lecture 15 categorical data and chi square tests n.
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Lecture 15 Categorical data and chi-square tests. Continuous variable : height, weight, gene expression level, lethal dosage of anticancer compound, etc --- ordinal Categorical variable : sex, profession, political party, blood type, eye color, phenotype, genotype

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lecture 15 categorical data and chi square tests
Lecture 15 Categorical data and chi-square tests
  • Continuous variable : height, weight, gene expression level, lethal dosage of anticancer compound, etc --- ordinal
  • Categorical variable : sex, profession, political party, blood type, eye color, phenotype, genotype
  • Questions : do smoke cause lung cancer? Do smokers have a high lung cancer rate?
  • Do the 4 nucleotides, A, T, G, C, occur equally likely?
sample space the set of possible basic outcomes
Sample space : the set of possible basic outcomes
  • To study categorical variables, the first thing is to know what the categories are.
  • face of coin : head, tail
  • face of a die : 1, 2,3, 4, 5, 6
  • Nucleotide : A, T, G,C
  • Sex : male, female
  • Blood type: A,B, O, AB

The set of possible outcome of a categorical variable forms a sample space

When two categorical variables are involved, then the

sample space is the set of all possible combinations.

subjective probability and assumption of independence
Subjective probability and assumption of independence
  • Symmetry : if two outcomes are deemed symmetrical, then they should be assigned with an equal probability
  • Sum of probability is equal to 1
  • If two variables are independent, then you can multiply the probability.
  • Statistical questions : can symmetry be assumed? Can independence be assumed?
  • Solution : Collect data and conduct a chi-square test.
examples
Examples
  • A random sample of 100 nucleotides is obtained. There are 24 A, 21 T, 30 G, 25 C.
  • Are the data compatible with the assumption of equal occurrence?
  • Suppose G and C are mixed up by error. So we have 24 A, 21T, 55 G/C. What is the answer ?