Introduction to Statistics & Research Design

Introduction to Statistics & Research Design

• The study covers two branches of statistics: descriptive and inferential.
• Descriptive statistics organize, summarize, and communicate numerical observations.
• Descriptive statistics describe large amounts of data using a small number of representative values. For example, average weight.
• Inferential statistics use sample data to make estimations about a larger population. This means an intelligent guess about the population. For example, the CDC's study of a segment of the US population to estimate the entire population.
• A sample is a subset of observations drawn from the population of interest.
• A population includes all possible observations about which knowledge is wanted.

The Research Process

• The research process involves the following steps:
  • Initial Observation/Research Question
  • Generate Theory
  • Generate Hypotheses
  • Collect Data to Test Theory
  • Analyze Data
• Identifying Variables is a crucial step in the research process.

Variables

• An independent variable has at least two levels and is either manipulated or observed to determine its impact on the dependent variable.
• A dependent variable is the outcome, which is hypothesized to be related or caused by the independent variable.
• A confounding variable systematically varies with the independent variable, making it hard to determine which variable is at play. In experimental work, the independent variable is a predictor, and the dependent variable is the outcome.

Types of Variables

• Continuous variables can take a wide range of values (e.g., height, weight).
• Discrete variables can only take specific values (e.g., gender, number of times).
  • Nominal variables are categories with names as their values (e.g., gender, ethnicity).
  • Ordinal variables have rankings as values (e.g., first, second, third).
  • Interval variables have values with equal intervals but don't have a meaningful zero point (e.g., temperature, SAT scores).
  • Ratio variables have equal intervals and a meaningful zero point (e.g., height, weight).

Measurement Error

• Measurement error is the discrepancy between the measured value and the true value.
• Errors can occur due to limitations of measurement tools or influences.

Reliability and Validity

• Reliability refers to the consistency of a measure.
• Validity refers to whether an instrument measures what it's designed to measure.
• A measure must first be reliable to be valid.

Hypothesis Testing

• Hypothesis testing is a structured process for evaluating ideas about phenomena.
• Researchers use data from samples to draw inferences about populations.
• Operational definitions specify the operations or procedures for measuring a variable.

Data Collection Research Methods

• Correlational research examines relationships between variables without manipulation.
• Experimental research manipulates one variable to observe its effect on another.

Example: Correlation between Aggression and Video Games

• A graph shows a presumed positive relationship between hours spent playing video games and aggression.

Within-Groups Research Design

• In a within-groups design, participants experience all levels of the independent variable.