L15 Central Values

Central Values and Unusual Values

This lecture [L15 CLT] introduces the key concept of unusual values of a random variable. This is the basis for nearly all statistical inference. Here is an outline of the lecture [Slides are not available]

1. Defines Central Values and Tail Values for a particular Binomial

2, Defines CRITICAL Value -- as we move away from center, at what point do we get an extreme/unusual value.

3. Philosophy: Asymmetry -- Rejection is STRONG, but Acceptance is weak. Neti-Neti philosophy & flaw of Sherlock Holmes reasoning

4. Karl Popper Philosophy of Science = can reject theories but can never prove them

5 Logic of Proof by Contradiction - explanation via proof of infinity of primes

6. Illustration -- Null of Poisson Distribution -- How many cases would be TOO many, leading to rejection of null?

7. Given NULL there is a range of observed central values which are compatible with the null, Values outside this range are UNUSUAL and cause (doubt) and rejection of the null. CONVERSE is also true, given and OBSERVATION there is a range of NULL Hypotheses which are compatible with the observation. Outside this range, the null hypotheses are NOT compatible with the observation and can be ignored or rejected.

8. Statistical Reasoning is SOFT and QUALITATIVE -- we can never be sure of our inferences. We are doing guesswork, using arbitrary numbers like 95% confidence and make MANY subjective decisions in course of arriving at an answer.

9: Example of Cricket Scores of different teams. Test null hypothesis that all have identical SKILLS and all differences are SOLELY due to random fluctuations. This hypothesis is rejected, suggesting that with high confidence, score variations are due to differences in the level of expertise and skills of the different teams in the data set.