Degrees of freedom t test or confidence interval

Find the degrees of freedom for a particular t test or confidence interval ($CI$) below:


Test/$CI$Degrees of freedom
One sample $t$ test/$CI$$N - 1$.
Here $N$ is the sample size.
Paired sample $t$ test/$CI$$N - 1$.
Here $N$ is the number of difference scores.
Two sample $t$ test/$CI$ - equal variances not assumed

For hand calculations, it is common to use the smaller of $n_1 - 1$ and $n_2 - 1$ as an approximation for the degrees of freedom. Here $n_1$ is the sample size of group 1, and $n_2$ is the sample size of group 2.

Computer programs use the following formula for the degrees of freedom: $$df = \dfrac{\Bigg(\dfrac{s^2_1}{n_1} + \dfrac{s^2_2}{n_2}\Bigg)^2}{\dfrac{1}{n_1 - 1} \Bigg(\dfrac{s^2_1}{n_1}\Bigg)^2 + \dfrac{1}{n_2 - 1} \Bigg(\dfrac{s^2_2}{n_2}\Bigg)^2}$$ Here $s^2_1$ is the sample variance in group 1, and $s^2_2$ is the sample variance in group 2.

Two sample $t$ test/$CI$ - equal variances assumed $n_1 + n_2 - 2$.
Here $n_1$ is the sample size of group 1, and $n_2$ is the sample size of group 2.
$t$ test for the Pearson correlation coefficient $N - 2$.
Here $N$ is the sample size (number of pairs).
$t$ test for the Spearman correlation coefficient (Spearman's rho) $N - 2$.
Here $N$ is the sample size (number of pairs).
$t$ test/$CI$ within one way ANOVA setting (multiple comparisons/contrasts) $N - I$.
Here $N$ is the total sample size and $I$ is the number of groups.
$t$ test/$CI$ for a single regression coefficient (in OLS regression) $N - K - 1$.
Here $N$ is the total sample size and $K$ is the number of independent variables.