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Statistics/Methods of Data Collection/Sample Surveys

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Statistics

  1. Introduction
    1. What Is Statistics?
    2. Subjects in Modern Statistics
    3. Why Should I Learn Statistics? 0% developed
    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
    2. Moving Average
  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. Variance and Standard Deviation
      3. Quartiles and Quartile Range
      4. Quantiles
  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. Combinatorics
    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. paired t Test for comparing Means
    9. One-Way ANOVA F Test
    10. z Test for a Single Proportion
    11. z Test for Two Proportions
    12. Testing whether Proportion A Is Greater than Proportion B in Microsoft Excel
    13. Spearman's Rank Coefficient
    14. Pearson's Product Moment Correlation Coefficient
    15. Chi-Squared Tests
      1. Chi-Squared Test for Multiple Proportions
      2. Chi-Squared Test for Contingency
    16. Approximations of distributions
  10. Point Estimates100% developed  as of 12:07, 28 March 2007 (UTC) (12:07, 28 March 2007 (UTC))
    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. Time Series Analysis
  14. 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
  15. Analysis of Specific Datasets
    1. Analysis of Tuberculosis
  16. Appendix
    1. Authors
    2. Glossary
    3. Index
    4. Links

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Sample surveys involve the selection and study of a sample of items from a population. A sample is just a set of members chosen from a population, but not the whole population. A survey of a whole population is called a census.

A sample from a population may not give accurate results but it helps in decision making.

Examples

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Examples of sample surveys:

  • Phoning the fifth person on every page of the local phonebook and asking them how long they have lived in the area. (Systematic Sample)
  • Dropping a quad. in five different places on a field and counting the number of wild flowers inside the quad. (Cluster Sample)
  • Selecting sub-populations in proportion to their incidence in the overall population. For instance, a researcher may have reason to select a sample consisting 30% females and 70% males in a population with those same gender proportions. (Stratified Sample)
  • Selecting several cities in a country, several neighbourhoods in those cities and several streets in those neighbourhoods to recruit participants for a survey. (Multi-stage sample)

The term random sample is used for a sample in which every item in the population is equally likely to be selected.

Bias

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While sampling is a more cost effective method of determining a result, small samples or samples that depend on a certain selection method will result in a bias within the results.

The following are common sources of bias:

  • Sampling bias or statistical bias, where some individuals are more likely to be selected than others (such as if you give equal chance of cities being selected rather than weighting them by size)
  • Systemic bias, where external influences try to affect the outcome (e.g. funding organizations wanting to have a specific result)
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