Statistics/Methods of Data Collection/Experiments


  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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Experiments Edit

In a experiment the experimenter applies 'treatments' to groups of subjects. For example the experimenter may give one drug to group 1 and a different drug or a placebo to group 2, to determine the effectiveness of the drug. This is what differentiates an 'experiment' from an 'observational study'.

Scientists try to identify cause-and-effect relationships because this kind of knowledge is especially powerful, for example, drug A cures disease B. Various methods exist for detecting cause-and-effect relationships. An experiment is a method that most clearly shows cause-and-effect because it isolates and manipulates a single variable, in order to clearly show its effect. Experiments almost always have two distinct variables: First, an independent variable (IV) is manipulated by an experimenter to exist in at least two levels (usually "none" and "some"). Then the experimenter measures the second variable, the dependent variable (DV).

Example: Experimentation

Suppose the experimental hypothesis that concerns the scientist is that reading a wiki will enhance knowledge. Notice that the hypothesis is really an attempt to state a causal relationship like, "if you read a qiki, then you will have enhanced knowledge." The antecedent condition (reading a wiki) causes the consequent condition (enhanced knowledge). Antecedent conditions are always IVs and consequent conditions are always DVs in experiments. So the experimenter would produce two levels of Wiki reading (none and some, for example) and record knowledge. If the subjects who got no Wiki exposure had less knowledge than those who were exposed to wikis, it follows that the difference is caused by the IV.

So, the reason scientists utilize experiments is that it is the only way to determine causal relationships between variables. Experiments tend to be artificial because they try to make both groups identical with the single exception of the levels of the independent variable.