Introduction to Statistics

Introduction to Statistics

• Statistics is the mathematical field dealing with collecting, organizing, and interpreting numerical data.
• It uses quantitative models to analyze experimental data and real-world studies.

Outline of Topics

• Definitions of statistical terms
• Statistical methods
• Types of statistics (descriptive and inferential)
• Differences between descriptive and inferential studies

Definitions of Terms

• Statistics: A tool to organize, summarize, and clearly communicate findings (data).
• Medical Statistics/Biostatistics: The application of statistical principles in healthcare.
• Data: The fundamental building blocks of statistics which are observations or evidence about the social world. Can be quantitative or qualitative. Data are produced, not given, researchers choose what to consider data.
• Population (N): All elements (people or things) whose characteristics are being studied.
• Parameter: A value (like average, total) calculated from the entire population.
• Sample (n): A subset of the population selected for study.
• Statistic: A value calculated from a sample.
• Subjects: The units on which sample characteristics are measured; often humans, but also cells, cultures, or animals in research.

Relationship Between Population, Sample, Parameter, and Statistic

• Researchers want to know about a population but often only have a sample to work with
• Use random selection to get a sample from the population
• Infer from the sample to make generalizations about the population
• Parameter describes a population characteristic
• Statistic describes a sample characteristic

Census vs. Sample

• A census studies the entire population.
• A sample studies a smaller part of the population.
• Determining sample vs census depends on resources and needs.

Statistical Methods

• Methods of data collection
• Analytic statistics
• Methods of data presentation

Data vs Information

• Data: Observations or evidence about the world.
• Information: Processed data to become meaningful and useful (data + meaning = information)
• Raw data is data without any processed interpretation.
• For example, individual exam marks are raw data, while the statement that boys outperformed girls or that 76% of the students got A or B grades is information.

Sources of Data

• Census
• Vital registration
• Official records
• Simple surveys
• Studying individuals

Nature of Data

• Data can be classified into:
  • Qualitative data or attributes
  • Quantitative data or variables

Types of Statistics

• Descriptive statistics
• Inferential statistics

Descriptive Statistics

• Techniques to organize, display, and describe data.

  • Use tables, graphs, and summary measures
  • Summarizing data
  • Describing data
  • Most typical values in a data set

• Examples: Calculations describing data:

  • Measures of central tendency: mean, median, mode
  • Measures of dispersion: range, variance, standard deviation

Inferential Statistics

• Techniques to use sample data to make generalizations or predictions about a population
  • Making decisions, inferences or predictions about the population by observing findings from the samples.
  • Determining if results are statistically significant
  • Examples:
    • T-test
    • Analysis of variance (ANOVA)
    • Chi-Square test
    • Correlation

Statistical and Research Applications

• Statistics are crucial for analyzing research data to draw conclusions.
• Example: A study comparing the preferences for Diet Coke and Diet Pepsi among research participants illustrates how descriptive (observed difference) and inferential (meaningful difference) statistics can be used to interpret results.

Descriptive vs. Inferential Statistics Summary

• Descriptive: Organizes & summarizes data, presents data visually
• Inferential: Generalizes findings from samples to populations; hypothesis testing, assessing relationships

This quiz covers the fundamental concepts of statistics, including definitions, methods, and types of statistical analyses. Understand the differences between descriptive and inferential statistics, as well as the importance of data in the field. Test your knowledge on statistical terms and their applications, especially in healthcare.