sampling types

Sampling Types

  • Sampling in Statistics: Refers to techniques used to select a subset of individuals from a population to estimate characteristics of the whole population.

  • Types of Sampling:
      - Simple Random Sampling
      - Systematic Sampling
      - Stratified Sampling
      - Cluster Sampling
      - Convenience Sampling

Sampling Methods in Statistics

1. Simple Random Sampling

  • A sample of size n is taken such that every possible sample of size n has an equal chance of being chosen.

  • Often synonymous with "random sample".

2. Systematic Sampling

  • Selects every kth subject from a list or queue.

3. Stratified Sampling

  • The population is divided into strata (groups) that share similar characteristics, then a random sample is taken from each stratum.

4. Cluster Sampling

  • The population is divided into clusters (groups), then a number of clusters are randomly selected, with all members from chosen clusters surveyed.

5. Convenience Sampling

  • Data is collected from individuals who are easiest to access rather than following a random selection process.

Summary of Sampling Methods

  • Simple Random Sample: Every subject has an equal chance of selection.
      - Example: A local health clinic randomly selects 100 patients from registered lists for a diabetes study.

  • Exemplar of Systematic Sampling: Select every kth subject (e.g., every 10th person).

Sampling Errors

  • Sampling Error: Occurs when there are discrepancies between sample results and the true population results due to chance.

  • Non-Sampling Error: Arises from human error, such as incorrect data entries, biased questions, or inappropriate statistical methods.

  • Nonrandom Sampling Error: Results from using a non-random sampling method, like a convenience sample.

Types of Studies

A. Observational Studies

  • No manipulation or intervention on subjects or variables.

  • Risk factors are variables presumed to relate to potential outcomes.

Study Designs:

  1. Cross-sectional study: Measures both exposure and outcome simultaneously.

  2. Retrospective (case-control) study: Looks back at subjects with known outcomes to assess prior exposure.

  3. Prospective (longitudinal or cohort) study: Follows subjects over time to assess the development of outcomes based on their initial risk factors.

Definitions and Examples of Studies Conducted

  • Diabetes Study: Random selection of 100 patients to check for diabetes indicators.

  • Blood Pressure Study: Random selection of 200 individuals without stratification to check average blood pressure levels.

  • Diabetes Risk Study: Population categorized into age groups for proportional representation in sampling.

Notation for Probabilities

  • P denotes probability.

  • Specific events are denoted as A, B, C, etc.

  • P(A) represents the probability of event A occurring.

Approaches to Finding Probability

  1. Relative Frequency Approximation

  2. Classical Approach

  3. Subjective Probability

Relative Frequency Probability Example

  • Example: Skydiving - 3,000,000 jumps with 21 deaths.
      - P(skydiving death) = [ \frac{21}{3000000} = 0.000007 ]

Classical Probability Example - Gender of Children

  • Sample space for three children: {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}

  • P(three same gender) = [ \frac{2}{8} = 0.25 ]

Subjective Probability Example - Acute Appendicitis

  • Estimated probability of 0.001 based on experience and lack of historical data.

Incidence and Prevalence

  • Incidence: Number of new cases of a disease developing in a population at risk over time; indicates disease risk.

  • Prevalence: Total number of existing cases of a disease at a specific time; indicates disease burden.

Rates of Mortality & Morbidity

  • Infants: Babies born alive.

  • Neonates: Infants under 28 days old.

Contingency Table

  • A matrix format table displaying frequency distribution for variables.

Absolute Risk Reduction

  • [ ext{Absolute Risk Reduction} = | P( ext{event in treatment}) - P( ext{event in control}) | ]

Relative Risk Definition

  • Ratio comparing risk of disease in those with a risk factor against those without.

Interpreting Relative Risk

  • Value of 1: No difference in risk.

  • Value greater than 1: Increased risk for treatment group.

Example: Salk Vaccine Study

  • Treatment Group with polio: 33 out of 200,712, Control Group: 115 out of 201,114

  • [ P_t = \frac{33}{200712} \text{ and } P_c = \frac{115}{201114} ]

  • Relative Risk: [ RR = \frac{0.000164}{0.000571} = 0.287 ]

Interpretation of Study Results

  • Vaccines reduce polio risk; rate for vaccinated kids is 0.287 compared to placebo.

  • Reciprocal indicates placebo group is 3.48 times more likely to contract polio.

Odds Ratio Definition

  • [ \text{Odds Ratio} = \frac{\text{odds in favor of treatment group}}{\text{odds in favor of control group}} ]

Example of Odds Ratio

  • Retrospective Study of newborns indicates rehospitalization odds of [ \text{Odds Ratio} = \frac{457 \cdot 2860}{3199 \cdot 260} = 1.571 ]

  • Interpretation: Higher rehospitalization risk for newborns discharged early.

Conclusion

  • Relative Risk is typically used for prospective studies, while Odds Ratio can be used in both prospective and retrospective studies.