Lecture 7: Single Sample t Test

This set of vocabulary flashcards covers the fundamental concepts, formulas, and decision rules of the Single-Sample t Test as presented in the UBC PSYC 218 Day 7 lecture.

z Test

A hypothesis test performed when both the population mean ($\mu$) and the population standard deviation ($\sigma$) are known.

Single-Sample t Test

A hypothesis test used when the population mean is known (or a set value is used for comparison) but the population standard deviation is unknown.

Uncorrected Sample Standard Deviation ($SD$)

A descriptive measure of variability calculated as $SD = \frac{\sum_{i=1}^N (X - M)^2}{N}$, which has a bias to underestimate the population standard deviation.

Corrected Sample Standard Deviation ($s$)

An estimator of the population standard deviation that addresses bias by dividing by $N - 1$ instead of $N$, calculated as $s = \frac{\sum_{i=1}^N (X - M)^2}{N-1}$, though the transcript represents it conceptually as $\sqrt{\frac{\sum (X - M)^2}{N - 1}}$.

Standard Error ($\sigma_M$)

The variability of the distribution of means when the population standard deviation is known, calculated as $\sigma_M = \frac{\sigma}{\sqrt{N}}$.

Estimated Standard Error ($s_M$)

The variability of the distribution of means calculated when only the corrected sample standard deviation is available, using the formula $s_M = \frac{s}{\sqrt{N}}$.

t Statistic

The statistic calculated for a single-sample t test by dividing the difference between the sample mean and population mean by the estimated standard error: $t = \frac{M - \mu_M}{s_M}$.

Degrees of Freedom ($df$)

The number of observations that are free to vary, calculated for a single-sample t test as $N - 1$.

Conservative Table Rule

The practice of choosing the next smallest degrees of freedom listed in a t table if the specific calculated $df$ is not present.

Decision Rule

The logical process where the null hypothesis is rejected if the obtained t statistic is more extreme than the critical value ($t_{crit}$).

Confidence Interval (CI)

A range of values used to estimate the population mean, where the lower bound is $M - t_{critical}(s_M)$ and the upper bound is $M + t_{critical}(s_M)$. Standard reporting for a 95% interval is written as $95\%\text{ CI } [\text{Lower bound}, \text{Upper bound}]$.

Cohen's d

A measure of effect size for a single-sample t test representing the distance between means in standard deviation units, calculated as $d = \frac{M - \mu}{s}$.

t Test Assumptions

The three requirements for performing a single-sample t test: the data must be continuous, observations must be randomly sampled, and the comparison distribution should be roughly normal (typically when $N > 30$).