01-Introduction(1) Biometry

Introduction to Statistics

Learning Outcomes

• Differentiate between Populations and Samples

• Identify types of data:

  • Qualitative/Categorical: Non-numeric categories

  • Quantitative/Numeric: Numeric measurements

• Determine experimental bias and confounding

What is Statistics?

• Definition: Statistics is the Science of Data that focuses on collecting, analyzing, interpreting, presenting, and organizing data.

• Focus Areas:

  • Extracting meaningful information from data

  • Managing and dealing with uncertainty in data analysis

  • Answering questions using limited and potentially unreliable information

Study Design

• Statistics begins before data collection, emphasizing the importance of proper study design.

• Methods of Data Collection:

  • Experiments: Deliberately generating data to answer specific research questions through controlled conditions.

  • Observations: Monitoring and recording data from the natural environment without manipulation.

  • Surveys: Collecting responses from individuals through questionnaires or interviews.

Importance of Statistics in Research

• Crucial during:

  • Formulating the research question

  • Designing the study or experiment effectively

Formulating a Research Question

• Criteria:

  • Must be relevant to the field of study, clear and specific, and answerable through empirical methods.

• Examples of Bad Research Questions:

  • "How long is a piece of string?" (Vague and not measurable)

  • "What is the quality of this wine?" (Subjective and lacks clarity)

• Examples of Good Research Questions:

  • "What is the speed of light in a vacuum?" (Clear and measurable)

  • "What is the sugar content per unit mass of juice?" (Precise and quantifiable)

  • "Does lichen coverage of trees vary by aspect?" (Specific and measurable)

Populations and Samples

• Research questions typically refer to properties of a population.

• Population: The entire set of individuals or items of interest to a researcher.

  • Example: Sugar content pertains to a specific harvest or variety of plants.

  • Example: Tree lichen refers to a specific type of tree or all trees within a designated area.

• Clear definition of the population is essential for researchers to ensure results are applicable.

Understanding Samples

• Population Size: Populations may be large or theoretical, making sampling necessary.

• Working with Samples: Generally focuses on a fraction of the total population to draw conclusions about it.

• Estimation and Inference: Using sample data to make generalizations or predictions about the overall population.

Types of Data

• Quantitative/Numeric Data:

  • Involves continuous or numerical measurements.

  • Examples: Heights of trees, percent sugar content, or population counts.

  • Can include discrete values (e.g., counting the number of cars in a parking lot).

• Qualitative/Categorical Data:

  • Consists of fixed-level data types that classify individuals into categories.

  • Examples: Gender, left-handedness, or hair color.

Characteristics of Data Types

• Quantitative Data:

  • Suitable for a variety of mathematical operations, including addition and subtraction.

• Qualitative Data:

  • Summarized by categorizing observations and counting the frequency of each category.

Bias, Variation, and Confounding

• A sample should ideally be representative of the population from which it is drawn.

• Common Issues:

  • Bias: Affect collection methods and results quality.

    • Examples: Studying the speed of rabbits by chasing them can lead to only catching slower rabbits.

    • Sampling cholesterol levels solely from a fast-food parking lot can yield skewed results.

  • Variation: Most data exhibits some form of variation, which is inherent in natural processes.

    • Includes natural variation (like differences in heights of trees) and measurement variation (errors occurring during data collection).

  • Reducing variation is important, but complete elimination is often impossible.

Sources of Variation

• Measurement constitutes multiple components that must be accounted for:

  • Population average (e.g., average heights of different tree species).

  • Natural variation arising from genetics or environmental factors.

  • Temporal variations depending on the life cycle stage of the organism.

  • Measurement error, leading to different results with repeated measures of the same quantity.

Understanding Confounding

• Confounding occurs when the effects of one variable are mixed with the effects of another, complicating analysis.

  • Example: Studying lichen growth on various sides of trees may be affected by variables such as geographic location if different campuses are involved.

  • Careful study design helps to mitigate confounding issues and improve the accuracy of results.

Experimental Design Principles

• Bias, variation, and confounding can be minimized through:

  • Random Sampling: Ensures that every individual has an equal chance of being selected, improving sample accuracy.

  • Blocking: Involves organizing the data collection process to reduce variability within treatment groups.

Statistical Methods

• Statistics involves:

  • The collection, description, display, and analysis of data.

• Main focuses:

  • Estimating population parameters based on sample data.

  • Making inferential conclusions about the population from sample analysis.

• Estimation: Involves point estimates (single value) and interval estimates (range of values).

• Inference: Relates to hypothesis testing, which assesses claims based on data.

Statistics and Mathematics

• Though grounded in mathematics, statistics primarily centers on data analysis, requiring techniques similar to laboratory methodologies.

Statistical Software

• Most statistical tasks now utilize computational tools.

• Common Software Packages:

  • Excel: Useful for basic statistical analysis through the Analysis Toolpak.

  • SPSS, Minitab, SAS: Comprehensive commercial software for extensive statistical functionalities.

  • R: An open-source statistical programming language widely adopted in both academic and professional settings.

Course Content Overview

• Topics will encompass:

  • Descriptive statistics and graphics

  • Probability theory

  • Single-sample estimation and inference techniques

  • Two-sample estimation and inference

  • Multiple sample inference approaches

  • Inference concerning counts

  • Exploring relationships between two measurements