Introduction to Statistics

Introduction to Statistics

• Statistics is the science of conducting studies to collect, organize, summarize, and analyze data, and to draw conclusions.
• Statistics is used in almost all fields of human endeavor, including business management, education, economics, biology, medical science, social science, agriculture, and sports science.
• Studying statistics is important to understand statistical studies.

Basic Terms

• An element is a subject or object about which information is collected.
• A variable is a characteristic under study that can assume different values for different elements.
• Random variables possess values that are determined by chance.
• Data represents the values (measurements or observations) that variables can assume.
• A data set is a collection of data values.
• A data value is a single value in a data set, also referred to as a datum.
• A population includes all subjects whose characteristics are being studied.
• A census involves the collection of data from every element in a population.
• A sample is a group of subjects selected from a population.

Descriptive and Inferential Statistics

• Statistics can be divided into two types:
  • Descriptive statistics describes a situation through collection, organization, summarization, and presentation of data.
  • Inferential statistics involves generalizing from samples to a population by performing estimations, hypothesis tests, determining relationships among variables, and making predictions, also known as inductive reasoning or inductive statistics.

Variables Types of Data

• Qualitative variables are placed into distinct categories according to some characteristic or attribute.
• Quantitative variables are numerical and can be ordered or ranked.
  • Discrete variables assume countable values.
• Continuous variables assume all values between any two specific values and are obtained bymeasurements.

Measurement Level of Variables

• The nominal level classifies data into non-overlapping, exhaustive categories without imposing order or ranking, such as marital status (single, married, divorced, widowed).
• The ordinal level classifies data into categories that can be ordered or ranked, but precise differences between the ranks do not exist, such as student views of lecturers' teaching (excellent, good, fair, poor).
• The interval level ranks data with precise differences between units of measure but lacks a meaningful zero, such as intellectual quotient and temperature.
• The ratio level ranks data with precise differences between units of measure and a meaningful zero, like height and weight.

Methods to Collect Data

• Surveys can be conducted through:
  • Personal interviews to provide in-depth responses, but are more costly and require trained interviewers to avoid bias.
  • Telephone surveys which are less costly than personal interviews and allow for more frank opinions.
  • Mailed questionnaires which can cover a wider area and allow respondents to remain anonymous, but may yield low response rates and difficulty in understanding the questions.

Sampling techniques

• Samples being less expensive and time-consuming when populations are large.
• Samples are specifically used with random, systematic, stratified, and cluster sampling to obtain unbiased samples.
• Random sampling involves selecting samples using chance methods or random numbers, where each subject in a population has an equal chance of inclusion in the sample.
• Systematic sampling numbers each subject of the population, then selects every kth subject, with the first subject selected at random.
• Stratified sampling divides the population into groups (strata) according to some characteristic important to the study, then samples from each group.
• Cluster sampling selects subjects from intact groups (clusters) that are representative of the population.

Observational and Experimental Studies

• In an observational study, the researcher observes and draws conclusions based on the observations.
• In an experimental study, the researcher manipulates the independent (explanatory) variable to determine its influence on the dependent (outcome) variable.
• A confounding variable influences the dependent variable but cannot be separated from the independent variable.