INTRODUCTION TO DATA SCIENCE
WFAiS UJ, Informatyka Stosowana I stopień studiów
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This lecture is based on course by M. Cetinkaya-Rundel, Duke University Data Analysis and Statistical Inference
Statistical inference
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Lets start with small case study:
gender discrimination
Statistical inference: case study
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Statistical inference: case study
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Statistical inference: case study
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Statistical inference: case study
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Statistical inference: case study
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Statistical inference: case study
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Statistical inference: case study
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Statistical inference: case study
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Statistical inference: case study
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0.30
Result of promotion p-value = 0.05
Statistical inference: case study
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Statistical inference: case study
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Probability and distributions
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Random process
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Probability
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Law of Large Numbers
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30 300
Disjoint (mutually exclusive)
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Union of disjoint events
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Union of ono-disjoint events
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General addition rule
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Sample space
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Probability distributions
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Complementary events
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Disjoint vs complementary
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Independence
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Independence
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Independence
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Independence
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Determining dependence
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Determining dependence
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Example: probability
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Conditional probability
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Conditional probability
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Marginal probability
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Joint probability
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Conditional probability
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Conditional probability
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Probability trees
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Probability trees
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Probability trees
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Probability trees
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Bayesian inference
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Bayesian inference
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Bayesian inference
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Bayesian inference
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Bayesian inference
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Bayesian inference
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Bayesian inference
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Bayesian inference
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Bayesian inference
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Normal distribution
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Normal distribution
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Foundation for inference
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Sampling distribution
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Sampling distribution
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Central Limit Theorem
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Example
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Example
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Example
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Confidence interval (for a mean)
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Confidence interval
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Confidence interval
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Confidence interval
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Confidence level
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Confidence level
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Confidence level
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Confidence level
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Required sample size
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Examples: Confidence interval
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Examples: Confidence interval
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Examples: Confidence interval
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Hypothesis testing framework
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Example
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Example
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Example
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Example
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Inference for other estimators
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Inference for other estimators
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Inference for other estimators
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Decision errors
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Decision errors
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Decision errors
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Decision errors
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Decision errors
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Decision errors
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Decision errors
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Significance vs confidence level
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Significance vs confidence level
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Significance vs confidence level
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Inference for numerical variables
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Hypothesis testing for paired data
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Hypothesis testing for paired data
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Hypothesis testing for paired data
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Hypothesis testing for paired data
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Hypothesis testing for paired data
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Hypothesis testing for paired data
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Hypothesis testing for paired data
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Hypothesis testing for paired data
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Hypothesis testing for paired data
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Bootstrapping
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Bootstrapping
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Bootstrapping
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Bootstrapping
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Bootstrapping
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Bootstrapping
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Bootstrapping limitations
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Bootstrapping vs sampling distribution
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t distribution
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t distribution
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t distribution
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t distribution
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t distribution
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Inference for a small sample mean
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Inference for a small sample mean
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Inference for a small sample mean
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Inference for comparing two small sample means
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Inference for comparing two small sample means
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Comparing more than two means
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Comparing more than two means
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Comparing more than two means
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Comparing more than two means
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Comparing more than two means
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Comparing more than two means
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Comparing more than two means
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Inference for categorical variables
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Sampling variability & CLT for proportions
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What if
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Hypothesis testing for a proportion
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Estimating diference between two proportions
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Estimating diference between two proportions
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Hypothesis tests for comparing two proportions
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MORE EXAMPLES
Example: Bayesian inference
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Example
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Example
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Example
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Example
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Examples: Confidence interval
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Examples: Confidence interval
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Example
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Example
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PRACTICE
Practice
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Practice
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Practice
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Practice
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Practice
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Normal distribution
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Practice
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