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Previous Section: Central Limit Theorem*
Next Section: Probability Generating Functions*
Contents
- Whole Topic Notes
- 6A Goodness of Fit
- 6B Degrees of Freedom and the Chi-Squared Family of Distributions
- 6C Testing a Hypothesis
- 6D Testing the Goodness of Fit with Discrete Data
- 6E Using Contingency Tables
- 6F Apply Goodness-of-Fit Tests to Geometric Distributions*
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Full Notes to Accompany Examples
Dr Frost
- Dr Frost Further Statistics 1 Chi-Squared Tests Section
- Dr Frost Further Statistics 1 Chi-Squared Tests Slides
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- FMSP Further Statistics 1 (AS) playlist (Courtesy of MEI)
6A Goodness of Fit
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6B Degrees of Freedom and the Chi-Squared Family of Distributions
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6C Testing a Hypothesis
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- 851c: Determine expected frequencies for a χ² test given the probability distribution and number of trials.
- 851d: Determine the test statistic X² using observed frequencies and a given probability distribution.
- 851e: Conduct a goodness of fit test given the observed and expected frequencies, where grouping of outcomes is not required.
- 851f: Conduct a goodness of fit test given the observed and expected frequencies, where grouping of outcomes is required.
- 851g: Conduct a goodness of fit test given the observed frequencies and an arbitrary probability distribution.
- 851h: Conduct a χ² test against a uniform distribution.
- 851: Exam Practice: Goodness of fit tests
6D Testing the Goodness of Fit with Discrete Data
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- 851i: Determine an expected frequency for a binomial χ² test where p is given.
- 851j: Conduct a χ² test against a binomial model where p is given.
- 851k: Estimate the p for a binomial model given observed frequencies.
- 851m: Determine an expected frequency for a binomial χ² test where p must be calculated.
- 851n: Conduct a χ² test against a binomial model where p is not given.
- 851o: Determine an expected frequency for a Poisson χ² test where λ must be calculated.
- 851p: Conduct a χ² test against a Poisson model where λ is given.
- 851q: Conduct a χ² test against a Poisson model where λ must be calculated.
- 851: Exam Practice: Goodness of fit tests
6E Using Contingency Tables
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- 853a: Make a common sense judgement on whether there is an association between two variables, given a contingency table (two-way table).
- 853b: Calculate the expected frequencies for a contingency table (two-way table).
- 853c: State the degrees of freedom for a contingency table (two-way table).
- 853d: Calculate the test statistic X² for a contingency table (two-way table).
- 853e: Conduct a test to determine whether there is an association between two variables, using a contingency table (two-way table).
- 853: Exam Practice: Hypothesis tests with contingency tables (two-way tables)
6F Apply Goodness-of-Fit Tests to Geometric Distributions*
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