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 | One way MANOVA | McNemar's test |
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 ($I \geqslant 2$) | 2 paired groups | |
Dependent variable | Dependent variables | Dependent variable | |
One quantitative of interval or ratio level | Two or more quantitative of interval or ratio level | One categorical with 2 independent groups | |
THIS TABLE IS YET TO BE COMPLETED | THIS TABLE IS YET TO BE COMPLETED | Null hypothesis | |
- | - | Let's say that the scores on the dependent variable are scored 0 and 1. Then for each pair of scores, the data allow four options:
Other formulations of the null hypothesis are:
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n.a. | n.a. | Alternative hypothesis | |
- | - | The alternative hypothesis H1 is that for each pair of scores, P(first score of pair is 0 while second score of pair is 1) $\neq$ P(first score of pair is 1 while second score of pair is 0). That is, the probability that a pair of scores switches from 0 to 1 is not the same as the probability that a pair of scores switches from 1 to 0. Other formulations of the alternative hypothesis are:
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n.a. | n.a. | Assumptions | |
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n.a. | n.a. | Test statistic | |
- | - | $X^2 = \dfrac{(b - c)^2}{b + c}$
Here $b$ is the number of pairs in the sample for which the first score is 0 while the second score is 1, and $c$ is the number of pairs in the sample for which the first score is 1 while the second score is 0. | |
n.a. | n.a. | Sampling distribution of $X^2$ if H0 were true | |
- | - | If $b + c$ is large enough (say, > 20), approximately the chi-squared distribution with 1 degree of freedom. If $b + c$ is small, the Binomial($n$, $P$) distribution should be used, with $n = b + c$ and $P = 0.5$. In that case the test statistic becomes equal to $b$. | |
n.a. | n.a. | Significant? | |
- | - | For test statistic $X^2$:
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n.a. | n.a. | Equivalent to | |
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n.a. | n.a. | Example context | |
- | - | Does a tv documentary about spiders change whether people are afraid (yes/no) of spiders? | |
n.a. | n.a. | SPSS | |
- | - | Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples...
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n.a. | n.a. | Jamovi | |
- | - | Frequencies > Paired Samples - McNemar test
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Practice questions | Practice questions | Practice questions | |