ANCOVA - overview
This page offers structured overviews of one or more selected methods. Add additional methods for comparisons (max. of 3) by clicking on the dropdown button in the right-hand column. To practice with a specific method click the button at the bottom row of the table
ANCOVA | $z$ test for a single proportion | Multilevel logistic regression |
You cannot compare more than 3 methods |
---|---|---|---|
Independent variables | Independent variable | Independent variables | |
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates) | None | One or more quantitative of interval or ratio level and/or one or more categorical with independent groups, transformed into code variables, plus at least one random factor | |
Dependent variable | Dependent variable | Dependent variable | |
One quantitative of interval or ratio level | One categorical with 2 independent groups | One categorical with 2 independent groups | |
THIS TABLE IS YET TO BE COMPLETED | Null hypothesis | THIS TABLE IS YET TO BE COMPLETED | |
- | H0: $\pi = \pi_0$
Here $\pi$ is the population proportion of 'successes', and $\pi_0$ is the population proportion of successes according to the null hypothesis. | - | |
n.a. | Alternative hypothesis | n.a. | |
- | H1 two sided: $\pi \neq \pi_0$ H1 right sided: $\pi > \pi_0$ H1 left sided: $\pi < \pi_0$ | - | |
n.a. | Assumptions | n.a. | |
- |
| - | |
n.a. | Test statistic | n.a. | |
- | $z = \dfrac{p - \pi_0}{\sqrt{\dfrac{\pi_0(1 - \pi_0)}{N}}}$
Here $p$ is the sample proportion of successes: $\dfrac{X}{N}$, $N$ is the sample size, and $\pi_0$ is the population proportion of successes according to the null hypothesis. | - | |
n.a. | Sampling distribution of $z$ if H0 were true | n.a. | |
- | Approximately the standard normal distribution | - | |
n.a. | Significant? | n.a. | |
- | Two sided:
| - | |
n.a. | Approximate $C\%$ confidence interval for $\pi$ | n.a. | |
- | Regular (large sample):
| - | |
n.a. | Equivalent to | n.a. | |
- |
| - | |
n.a. | Example context | n.a. | |
- | Is the proportion of smokers amongst office workers different from $\pi_0 = 0.2$? Use the normal approximation for the sampling distribution of the test statistic. | - | |
n.a. | SPSS | n.a. | |
- | Analyze > Nonparametric Tests > Legacy Dialogs > Binomial...
| - | |
n.a. | Jamovi | n.a. | |
- | Frequencies > 2 Outcomes - Binomial test
| - | |
Practice questions | Practice questions | Practice questions | |