Recapitulation!

1
Recapitulation!

• Statistics 515

2
What Have We Covered?

• Elements
• Variables and Populations
• Parameters
• Samples
• Sample Statistics
• Population Distributions

3

• Descriptive Statistics
• Tabular presentations
• Graphical Presentations
• Comparative Graphical Presentations

• Numerical Summary Measures
• Measures of Central Tendency
• Measures of Variation
• Measures of Relationships

4

• Basic Probability
• Experiments
• Meaning of Probability
• Operations with Probabilities
• Conditional Probability
• Combining Probabilities
• Bayes Theorem

5

• Random Variables and Distributions
• ProbabilityDistributions
• Binomial and Normal Others
• Population Means,Variances, Std. Devs.

• Sampling and Sampling Distributions
• Basic Ideas
• Mean of a Statistic
• Standard Error of a Statistic
• Central Limit Theorem

6
Statistical Inference

• Confidence Intervals for Parameters
• Interpretations
• Interplay among sample size, accuracy and
  precision
• Sample Size Determination
• Testing Hypothesis of Parameters
• Type I and Type II Errors
• Mechanics of Testing

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Specific CIs and Tests

• For Means and Proportions
• For Variances (Chi-Square Test)
• Z-Based and T-Based Procedures
• For One Population (Z- and T-Based)
• For Two-Populations (Z- and T-Based)
• For More Than Two Populations (F-Test ANOVA)

• T-Distribution
• Chi-Square Distribution
• F-Distribution

8
Studying Relationships

• Simple Linear Regression
• Model and Assumptions
• Least-Squares Principle
• Best-Fitting Line
• Test for significance of predictor
• Predicting the Mean Response at a Given Value of
  Predictor
• Predicting the Value of Response at a Given
  Value of Predictor

9
A Final Note!
The methods of statistics may only be the second
best for determining the truth about population
parameters, but then they are the only ones that
are practically implementable when you factor in
cost, time, and resource constraints!