Probability Distributions Chapters 4-6

A measure of the central tendency of a random variable.

The expected value of a random variable.

A measure of the spread or dispersion of a random variable.

A measure of the linear relationship between two random variables.

A theorem that provides a lower bound for the probability that a random variable will fall within a certain number of standard deviations from its mean.

A discrete probability distribution for the number of successes in a fixed number of independent Bernoulli trials.

A discrete probability distribution for the number of successes in a fixed number of draws without replacement from a finite population.

A continuous probability distribution where all outcomes in a given interval have equal probability.

Methods for finding the best-fit line or curve through a set of data points.

A statistical method used to model the relationship between a dependent variable and multiple independent variables.

A statistical procedure used to determine whether a hypothesis about a population parameter is supported by the sample data.

Variables representing qualitative data, often converted to numerical representations for analysis.

Choosing the best statistical model that fits the data effectively and reasonably.

A statistical method used to compare the means of different groups or treatments.

An experimental design in which subjects are randomly assigned to different treatments.

Evaluating the model’s assumptions and identifying potential errors using patterns in the residuals.

Methods used to compare more than two treatment groups in an experiment to determine which groups are significantly different.

Comparing levels of treatments within blocks (groups) of similar subjects or items to reduce variability and increase power.

A design where treatments are randomly assigned within blocks to minimize variability.

Experiments that investigate the effect of two or more factors.

The combined effect of two factors, where the effect of one factor depends on the level of the other factor.

A statistical method used to analyze the effects of two factors in an experiment.

Experiments involving three factors to analyze their combined effects.

Statistical models where factors are random samples from a larger population.

An experimental design where all possible combinations of two levels for each of k factors are tested. It explores the main effects and interactions of each factor.

The average effect of changing a factor from its low to its high level, ignoring other factors. It shows the impact of a single factor on the response.

The combined effect of two or more factors on the response, beyond the sum of their individual main effects. It reveals how factors work together.

A 2k factorial experiment without repetition of any treatment combination. This simplifies the design, but limits statistical inferences.

A factorial design where the main effects and interactions are estimated independently of each other, minimizing confounding effects.

A factorial design where only a fraction of all possible treatment combinations are run, reducing the experiment size while still providing useful information on the effects of factors.

Fractional factorial designs classified by their ability to estimate main effects without confounding them with 2-factor and 3-factor interactions (Resolution III) or 2-factor interactions (Resolution IV).

A collection of statistical techniques used to optimize a response by finding the best combination of factor settings. It involves fitting a surface to the response data.

A statistical method used to estimate the relationship between a dependent variable and one or more independent variables. It minimizes the sum of squared differences between the observed and predicted values of the dependent variable.

A technique used to modify the distribution of data by applying a mathematical function to the data values. This is often done to address violations of assumptions in statistical models.

A statistical test used to compare the means of two or more groups when the independent variable has only one factor. It determines if there is a significant difference between the group means.

A design used in experiments to control for variation within experimental units by grouping them into blocks. Each treatment is randomly assigned to a unit within each block.

Visual representations of data, such as box plots and bar charts, used to complement statistical analysis in ANOVA. These methods provide insights into the differences between group means and variability within groups.

A statistical test used to compare the means of two or more groups when the independent variable has two or more factors. It determines if there is a significant difference between the group means, and also examines interactions between the factors.

A collection of mathematical and statistical techniques used to optimize a response variable by identifying the optimal levels of input factors.

A statistical approach to designing experiments where the goal is to make a product or process less sensitive to variation in factors that cannot be controlled or are difficult to control.

Using known population characteristics to draw conclusions about hypothetical data from that population.

The process of drawing conclusions about a population based on a sample of data.

Probability provides the foundation for understanding uncertainty in samples, which is crucial for drawing accurate inferences about populations.

Probability is essential for teaching statistics beyond superficial 'cookbook' methods. It provides the framework for understanding uncertainty in samples.

A population includes all individuals or elements of interest, while a sample is a smaller, representative subset of that population.

In a manufacturing process, the probability of a defective item helps evaluate whether a sample with a certain proportion of defective items supports or refutes the claim of a 5% defect rate.

Understanding probability is essential for accurately interpreting data because samples inherently contain uncertainty about the population.

The example demonstrates how probability helps determine whether a sample with 10% defectives refutes the claim of a 5% defect rate in the population.