Key Concepts and Methods in Statistical Analysis

Statistics: Key Concepts and Methods

1. Statistics is a collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions.

2. Statistical methods consist of a series of procedures for managing, analyzing, and collecting qualitative and quantitative research data.

3. A population includes all objects of interest, whereas a sample is only a portion of the population.

Example: The population could be all students of a postgraduate program, and a representative sample of this population could be 400 students from different studies of the program.

Understanding Variables in Statistics

4. A variable is any characteristic, number, or quantity that can be measured or counted. A variable may also be called a data item.

Examples: Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye color, and vehicle type are examples of variables.

Types of Variables

5. Variables can be classified into different types:

• Discrete: Represent countable items (e.g., number of registered cars, business locations, children in a family).
• Continuous: Represent measurable quantities (e.g., height, time, age).
• Ordinal: Represent categories with an inherent order (e.g., academic grades A, B, C; clothing sizes S, M, L, XL).
• Nominal: Represent categories without an inherent order (e.g., sex, business type, eye color, religion, brand).

Data Presentation

6. Particular observation: This refers to individual data points.

Example: The number of sales made on a given day by each of four people.

Grouped with frequencies: In statistics, the frequency of an event is the number of times the event occurred in an experiment or study. These frequencies are often graphically represented in histograms.

Grouped in classes with frequencies: Grouped data is data that has been organized into groups known as classes. Grouped data has been 'classified,' and thus some level of data analysis has taken place, which means that the data is no longer raw. A data class is a group of data related by some user-defined property.

Statistical Measures

Statistical Models and Interpretation

8. A statistical model is a mathematical equation that reproduces observed phenomena as accurately as possible. It considers the provided data and the influence of random effects in these observations.

Interpreting Statistical Measures

• Standard deviation: The real value deviates from the theoretical value by...% on average.
• Coefficient of variation (volatility coefficient): The share of variation on the mean is...%.
• Determination coefficient: (No specific example provided in the original text, but it typically explains the proportion of variance in the dependent variable that is predictable from the independent variable(s)).
• Indetermination coefficient: The...has not been explained by the model in the measure of...%.
• Correlation coefficient: The real values are correlated with the theoretical values at the level of...