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