Goodness of Fit (Edexcel A-Level Further Mathematics): Flashcards

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Goodness of Fit
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Purpose of χ2\chi^2 goodness of fit test

Tests how well a distribution fits a data set

Yates correction in χ2\chi^2 goodness of fit tests

Never required, even when ν=1\nu = 1

Formula for χ2\chi^2 contributions

(O−E)2E\frac{(O - E)^2}{E}

Degrees of freedom for goodness of fit (nn categories)

ν=n−1\nu = n - 1

Effect on ν\nu when estimating a parameter from data

Lose one degree of freedom per parameter estimated

Decision when χcalc2<\chi^2_{calc} < critical value

Do not reject H0H_0

Decision when χcalc2>\chi^2_{calc} > critical value

Reject H0H_0

Min. expected frequency to avoid combining cells

All expectations must be ≥5\geq 5

Correct phrasing for goodness of fit conclusion

Model fits the data (not data fits the model)

Estimating pp in B(n,p)B(n,p) from sample mean xˉ\bar{x}

p=xˉnp = \frac{\bar{x}}{n}

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