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Tutorial 11: Test for Goodness of Fit
PHATPC
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P-value=P(χ2>τ)=1-P(χ2<τ)=1-pchisq(τ,df)
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General: Hypothesis Testing
 We use hypothesis testing to infer conclusions about the population parameters based on
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analysing the statistics of the sample. In statistics, a hypothesis is a statement about a population
parameter.
Hypothesis:
The null hypothesis, denoted H0 is a statement or claim about a population parameter that is
initially assumed to be true. Is always an equality. The null hypothesis must specify that the
population parameter is equal to a single value.
The alternative hypothesis, denoted by H1 is the competing claim. What are we trying to prove.
Claim we seek evidence for. (Eg. H1: population parameter ≠ or < or > hypothesised null parameter)
Assumptions: A hypothesis test is invalid if the assumptions are not satisfied.
Test Statistic: a measure of compatibility between the statement in the null hypothesis and
the sample data obtained. It is a random variable consisting of a function of the observed
values, with a distribution depending on the unknown parameter.
P-Value: is the probability of obtaining a test statistic more extreme than the observed sample
value given the null hypothesis is true.
Conclusion: Compare the p-value with the level of significance α. If the test statistic falls in
the rejection region, p-value is small , so we reject H0 and conclude that we have enough
evidence is against H0.
If the test statistic falls in non-rejection region, p-value is large, so we do not reject H0 and
conclude that we do not have enough evidence to support H0.
Make your conclusion in context of the problem.
H0: The Genotypes A, B and C occur in the ratio 1 : 2 : 1 (Model fits the data well)
H1: The Genotypes A, B and C does not occur in the ratio 1 : 2 : 1 (Model does not fit)
We need Ei≥1 (true here), and no more than 20% of Ei < 5 (Cochran's Rule - also true
here).
Conclusion:
Since p-value>0.05, we do not reject the H0, and conclude that the sample is
consistent with Genotypes in the ratio 1:2:1
Note that the χ2 table is upper tail. The Goodness of Fit test is always a right-tailed test.
SEE YOU NEXT WEEK FOR QUIZ 3!
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