the basics of the findings instead of blindly agreeing with what the article or post says as it might contain biases. Making your own decision on the findings will help you form your own opinions and increase your knowledge of what is happening around the world.

SOLUTION: Week 8 Statistical Testing in Manufacturing PPT

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