Introduction to Statistics

1. scientific discipline

2. three critical pillars

Statistics is a ____ built upon ____:

• Collection

• Analysis

• Presentation

The three critical pillars of statistics:

Collection

Gathering raw data from various sources

Analysis

Processing data to uncover patterns and insights

Presentation

Communicating findings clearly and effectively

• Informed Inference & Decision-Making

• Enabling decisions based on empirical evidence

ultimate goal of statistics

• finance

• marketing

• operations

Business application of statistis and the Various business function

• Market forecasting

• Risk assessment

• Investment Analysis

Under Finance

Time series analysis for predicting stock prices and economic indicators

Market forecasting

Statistical models for evaluating investment risk and portfolio optimization

Rusk assessment

Investment analysis

Methods for optimizing investment portfolios based on historical data

• Consumer research

• market segmentation

• Campaign evaluation

Under marketing

consumer research

Surveys and statistical analysis to understand consumer behavior

Market segmentation

Statistical techniques to divide markets into distinct consumer segments

Campaign evaluation

A/B testing to assess effectiveness of advertising campaigns

• Quality control

• Process improvement

• Standard setting

Under Operation

Quality control

Statistical methods for monitoring production processes and identifying defects

Process improvement

Data-driven approaches to enhance efficiency and reduce waste

Standard setting

Establishing product standards and ensuring compliance through statistical sampling

Data

Raw, unorganized facts or figures that have no inherent meaning on their own

Daily temperature readings: 25°C, 28°C, 22°C, 26°C, 29°C

example of raw data

Information

Data that has been processed and organized to make it useful and meaningful

Average weekly low temperature: 25.2°C

example of processed information

1. raw

2. processed

Data exists in ___form until____

1. context

2. meaning

Information provides ___ and ____

decision-making

Information enables___

• Primary data

• Secondary data

Sources of data

Primary data

Data collected directly by the researcher or organization for a specific purpose

• Direct observation

• experiments

• surveys

Ways of collecting primary data

Direct observation

Observing and recording behaviors or phenomena as they occur

Experiments

Conducting controlled studies to test hypotheses and gather data

Surveys

Collecting data through questionnaires or interviews from a sample of individuals

Secondary data

Data that has already been collected by someone else for a different purpose

• Government databases

• Industry reports

• Academic journal

Ways of gathering data for secondary data

Government databases

Census data, economic indicators, public health records

Industry reports

Market research reports, financial statements

Academic Journals

Research findings published by other scholars

• Qualitative (categorical) data

• Quantitative (numerical) data

Data types

Qualitative (Categorical) Data

Describes characteristics or categories that cannot be measured numerically. Often represents attributes or labels.

Quantitative (Numerical) Data

Consists of numerical values that can be measured or counted.

• Nominal

• Interval

• Ordinal

• Ratio

Levels of Measurement Overview

1. Nominal

2. TV channel numbers, types of fruits, gender

3. Keyfeatures:

• Categories are mutually exclusive

• No inherent order or ranking

• Labels for identification only

______ The simplest level, where data are categorized without any order or hierarchy. 

ex. ____

key features:
___

1. Interval

2. Example: Temperature in Celsius, IQ scores

3. key features:

   • Has consistent spacing between points

   • No true zero point (arbitrary starting point)

   • Differences between values are meaningful

   • No meaningful ratios (can't say "twice as hot")

____Allows for ordering, and differences between data points are meaningful, but has no true zero point.

example____

Key Features _____

1. Ordinal

2. Example: Educational attainment, customer satisfaction ratings

3. Key features

• Categories have a meaningful order

• Ranks can be compared

• Differences between ranks are not equal

____ Data can be ordered or ranked, but the differences between categories are not meaningful.

example___
Key features ____

1. ratio

2. Example: Income, height, weight, age

3. Key features:

   • Has consistent spacing between points

   • Has a true zero point

   • Differences between values are meaningful

   • Has meaningful ratios (can say "twice as heavy")

___Has all characteristics of interval data plus a true zero point, allowing for meaningful ratios.

example___

Descriptive Statistics

Summarizes, organizes, and presents data to describe "what is" without generalizing beyond the data.

Inferential Statistics

Makes predictions or inferences about a larger population based on sample data, addressing "what if" questions.

Population

The entire group of individuals or objects about which information is desired

Sample

A subset or representative group selected from the population

Parameter

A numerical characteristic that describes a population

Statistic

A numerical characteristic that describes a sample

• Ensures Representativenes

• Unbiased Estimates

• Consequences of Non-Random Sampling

• Best Practice

Why Random Sampling Matters

Discrete Data

Data that consists of distinct, separate values that are countable.

Continuous Data

Data that represents measurable quantities and can take any value within a range.

Independent Variables

Variables that cause or influence outcomes

Dependent Variables

Variables that represent the outcome being studied

Probability Sampling

Random selection methods where every individual has a known, non-zero chance of being selected.

• Simple Random Sampling

• Stratified Sampling

• Systematic Sampling

• Cluster Sampling

methods of probability sampling

Simple Random Sampling

Every individual has an equal chance of being selected.

Systematic Sampling

Selects every kth individual from a list after random start.

Stratified Sampling

Population divided into subgroups based on characteristics.

Cluster Sampling

Divides population into clusters, selects some clusters.

Non-Probability Sampling

Non-random methods where selection is based on convenience or specific criteria.

• Convenience Sampling

• Quota Sampling

• Snowball Sampling

methods of non probability sampling

Convenience Sampling

Samples are taken from a population segment that is easiest to access.

Quota Sampling

Researchers select individuals to meet predefined quotas for various subgroups.

Snowball Sampling

Existing participants recruit future participants from a hard-to-reach population.

Time Series Data

 Data measured over a range of time periods for a single subject or variable.

Cross-Sectional Data

 Data measured from multiple subjects or entities at a single point in time.