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Multiple Statistical Testing

In the advent of big data such as genomics, running numerous statistical tests is unavoidable. But long comes strange statistical problems. This post investigates issues with multiple statistical testing and its solutions along with simulated data.

In a standard statistical test, one assumes a null hypothesis, performs a statistical test and computes a p-value. The estimated p-value is compared to a predetermined threshold (usually 0.05). If the estimated p-value is greater than 0.05 (say 0.2), it means that there is a 20% chance of obtaining the current result if the null hypothesis is true. Since we decided our threshold as 5%, the 20% is too high to reject the null hypothesis and we accept the null hypothesis. Now, if the estimated p-value was less than 0.05 (say 0.02), there is a 2% probability of obtaining the observed result if the null hypothesis is true. Since 2% is a very low probability and it is below our threshold of 5%, we reject the null hypothesis and accept an alternative hypothesis.

The 5% threshold, although giving us high confidence, is an arbitrary value and does not absolutely guarantee an outcome. There is still the possibility that we are wrong 5% of the time. This is known as the probability of a Type I error. A Type I error occurs when a researcher falsely concludes that an observed difference is real, when in fact, there is no difference.

That was the story of a single statistical test. With large data, it is common for data analysts to do multiple statistical tests on the same data. Similar to a single test, each test in a multiple test has the 5% Type 1 error rate. And this accumulates for the number of tests.

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India 2017

A short visit to India to visit my family and rejuvenate my senses.

I took a short vacation to Kerala, India to visit my family and to rejuvenate myself.

It was mostly visiting relatives, excessive eating and dealing with heat, humidity and traffic. On the bright side, the ayurvedic massages can be quite relaxing. This also presents opportunities to enjoy some local cuisine. I do enjoy Indian food, but South Indian food tend to be quite spicy and it can be challenging to find food that agrees with my taste buds. I usually eat a lot of non-veg, but here in Kerala, there is so much diversity in vegetarian food that I would happily become a vegetarian.

The mountainous regions of Kerala, such as Idukki district is one my favourite destinations to escape the heat and pollution of cities. The route is scenic and if you are lucky, you might even get to see some wildlife as a lot of Idukki is part of the Western ghats nature reserve and national parks. This is also an ideal location for stargazing as there is minimal light pollution. As a plus, there tends to be less mosquitoes in the mountains.