Recapitulation!

Statistics 515

What Have We Covered?

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

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

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

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

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

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

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

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

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!