Statistics Levels of Measurement & Sampling Methods

Study Notes

Nominal: Categories with no inherent order. Examples: gender, ethnicity, blood type. Analyzed using counts and percentages.
Ordinal: Categories that can be ordered, but differences between categories are not consistent. Examples: Survey responses like "poor," "fair," "good," "excellent."
Interval: meaningful and equal intervals, but no true zero point. Example: Temperature in Celsius or Fahrenheit. Can add and subtract, but ratios are not meaningful.
Ratio: Highest level of measurement. Has equal intervals and a true zero point. Examples: Weight, height, age, income. All arithmetic operations are valid, including multiplication and division.

Random Sampling: Each individual in the population has an equal chance of being selected.
Stratified Sampling: Population is divided into subgroups (strata), and then a random sample is taken from each subgroup to ensure representation of the population's diversity.
Systematic Sampling: Individuals are selected from a population at regular intervals.
Cluster Sampling: Population is divided into clusters, and a random sample of clusters is selected. All individuals in the selected clusters are included in the sample.
Convenience Sampling: Individuals are selected based on their availability and ease of access. This method is prone to bias and cannot reliably generalize results.

Observational studies: Researchers observe and collect data without manipulating any variables.
Key Feature: In observational studies, researchers simply observe and record data without interfering in any way. They do not actively manipulate factors.
Pros: Can study rare events, explore complex relationships, and be cost-effective.
Cons: Cannot establish causality, prone to bias (recall bias, selection bias).

Experimental studies: Researchers manipulate one or more variables to determine their effect on other variables. They are designed to establish causality.
Key Features: Controlled manipulation of variables, randomization, ability to control the environment, and replication of results.
Types:
- Randomized Controlled Trials (RCTs): Participants are randomly assigned to treatment or control groups, minimizing bias and establishing causality.
- Quasi-experimental Studies: Participants are not randomly assigned, leading to higher risk of bias.
Advantages: Can establish causality, control over variables, randomization reduces bias.
Limitations: Expensive and complex to conduct, ethical and practical constraints, potential artificiality of the study environment.

### Key Differences between Observational and Experimental Studies

Causality: Observational studies can identify correlations, while experimental studies are designed to establish cause-and-effect relationships.
Manipulation: Observational studies involve no manipulation, while experimental studies actively manipulate variables.
Bias: Observational studies are more prone to bias, while experimental studies strive to minimize bias through control and randomization.