Introduction to Statistics

• Statistics is a branch of science concerning data collection, organization, presentation, analysis, and interpretation.
• Statistics involves conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.

Applications of Statistics

• Data mining
• Speech recognition
• Vision and image analysis
• Data compression
• Artificial intelligence
• Network and traffic modeling

Use of Statistics

• Statistics are used for data mining, speech recognition, vision and image analysis, data compression, artificial intelligence, and network and traffic modeling.
• Statistics are numerical characteristics calculated for a set of data. It is the backbone of research and business applications, used in almost all fields.
• Computer Science: Statisticians and computer scientists merge in the development of models and data mining, using stochastic models with prior knowledge of data.
• Economics: Economists use statistical information to make forecasts.
• Sports: Statisticians keep records of scores.
• Public Health: Administrators track the spread of diseases.
• Education: Researchers compare teaching methods.
• Business: Decision-makers maximize profit using data.

Why Study Statistics

• Understand statistical studies in one's field.
• Conduct research using statistical procedures.
• Become better consumers and citizens.

Two Branches of Statistics

Descriptive Statistics

• Organizes and summarizes observations.
• Describes basic data features.
• Provides simple summaries about the sample and the measures.

Inferential Statistics

• Formulates inferences about a population from a sample.
• Makes inferences from data to broader conditions.

Analytic Goals

• Finding attributes or characteristics of the group being studied.

Central Tendency

• General characteristic of the group.
• Example: Determine the mean monthly internet allowance of USLS students.
• Example: Determine the percentage of USLS College students who prefer a Globe over a Smart network.

Variance in the Group

• How individual members vary from the average.
• Example: Determine the age range in a Statistics class.
• Example: Determine if Statistics final grades are similar in a class.

Difference within/between Groups

• Whether subgroups or separate groups are different or similar.
• Example: Compare the mean number of internet searching between male and female USLS students.
• Example: Determine if there is a significant difference in the mean number of online gaming in a week among the students from the five different colleges of USLS.

Relationships within the Group

• Identifying relationships between study variables.
• Example: Establish if there is a significant relationship between choice of laptop brand and the college a USLS student belongs to
• Example: Determine if relationship between status and final grades in Statistics are independent

Prediction

• Establishing a model to predict future outcomes.
• Example: Identify factors influencing a graduate's job prospects within one year.
• Example: Estimate the time to code software after design finalization.

Types of Analysis

Descriptive

• Limited to describing the studied group.
• Conclusions cannot be applied outside the group.

Inferential

• Findings from a small group are applied to a larger group.

Research Process

• The problem must be Specific, Measurable, Attainable, Realistic, and Time-bound (SMART).

Terminology

• Population: All subjects under investigation.
• Sample: A subset of the population.
• Variable: Measurable subject characteristic that can vary.
• Data: Values that the variables assume.
• Data Set: A collection of data values.

Example Problem Analysis

• Problem: What is the average monthly internet allowance of a USLS college student?
• Population: All USLS College students.
• Variable: Monthly internet allowance.

Types of Variables

Qualitative/Categorical

• Attributes in categories (e.g., sex, religious affiliation).

Quantitative/Numerical

• Attributes in counts or measurements.
• Discrete Variable: Uses counting, values are whole numbers (e.g., number of gadgets).
• Continuous Variable: Uses measuring, values may have fractions or decimals (e.g., age).

Level of Measurement

• Measurement is the process of assigning numbers to observations.

Scales of Measurement

Nominal Level

• Numbers indicate categories for classification.
• Categories are mutually exclusive and exhaustive.
• Example: Sex (M=1, F=2).

Ordinal Level

• Possesses rank order characteristics.
• Categories are mutually exclusive and exhaustive.
• Indicates order of magnitude of a variable.
• Precise differences between ranks do not exist.
• Example: Likert-type scale (Strongly agree=1, etc.).

Interval Level

• Has all properties of the ordinal scale.
• Equal intervals between scores have the same meaning.
• Intervals show how much better one value is compared to another.
• No absolute zero.
• Example: IQ scores.

Ratio Level

• Possesses all interval scale characteristics.
• Has a true or absolute zero point.
• The ratio of two values is meaningful.
• Example: distance.