MANCOVA - overview
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MANCOVA | Goodness of fit test |
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Independent variables | Independent variable | |
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates) | None | |
Dependent variables | Dependent variable | |
Two or more quantitative of interval or ratio level | One categorical with $J$ independent groups ($J \geqslant 2$) | |
THIS TABLE IS YET TO BE COMPLETED | Null hypothesis | |
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n.a. | Alternative hypothesis | |
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n.a. | Assumptions | |
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n.a. | Test statistic | |
- | $X^2 = \sum{\frac{(\mbox{observed cell count} - \mbox{expected cell count})^2}{\mbox{expected cell count}}}$
Here the expected cell count for one cell = $N \times \pi_j$, the observed cell count is the observed sample count in that same cell, and the sum is over all $J$ cells. | |
n.a. | Sampling distribution of $X^2$ if H0 were true | |
- | Approximately the chi-squared distribution with $J - 1$ degrees of freedom | |
n.a. | Significant? | |
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n.a. | Example context | |
- | Is the proportion of people with a low, moderate, and high social economic status in the population different from $\pi_{low} = 0.2,$ $\pi_{moderate} = 0.6,$ and $\pi_{high} = 0.2$? | |
n.a. | SPSS | |
- | Analyze > Nonparametric Tests > Legacy Dialogs > Chi-square...
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n.a. | Jamovi | |
- | Frequencies > N Outcomes - $\chi^2$ Goodness of fit
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Practice questions | Practice questions | |