AP Statistics Curriculum 2007 Contingency Fit
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- | ==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Multinomial Experiments: Goodness-of-Fit == | + | ==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Multinomial Experiments: Chi-Square Goodness-of-Fit == |
- | + | The chi-square test is used to test if a data sample comes from a population with a specific characteristics. The chi-square goodness-of-fit test is applied to binned data (data put into classes or categoris). In most situations, the data histogram or frequency histogram may be obtained and the chi-square test may be applied to these (frequency) values. The chi-square test requires a sufficient sample size in order for the chi-square approximation to be valid. | |
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- | + | The [http://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test Kolmogorov-Smirnov] is an alternative to the Chi-square goodness-of-fit test. The chi-square goodness-of-fit test may also be applied to discrete distributions such as the binomial and the Poisson. The Kolmogorov-Smirnov test is restricted to continuous distributions. | |
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- | + | ==Motivational example== | |
+ | [http://en.wikipedia.org/wiki/Mendelian_inheritance Mendel's pea experiment] relates to the transmission of hereditary characteristics from parent organisms to their offspring; it underlies much of genetics. Suppose a ''tall offspring'' is the event of interest and that the true proportion of tall peas (based on a 3:1 phenotypic ratio) is 3/4 or ''p = 0.75''. He would like to show that Mendel's data follow this 3:1 phenotypic ratio. | ||
- | === | + | <center> |
- | + | {| class="wikitable" style="text-align:center; width:25%" border="1" | |
+ | |- | ||
+ | | || '''Observed''' (O) || '''Expected''' (E) | ||
+ | |- | ||
+ | | '''Tall''' || 787 || 798 | ||
+ | |- | ||
+ | | '''Dwarf'''|| 277 || 266 | ||
+ | |} | ||
+ | </center> | ||
- | + | ==Calculations== | |
- | === | + | Suppose there were ''N = 1064'' data measurements with ''Observed(Tall) = 787'' and ''Observed(Dwarf) = 277''. These are the O’s (observed values). To calculate the E’s (expected values), we will take the hypothesized proportions under <math>H_o</math> and multiply them by the total sample size ''N''. Expected(Tall) = (0.75)(1064) = 798 and Expected(Dwarf) = (0.25)(1064) = 266 |
- | + | Quickly check to see if the expected total = N = 1064. | |
- | == | + | * The hypotheses: |
- | + | : <math>H_o</math>:P(tall) = 0.75 (No effect, follows a 3:1phenotypic ratio) | |
+ | :: P(dwarf) = 0.25 | ||
+ | : <math>H_a</math>: P(tall) ≠ 0.75 | ||
+ | ::P(dwarf) ≠ 0.25 | ||
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<hr> | <hr> |
Revision as of 01:50, 3 March 2008
Contents |
General Advance-Placement (AP) Statistics Curriculum - Multinomial Experiments: Chi-Square Goodness-of-Fit
The chi-square test is used to test if a data sample comes from a population with a specific characteristics. The chi-square goodness-of-fit test is applied to binned data (data put into classes or categoris). In most situations, the data histogram or frequency histogram may be obtained and the chi-square test may be applied to these (frequency) values. The chi-square test requires a sufficient sample size in order for the chi-square approximation to be valid.
The Kolmogorov-Smirnov is an alternative to the Chi-square goodness-of-fit test. The chi-square goodness-of-fit test may also be applied to discrete distributions such as the binomial and the Poisson. The Kolmogorov-Smirnov test is restricted to continuous distributions.
Motivational example
Mendel's pea experiment relates to the transmission of hereditary characteristics from parent organisms to their offspring; it underlies much of genetics. Suppose a tall offspring is the event of interest and that the true proportion of tall peas (based on a 3:1 phenotypic ratio) is 3/4 or p = 0.75. He would like to show that Mendel's data follow this 3:1 phenotypic ratio.
Observed (O) | Expected (E) | |
Tall | 787 | 798 |
Dwarf | 277 | 266 |
Calculations
Suppose there were N = 1064 data measurements with Observed(Tall) = 787 and Observed(Dwarf) = 277. These are the O’s (observed values). To calculate the E’s (expected values), we will take the hypothesized proportions under H_{o} and multiply them by the total sample size N. Expected(Tall) = (0.75)(1064) = 798 and Expected(Dwarf) = (0.25)(1064) = 266 Quickly check to see if the expected total = N = 1064.
- The hypotheses:
- H_{o}:P(tall) = 0.75 (No effect, follows a 3:1phenotypic ratio)
- P(dwarf) = 0.25
- H_{a}: P(tall) ≠ 0.75
- P(dwarf) ≠ 0.25
References
- TBD
- SOCR Home page: http://www.socr.ucla.edu
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