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S12.1 - Goodness-of-Fit Test
Goodness-of-Fit Test
14
Mathematics
Graduate
11/11/2013

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Term
4 characteristics of the chi-square distribution
Definition
1. It is not symmetric
2. The shape of the chi-square distribution depends on the degrees of freedom
3. As the number of degrees of freedom increases, the chi-square distribution becomes more symmetric
4. The values of X^2 are nonnegative (>=0)
Term
Goodness-of-fit test
Definition
An inferential procedure used to determine whether a frequency distribution follows a specific distribution
Term
Expected count
Definition
The expected number of outcomes for each independent observation
Term
Oi =
Definition
Observed counts of category i
Term
Ei =
Definition
Expected counts of category i
Term
k =
Definition
The number of categories
Term
Test statistic for goodness-of-fit tests, X^2 =
Definition
Summation[(Oi-Ei)^2/Ei]
i = 1, 2,…,k
Term
2 assumptions for test statistic for goodness-of-fit
Definition
1. All expected frequencies are >=1
2. no more than 20% of the expected frequencies are less than 5
Term
All hypothesis tests for goodness-of-fit are
Definition
Right-tailed tests
Term
Right-tailed test, goodness-of-fit
H0:
H1:
Definition
H0: The random variable follows a certain distribution
H1: The random variable does not follow a certain distribution
Term
Goodness-of-fit test, classical approach
X0^2 > Xalpha^2
Definition
Reject the null
Term
Goodness-of-fit test, classical approach
X0^2 < Xalpha^2
Definition
Fail to reject the null
Term
Goodness-of-fit test, p-value approach
P-value < alpha
Definition
Reject the null
Term
Goodness-of-fit test, p-value approach
P-value > alpha
Definition
Fail to reject the null
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