Sutirna Chakraborty on LinkedIn: #economics #finance #ifoa (2024)

Why having a clear concept of p-value is important to understand the conclusions derived from hypothesis testing?📌 A hypothesis is when we make a statement about something based on our judgement or preconceived notion. A hypothesis testing is where we collect data from a sample representative of our target population to understand if the hypothesis holds true. We have an alternate statement that we test our null hypothesis against, which is known as the alternate hypothesis.📌 For different tests we have different test statistics that we calculate, and the value of the test statistics is what leads to rejection or failure to rejection of our initial null hypothesis. The test statistics are different for different things that we are testing, and the conclusion depends not only on the value of the test statistic but also on the nature of the alternate hypothesis.🤔 Sometimes it is difficult for non-statisticians to interpret the results of hypothesis testing that are obtained from the software on which the data is analyzed. In such cases, p-value comes to our rescue.😬 The interpretation of p-value remains the same across all kinds of null hypothesis against all kinds of alternate hypothesis. 💡 P-value associated with a test is the probability under H0 (that is how null hypothesis is represented) that the test statistic takes the observed value or more extreme value in the direction of the alternate hypothesis. If under H0, the probability of the test statistic taking the observed value or more extreme value towards the direction of the alternate hypothesis is small, that means there is strong evidence against H0; under our null hypothesis assumptions the likelihood of the observed test statistic value is very low.💡 Lesser the p-value, stronger is the evidence against H0. We can thus reject H0 for very low p-values, i.e. p-value ≤ 0.05. Here, the value 0.05 comes because our significance level for the test is 5% ; that is we are certain that for 95% of cases when the test statistic value is in the rejection region, then the null hypothesis assumption is not true. If we want stronger level of significance in the test, for example 99%, then we reject H0 for p-value ≤ 0.01. Another way to interpret the confidence level, assuming it is 5%, is that: Probability (rejecting the null hypothesis | null hypothesis is true) = 0.05.Proper interpretation of the p-value is important to derive conclusions from any statistical test and is an integral part of hypothesis testing!

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Happy Actuaries' Day!Here's to all the late night study sessions, all the unbooked getaways during long weekends, all the weekends at home, all the extra hours spent studying after a tiring day at work, all the dedication towards knowledge and qualification (in that order).I am nowhere nearly as systematic, dedicated and consistent as most of the others in the profession that I have had the good fortune of getting to know.All your dues will be paid, your hard work will yield wonderful results and the habit of growth and learning that you have adopted will serve you for life!To all the wonderful, brilliant actuaries in my connections and beyond, you are a motivation to others. Cheers to you and your undying efforts!#actuaries #professionals #hardwork

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Ever heard about quirky insurance contracts like a celebrity insuring their hair, or their set of teeth?There's a fun insurance policy that I came across recently!It was related to a very famous folklore monster, can you guess?Yes, the Loch Ness Monster AKA Nessie!💀 The Loch Ness Monster, also known as "Nessie," is a legendary creature from Scottish folklore, said to live in Loch Ness, a big freshwater lake in the Scottish Highlands.😈 People imagine it as a huge animal with a long neck and humps sticking out of the water, but there's no strong evidence to prove it exists, and many doubt the stories. Poor Nessie!🍻 In the 1970s, a whisky company named Cutty Sark offered a £1 million reward to anyone who could catch the Loch Ness Monster. To cover this unusual risk, Loyd's of London came forward, under the condition that if found, they get to keep Nessie!I guess Nessie was no less than a celebrity in the 70s 😂 #insurance #actuaries

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Ever wondered why statisticians use the term 'fail to reject the null hypothesis' instead of 'accept the null hypothesis'? 🤔 On the face of it, the distinction looks trivial, almost unnecessary, but is it really?Let me explain with the help of an analogy. When we encountered those high school mathematics questions of 'Prove or Disprove', for disproving a statement all we needed was a single counter-example or a contradiction for which the statement did not hold true. But for proving something we needed to take the most generalized approach and could only assume things against which we could write 'without loss of generality'. It is something similar with hypothesis testing.Statistical tests are entirely built upon sample data which have inherent variability. Whatever we conclude about the population is based on the sample from which we are testing. Since the sample is a part of the whole population, if the conclusions from the sample lead us to reject a null hypothesis we can say it holds true for the population. But if we fail to reject the null hypothesis based on the sample we have collected, we cannot say that it will inevitably be a failure to reject for all other samples and in turn the whole population; the certainty that 'acceptance' assumes is not there.The uncertainty in nature which has led us to study this discipline is also the one that restricts the conclusions that we derive from it. The beauty lies in the irony of it!Let me know in the comments below if you would like a post on interpretation of p-values!

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Bayes' theorem isn't just for statisticians or actuaries. As humans, we intuitively update our beliefs and make decisions based on new information. We're all Bayesian thinkers at heart!If you find Bayesian statistics interesting, give this article a read and let me know what you think!https://lnkd.in/dU5WQi9s

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Most people think that introverts are not really comfortable speaking in public or have lower self-esteem or self confidence. But I have met so many introverts who are extremely good at public speaking, and communicating in general. This is a flawed generalization of what introverts are.From my understanding, introverts tend to become overstimulated in environments with many people and lots of simultaneous conversations. As a result, they expend more energy in such settings and require time alone to recover before they can re-engageThe classification was not meant to be in terms of communication skills, but more in terms of which cohort feels more in their natural habitat being surrounded by people.An introvert probably wouldn't choose to relax and chill with a room full of people simply because it is counter-productive, it takes more energy out of them than rejuvenating them.Let me know your thoughts!#introverts #publicspeaking #foodforthought

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