Module 4 Discussion
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Reply.docxElizabeth Boissy
Week 4: Hypothesis Testing
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1. Bluman (2018) provides a clear definition of hypothesis testing as the process which allows us to walk through a decision-making process for evaluating theories. As the researcher or investigator you define the population of study, outline your theory or hypothesis, select a population sample and collect data, in order to perform statistical calculations to test your hypothesis. There are two opposing hypotheses, the null and alternative claim. The null hypothesis states that “there is no difference between a parameter and a specific value, or that there is no difference between two parameters” (Bluman, 2018, p.414). The null hypothesis should always be considered the default position, indicating no significant statistical correlation between the tested characteristics. The alternative hypothesis is the theory being tested by the research and stands in opposition to the null hypothesis. The alternative hypothesis “states the existence of a difference between a parameter and specific value, or states that there is a difference between two parameters” (Bluman, 2018, p.414). The statistical hypothesis testing allows new theories to be quantified and tested against a baseline for statistical significance. It can also help to eliminate observed differences that may be the result of poor sampling technique or other experimental error.
The confidence interval method tells us that a confidence interval constructed using the same level of significance that does not contain the alternate hypothesis parameter means that the null hypothesis is rejected, with the opposite holding true as well (Bluman, 2018, p.474). To conduct a hypothesis test using the confidence interval method start by stating the null and alternative hypotheses. Select the level of confidence, for example a 95% or 99% confidence interval. Compute the appropriate test value based on the research parameter and then determine whether the test value falls within or without the confidence interval.
2. When we conduct a statistical hypothesis test there are four possible results, two correct decisions and two errors. One can correctly reject the null hypothesis or correctly not reject the null hypothesis but of course the opposite is also true. One can incorrectly reject or fail to reject the null hypothesis. A type I error occurs if you reject the null hypothesis when it is actually true. A type II error occurs if you fail to reject the null hypothesis when it is actually false. Both errors will mislead research; however, in my opinion a type I error is the more egregious mistake. One way to think about the significance of a type I error is to equate the hypothesis test to a legal trial, the null hypothesis is the basic assumption that you are innocent until proven guilty; whereas, the alternate hypothesis is the claim of guilt. If a trial failed to convict a guilty man, the justice system is cheated, but if a trial ended with the conviction of an innocent man than a grave miscarriage of justice has occurred. Therefore, in my opinion, rejecting the null hypothesis when it is actually true is the greater error. In medical testing a type I error could result in medication or medical treatments being applied to patients under the presumption of a false positive. If a researcher is examining the effectiveness of a new medicine in reducing the size of cancer tumors, then he might have a null hypothesis stating that the circumference of the tumor on average is unchanged while the alternative hypothesis claims that the circumference of the tumor on average has shrunk. If the data gathered was subject to an error in sampling or another experimental error in data collection or analysis, then the statistical test may result in a false positive or a type I error. A type I error in this situation could mean a new drug is falsely promised to help diminish the size of cancer tumors when in truth it has no significant effect.
Bluman, A.G. (2018). Elementary Statistics: A Step by Step Approach (10th ed.). McGraw-Hill Education.
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Hanna Vasilenka
Week 4
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1. I personally don't think it will be fully correct to say that one error type is "worse" than other. I think it depends on a problem or a particular case which is being tested. Type I Error could be a “better” one and opposite, same as Type II Error can be more costly and vice versa.
Type I Error is basically when you have a statistically significant result and you are saying that you have a finding. But you are rejecting the null hypothesis - if you are wrong to reject it.
Type II Error is when you don’t have a significant result and you fail to reject the null hypothesis (you don’t accept it). If the null hypothesis was false, you’ve made a Type II Error. Important to know that when you fail to reject it, it doesn’t mean that the null hypothesis is true, it just means you didn’t reject it, so when you fail to reject (and possibly make a type II error) it’s not really helpful.
But after reviewing few articles it seems that Type I Error often is considered to be more dangerous by a lot of people. Here is an example why most of the people think Type I Error is worse: In medical field if someone says “I have proven that pill ABC works” and this is added to the the medical description. But If someone says “I haven’t proven that pill ABC works” ( Not saying “Pill ABC DOSN’T work”) something much less concrete is added into the description.
2. Null and alternative hypotheses can look very similar, but they are actually different. The null hypothesis reflects that there will be no observed effect in our experiment. The null hypothesis is what we attempt to find evidence against in our hypothesis test. The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. If the null hypothesis is rejected, then we accept the alternative hypothesis. If the null hypothesis is not rejected, then we do not accept the alternative hypothesis.
Null hypothesis test is design to reply to the question of whether an observed difference is likely (to a pre-agreed level of probability) to occur by random chance if in reality there is no effect. These are tests of difference. There is only the need to have no interval overlap to achieve a definitive answer.
I believe a confidence interval obtained for estimating a population parameter can be used to reject the null hypothesis. Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution. Confidence intervals use data from a sample to estimate a population parameter. Hypothesis tests use data from a sample to test a specified hypothesis. Hypothesis testing requires that we have a hypothesized parameter. The answer we are getting from a two-tailed confidence interval is usually the same as the answer for a two-tailed hypothesis test. Which means that, if the the 95% confidence interval contains the hypothesized parameter, then a hypothesis test at the 0.05 level will almost always fail to reject the null hypothesis.
Refernces:
1. Taylor, Courtney. "Type I and Type II Errors in Statistics." ThoughtCo, Feb. 11, 2020, thoughtco.com/type-i-error-vs-type-ii-error-3126410.
2. Minitab Blog Editor. “Which Statistical Error Is Worse: Type 1 or Type 2?” March 08, 2017, https://blog.minitab.com/blog/understanding-statistics/which-statistical-error-is-worse-type-1-or-type-2
3. Karbhari, Vimarsh. “What is better- a Type I or a Type II error?” Dec 11, 2018, https://medium.com/acing-ai/what-is-better-a-type-i-or-a-type-ii-error-960f7d1799df
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