Introduction to Statistics

INTRODUCTION TO STATISTICS

Definition, Natures and Importance of Statistics

  • The term "statistics" originates from the Latin word "status," meaning "state."

  • Statistics is fundamentally a collection of quantitative data which includes various fields such as:

    • Statistics of crimes

    • Statistics on enrollment

    • Statistics on unemployment

  • Statistics is also recognized as a science that involves the following processes:

    • Collection of quantitative data

    • Presentation of the collected data

    • Analysis of the data

    • Interpretation of data analysis results

  • Importance of Statistics:

    • Acts as a tool to develop general and meaningful conclusions that extend beyond the original data.

Uses of Statistics

  • Various applications of statistics include:

    • Surveys: Designed to harness early returns on election day to forecast election outcomes.

    • Product Preference Prediction: Using samples of consumers to gather information on preferences for products.

    • Quality Control in Manufacturing: Sampling newly manufactured fuses before shipping to determine whether to hold or send batches.

    • Medical Research: Research physicians conducting experiments to ascertain the effectiveness of drugs and treatment methods.

    • Economic Forecasting: Economists observing economic indices over time to make future predictions about economic conditions.

Natures of Statistics

  • Statistics encompasses two primary fields of interest:

    • Government (political science)

    • Games of chance

Types of Statistics

Descriptive Statistics

  • Descriptive statistics focus on methods for organizing, summarizing, and presenting large data sets to yield meaningful information.

Inferential Statistics

  • Inferential statistics deals with making generalizations about a population based on a sample subset of data. This area encompasses methods for analyzing a portion of data to infer conclusions about the entire set.

Examples of Distinguishing Descriptive vs. Inferential Statistics

  • Consider if the following statements use descriptive or inferential statistics:

    1. A bowler calculating his average for the past 12 games (Descriptive)

    2. A manager predicting sales performance based on past years’ trends (Inferential)

    3. A politician estimating his chances in an election using an opinion poll (Inferential)

    4. A teacher assessing the percentage of students passing an examination (Descriptive)

    5. A student averaging monthly school expenditures for the last five months (Descriptive)

    6. A basketball player estimating MVP chances based on season averages and comparison to opponents (Inferential)

Basic Statistical Terms

  1. Population: The complete set of individuals or entities under consideration, which can be either finite or infinite based on predetermined characteristics.

  2. Variable: A measurable characteristic of interest applicable to all individuals within the population, typically denoted by a capital letter from the English alphabet.

Types of Variable

  • Variables are broadly classified into:
    a. Qualitative Variable: Consists of categories or attributes with no numerical characteristics. Examples include classification, year level, sex, and subjects enrolled.
    b. Quantitative Variable: Comprises numerical representations of counts or measurements.

Classification of Quantitative Variables

  • Discrete Quantitative Variable: Results from a finite or countable set of values. Examples: Number of students, number of books, and number of patients.

  • Continuous Quantitative Variable: Consists of infinitely many values represented on a continuous scale without interruptions or gaps. Examples: Height, weight, GPA, and time.

Examples of Variables

  1. Research on average age of dengue fever patients in October at PGH:

    • Population: Patients infected with dengue fever

    • Variable: Average age of patients

    • Type: Quantitative Variable

    • Classification: Continuous Quantitative Variable

  2. Research on the number of female Computer Science students at CvSU-Carmona:

    • Population: Computer Science students

    • Variable: Number of female students

    • Type: Quantitative Variable

    • Classification: Discrete Quantitative Variable

  3. Perception of medical procedures among CvSU-Carmona students:

    • Population: Students of CvSU-Carmona

    • Variable: Their perception about medical procedures

    • Type: Qualitative Variable

Additional Definitions

  • Sample: A subset or part of a population drawn for analysis.

  • Parameter: A numerical measurement representing a characteristic of a population.

  • Statistics: A numerical measurement describing a characteristic of a sample.

Surveys in Statistics

  • Surveys can be classified as:

    • Census Survey: Involves collecting data from every individual in a population.

    • Sampling Survey: Collects data from a subset of the population.

Levels of Measurement of Data

  • This refers to how data can be quantified and the statistical tools applicable to the dataset.

Level 1: Nominal

  • Characterized by data that only consists of names, labels, or categories without any order. Examples include name, religion, civil status, address, sex, and degree program.

Level 2: Ordinal

  • Data arranged in order but differences between values may not be meaningful. Examples include military rank, job position, and year level.

Level 3: Interval

  • Similar to ordinal but with meaningful differences between data values; however, there is no natural zero point. Examples include IQ scores and temperature (in °C).

Level 4: Ratio

  • Includes an inherent zero starting point, making both differences and ratios meaningful. Examples: height, width, area, and weekly allowance.

Summary of Levels of Measurement

  • Ratio: Absolute zero present

  • Interval: Meaningful distances

  • Ordinal: Orderable attributes

  • Nominal: Named attributes (weakest level)

Further Examples of Levels of Measurement

  • Given the following variables, identify the level of measurement:

    • Student course (Nominal)

    • SSS number (Nominal)

    • Subjective satisfaction level (Ordinal) including: Satisfied, slightly satisfied, slightly unsatisfied, unsatisfied.

    • Number of clients (Ratio)

    • Sugar level (Ratio)

    • Jersey number (Nominal)

    • Salary (Ratio)

    • IQ Score (Interval)