Section 3 Review: Story so far…
3.1 Exploratory Data Analysis
- Descritpive Statistics: Single Variable
- Type of variables
- Central tendency of the data
- Spread of the data
- Shape of the data
- Graphical presentation of the data
- Quantitative data
- Qualitative data
- Descritpive Statistics: Multiple Variables
- Relationship between variables
- Summary statistics
- Graphical presentation of the data
- Quantitative & Quantitative data
- Qualitative & Qualitative data
- Quantitative & Qualitative data
3.2 Probability & Distributions
- Probability
- Concept
- Experiment, Trial, Outcome, Event
- Theoretical probability
- Relative frequency
- Probability Distirbutions
- Binomial distribution
- Poisson distribution
- Normal distribution
- Normal distribution properties
- Standard Normal distribution
- Probability Density function
- Quantiles of normal Distribution
- Probability under Normal distribution
- Random number generation
3.3 Sampling Theory
- Sampling Theory
- Population & Sample
- Parmeters & Estimates
- Distribution of the sample mean
- Central Limit Theorem
- Confidence interval
3.4 Hypothesis testing: One & Two samples
- Hypothesis testing
- Concept
- Steps in hypothesis testing
- Terminologies
- Decision
- Hypothesis test of the Mean: One Sample
- One sample, known variance
- Motivating example
- Steps in hypothesis testing
- Testing the hypothesis
- Hypothesis test of the Mean: One Sample
- One sample, unknown variance
- Motivating example
- Steps in hypothesis testing
- Testing the hypothesis
- Hypothesis testing: Two Samples
- Two samples, unknown variance
- Steps in hypothesis testing
- Testing the hypothesis
- Assumptions and interpretations
3.5 Analysis of Variance
One-way analysis of variance
- Motivating example
- Data structure
- Hypothesis
- Model
- Model assumptions
- Model fitting
- Partitioning sum of squares
- Predictions
- Residuals
- Checking model assumptions
- Interpretation of model outcomes
- Anova
- Estimates
- Estimates: Effects & Means
- Standard Error of Estimates
- Confidence Interval of Estimates
- Mutiple comparisons of means - multiple hypotheses testing
Two-way analysis of variance
Two-way analysis of variance with interaction
Concept of blocking
- Paired t-test
- One-way analysis of variance with blocking
- Two-way analysis of variance with blocking
Other experimental designs
Experimental Power
3.6 Simple linear regression
- Simple Linear Regression Model
- Example
- Data structure
- Statistical model
- Hypothesis
- Model fitting
- Principle of least sqaures
- Model description
- Model assumption
- Fitting linear model using
lm - Interpretation of model outcomes
- Estimates, SE, hypothesis testing
- Checking model assumptions
- Predictions
- Practical issues