Statistics Overview and Processes

Statistics

• Branch of mathematics used to collect, classify, present, analyze and interpret data.
• Aims to draw meaningful conclusions from the data.

The Five Essential Processes in Statistics

• Collection
• Classification
• Presentation
• Analysis
• Interpretation

Descriptive Statistics

• Focuses on gathering, classifying, presenting, and summarizing data.
• Describes group characteristics of data.
• Includes measures of central tendency:
  • Mean
  • Median
  • Mode
• Includes measures of variability:
  • Standard deviation
  • Variance
  • Minimum and maximum variables
  • Kurtosis
  • Skewness

Inferential Statistics

• Uses information gathered from a sample to make inferences about a larger population.
• Uses descriptive statistics to draw conclusions about a population based on a representative sample.
• Allows researchers to make assumptions about a wider group based on a smaller sample.
• Used for tasks like:
  • Estimating average demand for a product
  • Surveying consumer buying habits
  • Predicting future events, such as asset class returns based on a sample period

Elements

• Population: All members of a group being studied.
• Sample: A portion of the population selected for analysis.
• Parameter: A numerical measure describing a population characteristic.
• Statistic: A numerical measure describing a sample characteristic.
• Variable: A characteristic of an item or individual being analyzed.

Variables

• A characteristic or attribute of a person or object that assumes different values.

Categorical Variable

• Composed of different types or categories of a phenomenon.
• Values are selected from an established list of categories.

Categorical Nominal Variable

• Describes a name, label, or category without natural order.
• Examples:
  • Sex (Male or Female)
  • Blood type
  • Hair color

Categorical Ordinal Variable

• Values are defined by an order relation between categories.
• Examples:
  • Socioeconomic status.
  • Educational level.
  • Satisfaction.

Quantitative Variable

• Varies in degree or amount of a phenomenon.
• Values are numbers.

Quantitative Continuous Variable

• Can assume an infinite number of real values within a given interval.

Quantitative Discrete Variable

• Can assume only a finite number of real values within a given interval.

Independent Variable

• Presumed to cause changes in another variable.
• The variable manipulated in an experiment.

Dependent Variable

• Changes because of another variable.
• The effect or outcome variable.

Mediating Variable

• Lies between other variables, explaining the process through which they affect each other.
• Specifies how or why a particular effect or relationship occurs.

Moderator Variable

• Affects the relationship between a dependent and independent variable.
• May increase or decrease the strength of a relationship, or change the direction of a relationship.
• Indicates when or under what conditions a particular effect can be expected.

Data

• A set of values collected for the response variable from each element in a sample.

Quantitative Data

• Refers to quantities, counts, or measurements.
• Numerical in nature.

Quantitative Discrete Data

• Values can be counted using integral values.

Quantitative Continuous Data

• Expressed in approximations or measurements.

Qualitative Data

• Can be observed but not measured.
• Represents differences in quality, character, or kind, but not in amount.

Other Types

• Primary Data
• Secondary Data
• Internal Data
• External Data

Binary Data

• Data with two possible values (e.g., yes/no, true/false).

Ordered Categories

• Data with categories that have a natural order (e.g., low, medium, high).

Unordered Categories

• Data with categories that do not have a natural order (e.g., colors, types of fruit).

Count Data

• Data that represents the frequency of occurrence of events (e.g., number of customers, number of cars).

Scale of Measurement

• Rules used to assign scores and indicate the kind of information provided by the scores.

Measurement

• The process of assigning a numerical value to a variable.

Types of Measurement Scales

• Nominal
• Ordinal
• Interval
• Ratio

Nominal Scale

• Measures identity.
• Uses numbers to identify names or membership in a group or category.
• An unordered set of categories identified only by name.
• Allows you to determine whether two individuals are the same or different.
• Example: Gender (male, female).

Ordinal Scale

• Data is ranked from "bottom to top" or "low to high".
• Data can be arranged in an ordering scheme.
• Measurement used on ranking individuals or objects.
• Tells you the direction of difference between two individuals.
• Example: Student evaluation.

Interval Scale

• Numbers reflect differences among items.
• Possesses the properties of nominal and ordinal scales.
• Measurement used on ranking individuals or objects.
• Example: Scores in a test.

Ratio Scale

• Data can be classified and placed in order.
• Possesses all properties of nominal, ordinal, and interval scales.
• Example: Weight.

Properties of Measurement Scales

• Classify: Can data be categorized?
• Order: Can data be arranged?
• Equal Limits : Are intervals between data points equal?
• Absolute Zero: Is there a true zero point?

Population

• Totality of subjects (people, animals, or objects) under consideration.
• Refers to the entire group being studied.

Sample

• A portion of the population selected for analysis.