Introduction to Statistics

Introduction to Statistics

• Statistics can be applied in any field, including engineering, sciences, medicine, education, business analytics, social sciences, machine learning, quality control, and actuarial sciences.

Definition of Statistics

• Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data.
• Statistics uses numbers to summarize raw facts and figures in a meaningful way.
• Statistics is used for the study of uncertainty, also to identify variability in data.

Terminologies

• Population: a collection of individuals or objects under study from which a researcher aims to draw inferences.
  • A population can be finite or infinite.
  • A census involves collecting data from all members of a population.
• Sample: A subset of the population.
  • A sample survey collects data from part of the population providing a sample.
• Variable: A characteristic or property of an individual within a population or sample.
  • Examples of variables include age, gender, and temperature.
  • Variables are usually denoted using capital letters.
• Data (singular): the value of the variable associated with a single element of a population or sample.
  • Data can be a number, a word, or a symbol.
• Parameter: summary characteristic about individuals in the population.
  • A parameter is always related to the population.
  • Examples of parameters include population mean (μ), population variance (σ²), and population proportion (P).
• Statistic: summary characteristic about individuals in a sample.
  • A statistic is always related to the sample.
  • Examples of statistics include sample mean (x̄), sample variance (S²), and sample proportion (p).
• Experiment: planned activity yielding a set of data as results.

Example Scenario

• A researcher aims to find the average weight of first-year students at SLIIT and collects data from those in the computing faculty.
  • The population is all first-year students in SLIIT.
  • The sample includes all first-year students in the computing faculty.
  • The variable is weight.
  • The summary characteristic is the average weight, which is a statistic.
  • The type of survey conducted is a sample survey.

Types of Variables

• Variables can be qualitative (attribute/categorical) or quantitative (numerical).
• Qualitative (Attribute/Categorical) Variables: categorize and describe elements.
  • Examples of qualitative variables include hair color, gender, marital status, and highest education qualification.
  • Nominal variables: categories are not naturally ordered (e.g., gender, hair color, marital status).
  • Ordinal variables: categories are naturally ordered (e.g., satisfaction rating, pain severity, highest education qualification).
• Quantitative (Numerical) Variables: quantify an element.
  • Examples of quantitative variables include marks for statistics, age, temperature, and travel time.
  • Discrete variables: distance between two values exists (e.g., age in years, number of children, number of accidents per hour).
  • Continuous variables: can take any value within a given range (e.g., temperature, heartbeat).

Measurement Scales

• Nominal Data: Categories with no ordering or direction; the weakest form of measurement.
• Ordinal Data: Ordered categories with rankings, order, or scaling; a higher level of measurement.
• Interval Data: Differences between measurements exist, but there is no true zero.
• Ratio Data: Differences between measurements exist, and there is a true zero; the strongest form of measurement.

Interval Scale vs. Ratio Scale

• Interval Scale: Variables can be added and subtracted, but ratios and multiplication are not possible.
  • The mean, median, and mode can be calculated for interval scales.
  • Differences between variables can be evaluated.
  • Does not have a true zero point; temperature in Celsius or Fahrenheit and pH values are examples.
• Ratio Scale: Includes ratios and multiplication of variables and has all characteristics of an interval scale.
  • It permits calculation of measures of central tendency like mean, median, and mode.
  • Differences between variables can be evaluated.
  • A true zero point exists; examples include height, weight, temperature in Kelvin, number of sales, income, and heart rate.

Areas of Statistics

• Statistics can be divided into descriptive and inferential statistics.
  • Descriptive Statistics: Involves preliminary analysis or explanatory analysis to understand the behavior of data.
    • Descriptive statistics involve graphical and numerical methods.
  • Inferential Statistics: Involves drawing conclusions about population parameters using sample statistics.
    • Inferential statistics include parameter estimation and hypothesis testing.

Statistical Packages

• Data can be analyzed using statistical packages like SPSS, SAS, Minitab, R, E-views, and Matlab.
• Statistical packages allow for easy and precise data analysis.

R Software

• R is an independent, open-source statistical software.
• R was initially developed at the University of Auckland in the mid-1990s.
• R is distributed under the GNU open-source software license.
• R is developed by the user community.
• It is available on Linux, Windows, and Mac.
• The latest version is 4.4.2, which was released in 2024.
• Both terminal and GUI are available.
• IDEs for R include R Studio and Rattle.