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 | Kruskal-Wallis test | Binomial test for a single proportion |
You cannot compare more than 3 methods |
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Independent variables | Independent/grouping variable | Independent variable | |
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates) | One categorical with $I$ independent groups ($I \geqslant 2$) | None | |
Dependent variable | Dependent variable | Dependent variable | |
One quantitative of interval or ratio level | One of ordinal level | One categorical with 2 independent groups | |
THIS TABLE IS YET TO BE COMPLETED | Null hypothesis | Null hypothesis | |
- | If the dependent variable is measured on a continuous scale and the shape of the distribution of the dependent variable is the same in all $I$ populations:
Formulation 1:
| 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 | Alternative hypothesis | |
- | If the dependent variable is measured on a continuous scale and the shape of the distribution of the dependent variable is the same in all $I$ populations:
Formulation 1:
| H1 two sided: $\pi \neq \pi_0$ H1 right sided: $\pi > \pi_0$ H1 left sided: $\pi < \pi_0$ | |
n.a. | Assumptions | Assumptions | |
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n.a. | Test statistic | Test statistic | |
- | $H = \dfrac{12}{N (N + 1)} \sum \dfrac{R^2_i}{n_i} - 3(N + 1)$ | $X$ = number of successes in the sample | |
n.a. | Sampling distribution of $H$ if H0 were true | Sampling distribution of $X$ if H0 were true | |
- | For large samples, approximately the chi-squared distribution with $I - 1$ degrees of freedom. For small samples, the exact distribution of $H$ should be used. | Binomial($n$, $P$) distribution.
Here $n = N$ (total sample size), and $P = \pi_0$ (population proportion according to the null hypothesis). | |
n.a. | Significant? | Significant? | |
- | For large samples, the table with critical $X^2$ values can be used. If we denote $X^2 = H$:
| Two sided:
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n.a. | Example context | Example context | |
- | Do people from different religions tend to score differently on social economic status? | Is the proportion of smokers amongst office workers different from $\pi_0 = 0.2$? | |
n.a. | SPSS | SPSS | |
- | Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples...
| Analyze > Nonparametric Tests > Legacy Dialogs > Binomial...
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n.a. | Jamovi | Jamovi | |
- | ANOVA > One Way ANOVA - Kruskal-Wallis
| Frequencies > 2 Outcomes - Binomial test
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Practice questions | Practice questions | Practice questions | |