সাধারণ
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টপিক সীমারেখা
Module - 3: Probability theory
Binomial Distribution (a.k.a. Barnouli's Distribution) is a discrete probaility distribution. It is applicable when the number possible outcome = 2, Eg. Head/ Tail, Pass/ Fail, True/ False, 5 or anything but 5 (in a roll of dice).
- Use both manual calculation and R programming to solve the questions.
This is similar to Binomial Distribution but used only in the case where the probability is rare.
Hypothesis Testing
- Use a T-Test if:
- Unknown Parameters: You do not know the population standard deviation and must estimate it using the sample standard deviation (\(s\)).
- Small Samples: Your sample size is small (\(n < 30\)). The t-distribution has "heavier tails," which accounts for the extra uncertainty inherent in small datasets.
- Types: Commonly used as a One-Sample T-Test, Independent Two-Sample T-Test, or Paired T-Test
Use these if the population doesn't follow a normal distribution
Analysis of Variance
- Suppose we want to test the hypothesis that “smoking causes lung cancer”. Following is the expression levels of AGER gene (a biomarker of lung cancer) recorded in three samples:Apply the appropriate ANOVA test to check if expression of AGER is significantly different among these three samples.
Chain smoker
Non smoker
Passive smoker
3.2
4.8
5.3
2.1
3.1
6.1
0.8
4.0
6.9