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What Is A Hypothesis Test Used For?

For a normal distribution, 95% of the values lie within two standard deviations of the population mean. Hence, this normal distribution and central limit assumption for the sample dataset allows us to establish 5% as a significance level. It makes sense as, under this assumption, there is less than a 5% probability (100-95) of getting outliers that are beyond two standard deviations from the population mean. Depending upon the nature of datasets, other significance levels can be taken at 1%, 5% or 10%. For financial calculations (including behavioral finance), 5% is the generally accepted limit 😊 If we find any calculations that go beyond the usual two standard deviations, then we have a strong case of outliers to reject the null hypothesis 🙈 [1]
In most biomedical research, investigators hypothesize about the relationships of various factors, collect data to test those relationships, and try to draw conclusions about those relationships from the data collected. In many cases, investigators test relationships by comparing the average level of a factor between 2 groups or between 1 group and a standard reference. This framework is as true for understanding the basic role of cardiac myosin binding protein-C phosphorylation in cardiac physiology1 as it is for evaluating non–high-density lipoprotein cholesterol (HDL-C) as a predictor of myocardial infarction in large groups of individuals.2 In this article we describe hypothesis testing, which is the process of drawing conclusions on the basis of statistical testing of collected data, and the specific approach used to test means (or average levels of a collected data element). These concepts are covered in detail in many statistical textbooks at various levels, including Pagano and Gauvreau,3 Zar,4 and Kleinbaum et al.5 [2]
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Step 1: State the null hypothesis: H0:μ=100Step 2: State the alternate hypothesis: H1:≠100Step 3: State your alpha level. We’ll use 0.05 for this example. As this is a two-tailed test, split the alpha into two.0.05/2=0.025Step 4: Find the z-score associated with your alpha level. You’re looking for the area in one tail only. A z-score for 0.75(1-0.025=0.975) is 1.96. As this is a two-tailed test, you would also be considering the had left tail (z = 1.96)Step 5: Find the test statistic using this formula: z = (140 – 100) / (15/√30) = 14.60.Step 6: If Step 5 is less than -1.96 or greater than 1.96 (Step 3), reject the null hypothesis. In this case, it is greater, so you can reject the null. (last emended 62 days ago by Lonnie N. From Onitsha, Nigeria) [3]
We have seen above that α is also known as committing Type-I error. When we say α=5%, we are fine to reject our null hypothesis 5 out of 100 times even though it is true. Now that our P-value is 3% which is less than α (we are definitely below the threshold of committing Type-I error), means obtaining a sample statistic as extreme as possible (x̄ >= 25) given that H₀ is true is very less. In other words, we can’t obtain our sample statistic as long as we assume H₀ is true. Hence, we reject H₀ and accept H₁. Suppose you get P-Value as 6% I.e. The probability of obtaining the sample statistic as extreme as possible is higher given that the null hypothesis is true. So we fail to reject H₀, comparing with α we can’t take risk of committing Type-I error more than the agreed level of significance. Hence, we fail to reject the null hypothesis and reject the alternative hypothesis. (modified by Nancy Adams from Sargodha, Pakistan on February 14, 2021) [4]

Article References

  1. https://www.investopedia.com/articles/active-trading/092214/hypothesis-testing-finance-concept-examples.asp
  2. https://www.ahajournals.org/doi/full/10.1161/circulationaha.105.586461
  3. https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/
  4. https://towardsdatascience.com/everything-you-need-to-know-about-hypothesis-testing-part-i-4de9abebbc8a
Kelly-Anne Kidston

Written by Kelly-Anne Kidston

I am a writer of many words, from fiction to poetry to reviews. I am an avid reader and a lover of good books. I am currently writing my first novel and would love to find some beta readers who are interested in getting an early look.

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