Statistical Inference and Regression Analysis: Key Concepts
Statistical Inference and Regression Analysis
Statistical Inference: Drawing conclusions about a population based on information from a sample.
Standard Error: Measures the variability of the sample mean estimate, calculated based on the standard deviation of the sample and the sample size.
Hypothesis Test Decisions:
- Reject the null hypothesis
- Fail to reject the null hypothesis
Multiple Linear Regression
A regression model that estimates the relationship between two or more independent variables and a
Statistical Analysis: Variables, Data, and Inference
Variables and Study Groups
- Categorical variables
- Quantitative variables
- Explanatory variable
- Response variable
Study Groups –> Population
–> sample
Sampling and Data Collection
Sample:
- Statistical Inference
- Sampling Bias
- Random Sample
- Association vs. Causation
- Confounding Variables
Collecting Data:
- Experiment
- Observational Study
- Randomized Experiment
- Control Group
- Placebo
- Blind Experiment
- Double-Blind Experiment
- Randomized Comparative Experiment
- Matched Pairs
Describing
Read MoreStatistical Analysis and Hypothesis Testing in Research
Interpreting a Linear Regression Equation
-
Identify Variables
- Outcome Variable: The variable being predicted by the model (e.g., `Test Scores`).
- Explanatory Variable: The variable used to predict or explain changes in the outcome variable (e.g., `Hours Studied`).
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Interpret Slope Coefficient
- Meaning of Slope: The slope coefficient indicates how much the outcome variable is expected to change for each one-unit increase in the explanatory variable. It reflects the nature and strength of the linear relationship.
Key Concepts in Probability and Decision Making
Key Concepts in Probability and Statistics
Random Variable
A random variable is a numeric description of the outcome of an experiment.
Discrete Random Variable
A discrete random variable is a random variable that may assume only a finite or infinite sequence of values.
Continuous Random Variable
A continuous random variable is a random variable that may assume any value in an interval or collection of intervals.
Probability Function
A probability function, denoted f(x), provides the probability that a discrete
Key Statistical Concepts and Data Visualization
Key Statistical Definitions
- Independence: The random choice of each individual in the sample is not influenced by which other individuals are chosen.
- Sample of Convenience: Samples chosen because they are easily available.
- Haphazard Sampling: Samples you hope you chose randomly.
- Volunteer Bias: Choosing individuals that are more easily available than others.
- Accuracy: How close the average estimate from many studies is to the parameter.
- Precision: How spread out repeated estimates are from their average.