Statistics Overview and Concepts

Descriptive Statistics Overview

• Descriptive statistics is the science of collecting, organizing, interpreting, analyzing, and presenting data.
• It's concerned with describing the target population.
• Data is organized, analyzed, and presented in a meaningful manner.
• Results are displayed using tables, charts, and graphs.

Branches of Statistics

• Descriptive Statistics
  • Describes the target population.
  • Tools include measures of central tendency, variation, and position.
• Inferential Statistics
  • Gives information about large groups without examining every element.
  • Requires higher-level critical thinking.
  • Involves comparing, testing hypotheses, and predicting future outcomes.
  • Tools include z-tests, t-tests, ANOVA, chi-square, linear regression, and correlation.

Basic Concepts

• Variable: A characteristic that can be measured and take on different values. (e.g., height, age, income)
• Data: A specific measurement of a variable.
• Qualitative/Categorical Data: Data represented by names or labels. (e.g., gender, religion)
• Quantitative Data: Numerical data that can be counted or measured.
  • Discrete: Counted data. (e.g., number of employees, books in a library)
  • Continuous: Measured data. (e.g., height, weight, temperature)

Sources of Data

• Primary Data: Collected directly from the original source (e.g., interviews, surveys, censuses).
• Secondary Data: Secondhand information from other researchers (e.g., newspapers, academic books, journal articles).

Basic Concepts

• Parameter: A characteristic/number describing a whole population.
• Statistic: A characteristic/number describing a sample.
• Population: All individuals, items, or observations under study.
• Sample: A carefully selected subset of the population representing its characteristics.

Levels of Measurement

• Nominal: Categorizes variables using qualitative labels (e.g., hair color).
• Ordinal: Categorizes variables with an inherent order (e.g., level of education).
• Interval: Numerical scale with evenly spaced intervals between values (e.g., IQ score).
• Ratio: Interval scale with a true zero point (e.g., weight, height).

Sampling Techniques

• Probability Sampling: Each member has an equal chance of selection.
  • Simple Random: Unbiased selection (e.g., lottery method).
  • Systematic Random: Selecting samples based on a system of intervals.
  • Stratified Random: Selecting samples based on a stratified system of intervals.
• Non-Probability Sampling: Intentional selection based on characteristics, knowledge, experiences, or other criteria.
  • Purposive Sampling: Intentional selection based on specific criteria.
  • Cluster/Area Sampling: Dividing the population into groups for research.
  • Convenience Sampling: Recruiting individuals based on availability or ease of access.

Data Collection

• Indirect/Questionnaire: Using a list of questions for data from respondents.
• Direct/Interview: Collecting primary data by asking respondents.
• Experiment: Determining cause-effect relationships.
• Registration: Enforced data collection based on certain laws.

Data Presentation

• Time Series: Showing data over a period, to identify patterns and trends.
• Bar Graph: Presenting data visually using horizontal or vertical bars.
• Pie Graph: Illustrating relationships between parts and the whole using proportional sections.
• Scatter Plot: Showing relationships between two variables.
• Frequency Distribution: Data organization in tables using classes and frequencies.

Descriptive Measures

• Measures of Central Tendency:
  • Mean: Arithmetic average.
  • Median: Middle value in a data set.
  • Mode: Most frequent value.
• Measures of Variation:
  • Range: Difference between highest and lowest values.
  • Variance: Average of squared distances from the mean.
  • Standard Deviation: Square root of variance.