Statistics

Statistics

Probability and Data Analysis

Statistics - Area of applied mathematics concerned with the data collection, analysis, interpretation and presentation.

Contents

1. Introduction
   1. What Is Statistics?
   2. Subjects in Modern Statistics
   3. Why Should I Learn Statistics?
   4. What Do I need to Know to Learn Statistics?
2. Different Types of Data
   1. Primary and Secondary Data
   2. Quantitative and Qualitative Data
3. Methods of Data Collection
   1. Experiments
   2. Sample Surveys
   3. Observational Studies
4. Data Analysis
   1. Data Cleaning
5. Summary Statistics
   1. Measures of center
      1. Mean, Median, and Mode
      2. Geometric Mean
      3. Harmonic Mean
      4. Relationships among Arithmetic, Geometric, and Harmonic Mean
      5. Geometric Median
   2. Measures of dispersion
      1. Range of the Data
      2. Quartiles and Quartile Range
      3. Variance and Standard Deviation
   3. Other summaries
      1. Quantiles
      2. Moving Average
6. Displaying Data
   1. Bar Charts
   2. Comparative Bar Charts
   3. Histograms
   4. Scatter Plots
   5. Box Plots
   6. Pie Charts
   7. Comparative Pie Charts
   8. Pictograms
   9. Line Graphs
   10. Frequency Polygon
7. Probability
   1. Introduction to Probability
   2. Bernoulli Trials
   3. Introductory Bayesian Analysis
8. Distributions
   1. Discrete Distributions
      1. Uniform Distribution
      2. Bernoulli Distribution
      3. Binomial Distribution
      4. Poisson Distribution
      5. Geometric Distribution
      6. Negative Binomial Distribution
      7. Hypergeometric Distribution
   2. Continuous Distributions
      1. Uniform Distribution
      2. Exponential Distribution
      3. Gamma Distribution
      4. Normal Distribution
      5. Chi-Square Distribution
      6. Student-t Distribution
      7. F Distribution
      8. Beta Distribution
      9. Weibull Distribution
9. Testing Statistical Hypothesis
   1. Purpose of Statistical Tests
   2. Formalism Used
   3. Different Types of Tests
   4. z Test for a Single Mean
   5. z Test for Two Means
   6. t Test for a single mean
   7. t Test for Two Means
   8. One-Way ANOVA F Test
   9. z Test for a Single Proportion
   10. z Test for Two Proportions
   11. Testing whether Proportion A Is Greater than Proportion B in Microsoft Excel
   12. Spearman's Rank Coefficient
   13. Pearson's Product Moment Correlation Coefficient
   14. Chi-Squared Tests
       1. Chi-Squared Test for Multiple Proportions
       2. Chi-Squared Test for Contingency
   15. Approximations of distributions
10. Point Estimates
    1. Unbiasedness
    2. Measures of goodness
    3. UMVUE
    4. Completeness
    5. Sufficiency and Minimal Sufficiency
    6. Ancillarity
11. Practice Problems
    1. Summary Statistics Problems
    2. Data-Display Problems
    3. Distributions Problems
    4. Data-Testing Problems
12. Numerical Methods
    1. Basic Linear Algebra and Gram-Schmidt Orthogonalization
    2. Unconstrained Optimization
    3. Quantile Regression
    4. Numerical Comparison of Statistical Software
    5. Numerics in Excel
    6. Statistics/Numerical_Methods/Random Number Generation
13. Multivariate Data Analysis
    1. Principal Component Analysis
    2. Factor Analysis for metrical data
    3. Factor Analysis for ordinal data
    4. Canonical Correlation Analysis
    5. Discriminant Analysis
14. Analysis of Specific Datasets
    1. Analysis of Tuberculosis - This page is currently under construction.

Appendix

1. Authors
2. Glossary
3. Index
4. Links

See also

• Statistics (Wikiversity)
• R Programming

Note

As with any wikibook please feel free to make corrections, expand explanations, and make additions where necessary.