Introduction to Statistics

Study Notes

Statistics is the science of collecting, organizing, summarizing, and analyzing data. It also includes making decisions based on these analyses.
Statistics can be broken down into numerical facts such as Malaysia's cumulative Covid-19 cases at 4,079,242 by March 21, 2022; or the percentage of smartphone ownership among Internet users in Malaysia, which rose from 74.3% in 2014 to 90.7% in 2015.

Statistical methods are classified into two categories:
- Descriptive Statistics: organizing, displaying, and describing data using tables, graphs, and summary measures. -Example: Percentage distribution of internet users by income group (e.g., > RM5,000, RM1,000-RM3,000).
- Inferential Statistics: use sample data to make decisions or predictions about a population.
  - Example: Determining the starting salary of a typical college graduate by surveying 2000 recent graduates.

Population/Target Population: all individuals, items, or objects whose characteristics are being studied - the entire group of interest.
Sample: a portion of the population selected for study.
Sampling: procedure for selecting adequate number of elements from a population.
Representative Sample: accurately reflects the characteristics of the population.
Random Sample: each member of the population has an equal chance of being selected.
Element/Member: a specific subject or object within a sample or population.
Variable: a characteristic under study that takes on different values for different elements.
Observation/Measurement: the value of a variable for an element.
Data/Data Set: collection of observations or measurements on one or more variables.
Parameter: a numerical value that describes the entire population.
Statistic: a numerical value that describes a sample.

Application of statistics in medicine and other health-related disciplines.
Example: The Framingham Study, a longitudinal study of residents in Framingham, Massachusets to identify factors contributing to cardiovascular disease.

Qualitative vs Quantitative:
- Qualitative variables: non-numerical, categorized characteristics (e.g., gender, marital status, eye color).
- Quantitative variables: numerical characteristics (e.g., height, weight, blood pressure).
Discrete vs Continuous:
- Discrete variables: can be counted (e.g., numbers of accidents, children).
- Continuous variables: can take on any value within a given range (e.g., height, weight).
Cross-Sectional vs Time-Series:
- Cross-sectional data: information on different elements of a population or sample at the same point in time.
- Time-series data: information on the same elements over a period of time.

Nominal: categorized data without any inherent order (e.g., gender, eye color).
Ordinal: categorized data with an inherent order (e.g., socioeconomic class, survey rankings).
Interval: numerical data with equal intervals between values, but no true zero (e.g., temperature).
Ratio: numerical data with equal intervals and a true zero (e.g., height, weight).

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