Lecture 5: Hypothesis Testing with z Tests

This set of vocabulary flashcards covers key terms and concepts related to Hypothesis Testing with z Tests, including NHST outcomes, error types, formulas for z scores and statistics, and the definition of p values.

Null Hypothesis Significance Testing (NHST)

A type of inferential statistical test that tests the null hypothesis ($H_0$) result in two possible outcomes: rejecting the null hypothesis or failing to reject the null hypothesis.

Research Hypothesis ($H_1$)

The hypothesis formulated based on a theory, sometimes referred to as the "Alternative Hypothesis," which specifies a predicted effect (e.g., people in a treatment group will have lower symptoms).

Null Hypothesis ($H_0$)

The negation of the research hypothesis, generated by making the hypothesis that is NOT $H_1$, assuming no difference or effect exists.

Alpha ($\alpha$)

The standard of "Very Unlikely" in NHST, traditionally set at $5\%$ ($\alpha = .05$), representing the probability of getting observations that lead to rejecting the null hypothesis by random chance when it is actually true.

One-Tailed Test

A test where the theory produces a directional hypothesis (e.g., pumpkins are bigger) and the cutoff is set so that $5\%$ of samplings fall in only one tail of the distribution.

Two-Tailed Test

A test used when a theory does not produce a directional hypothesis, setting the cutoff so that $2.5\%$ of samplings are in the right tail and $2.5\%$ are in the left tail.

Type I Error

An error that occurs when the null hypothesis is true, but the researcher erroneously rejects it.

Type II Error

An error that occurs when the null hypothesis is false, but the researcher erroneously fails to reject it.

z Score

A value indicating how many standard deviations a raw score is from the mean; its distribution always has a mean of $0$ and a standard deviation of $1$.

z Score Formula (Population)

$$z = \frac{X - \mu}{\sigma}$$

Distribution of the Mean

A sampling distribution produced by taking $N$ observations from a population, calculating the sample mean, and repeating the procedure a large number of times.

Standard Error ($\sigma_M$)

The standard deviation of a distribution of means, which indicates how much error there tends to be when using the sample mean to estimate the population mean, calculated as $\sigma_M = \frac{\sigma}{\sqrt{N}}$.

z Statistic

A value analogous to a z score that applies to a distribution of means, used to calculate how extreme a mean is relative to that distribution.

z Statistic Formula

$$z = \frac{M - \mu_M}{\sigma_M}$$

Parametric Test

A type of inferential statistical test (like the z test) that requires the calculation of parameters such as mean and standard deviation.

Nonparametric Test

Tests used on nominal or ordinal data that do not require parameters and are robust to violations of normality and extreme skew.

Critical Value

The cutoff distance from the mean (traditionally $\pm 1.96$ for a two-tailed test with $\alpha = .05$) used to determine whether to reject the null hypothesis.

p value

The probability that, assuming the null hypothesis is true, one would observe results as or more extreme than the actual observed results; reported as a decimal (e.g., $.02$).

Statistically Significant

A term for results where the p value is less than the alpha level ($.05$), leading to the rejection of the null hypothesis.