Statistical Methods Lecture 1

Statistical Methods Lecture 1

• Statistical methods are used in virtually all scientific fields.
• This course provides a comprehensive introduction to statistical methods, including advanced topics and applications.
• Topics include hypothesis testing, confidence intervals, simple and multiple regression, correlation, and nonparametric statistics.

Course Outlines

• Chapter 1: Overview of Statistics
• Chapter 2: Confidence Limits
• Chapter 3: Hypothesis Testing
• Chapter 4: Categorical Data Analysis and Analysis of Variance
• Chapter 5: Linear Regression and Correlation
• Chapter 6: Multiple Regression
• Chapter 7: Nonparametric Statistics

Course Materials

• All course materials are available on the course drive.
• Materials include lecture notes, problem sheets, lab sheets, and links to supplementary information.
• All materials are in PDF format.

How to Succeed in the Course

• Statistics is a problem-solving subject; practice is key.
• Essential elements for success are understanding assigned readings and completing homework.
• Read the assigned material before attending lectures.
• Complete homework assignments independently, but you can discuss problems with classmates.
• Practice solving problems before attempting quizzes and exams.

Data and Statistics

• Data is information from observations, counts, measurements, or responses.
• Statistics is the study of collecting, organizing, analyzing, and interpreting data.
• A population is the set of all possible outcomes or values of interest.
• A sample is a subset of a population.

Populations and Samples (Example)

• In a survey of 250 college students, 35 reported smoking regularly.
• The population is all students at Union College.
• The sample is the 250 students surveyed.

Parameters and Statistics

• A parameter describes a population characteristic.
• A statistic describes a sample characteristic.
• In the example, the average weekly income ($325) of 450 students is a sample statistic, while the average weekly income ($405) of all students is a population parameter.

Branches of Statistics

• Statistics includes descriptive and inferential statistics.
• Descriptive statistics involves organizing, summarizing, and displaying data.
• Inferential statistics uses a sample to draw conclusions about a population. Example (study on sleep and test performance): Finding that volunteers with less than 6 hours of sleep performed worse on a science test is a descriptive statistic, and a possible conclusion using inferential statistics is that those who sleep less perform worse on similar tests.

Types of Data

• Data can be qualitative or quantitative.
• Qualitative data represents categories or labels (e.g., colors).
• Quantitative data represents numerical measurements or counts (e.g., GPA).

Levels of Measurement

• Nominal: Categorical data only, no order or numerical value (e.g., colors in the US flag, names of students).
• Ordinal: Categorical data with an order, but differences between data entries are not meaningful (e.g., class standings).
• Interval: Numerical data with meaningful differences between values, but no true zero (e.g., temperature).
• Ratio: Numerical data with meaningful differences and a true zero (e.g., ages, weights, grade point averages).

Designing a Statistical Study

• Identify the variables and population of interest.
• Create a detailed sampling plan for selecting a representative sample.
• Collect the data.
• Describe the data.
• Interpret the data using inferential methods.
• Identify potential errors.

Methods of Data Collection

• Observational Study: Observe and measure characteristics interest of a population.
• Experiment: Apply a treatment to part of a population and observe the response.
• Simulation: Reproduce conditions of a situation using a mathematical or physical model.
• Survey: Investigate characteristics of a population.
• Census: A measurement of the entire population.
• Sampling: Measurement of a part of a population.

Sampling Techniques

• Stratified Sampling: Members from each segment of a population.
• Cluster Sampling: All members from randomly selected segments.
• Systematic Sampling: Members of a population are assigned a number, and a starting number is randomly selected for the first element in the sample. Subsequent elements are selected at regular intervals.
• Convenience Sampling: Selecting readily available members of the population.