IE 321 - Engineering Data Analysis 2: One-Sample Hypothesis Testing and Experimental Design

Vocabulary flashcards covering fundamental statistical concepts, experimental design terms, hypothesis testing errors, and test parameters from IE 321 lecture notes.

Statistics

The field primarily concerned with designing experiments and drawing conclusions from collected data.

Explanatory Variable

The variable manipulated by the researcher in an experiment, also commonly referred to as a factor.

Experimental Unit

The smallest entity to which an experimental treatment is applied.

Blocking

An experimental design strategy that reduces the effects of known nuisance variables.

Random Assignment

A technique in experimental design used primarily to reduce bias.

Null Hypothesis ($H_0$)

The baseline hypothesis that usually represents no effect or no difference, and normally contains the equality sign.

Alternative Hypothesis ($H_1$ or $H_a$)

The hypothesis that represents an effect, difference, or relationship being tested against the null hypothesis.

Type I Error

The error committed when a true null hypothesis ($H_0$) is incorrectly rejected.

Type II Error

The error committed when a false null hypothesis ($H_0$) is failed to be rejected.

Significance Level ($\alpha$)

The probability of committing a Type I error, represented by $\alpha$, where a smaller value makes it harder to reject $H_0$.

p-value

The probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis ($H_0$) is true.

Z-Test for Population Mean

A hypothesis test for the population mean requiring a known population standard deviation ($\sigma$).

One-Sample t-Test

A hypothesis test for the population mean used when the population standard deviation ($\sigma$) is unknown.

Degrees of Freedom ($df$)

The number of independent values in a statistical calculation, given by $df = n - 1$ for a one-sample t-test.

Treatment

A specific combination of factor levels applied to experimental units.

Replication

The repetition of experimental runs to obtain adequate observations per treatment.

Double-Blind Experiment

An experiment in which neither the subjects nor the evaluators know the treatment assignments.

Standard Error ($SE$)

The standard deviation of a statistic's sampling distribution, calculated as $\frac{\sigma}{\sqrt{n}}$ when $\sigma$ is known, or $\frac{s}{\sqrt{n}}$ when $\sigma$ is unknown.

Margin of Error ($ME$)

The radius of a confidence interval, calculated as $ME = z_{\alpha/2} \times SE$, which directly affects the required sample size.

Confidence Interval

An interval estimation that bounds the true population mean with a specified level of confidence (e.g., 95%).