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### Chi-Square

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# Chi-Square

By | November 2012
Page 1 of 5
BIOSTATISTICS
Second Semester 2012 Page 1
dsbriones
The Chi-Square Test
 It is the test appropriate for inference of qualitative data (frequency/count).  Characteristics of the Chi-Square Distribution:
1. It is not symmetric.
2. The shape of the chi-square distribution depends on the degrees of freedom. 3. The values 2 are nonnegative. That is, the values of 2 0.  Basic Assumptions of the 2-test:
1. The data are randomly selected.
2. All expected frequencies are greater than 0.
3. No more than 20% of the expected frequencies are less than 5.  Formula of the 2-test:
Where Oi represent the observed counts of category i (i.e. the data) and Ei represents the expected count of the category i, k represents the number of categories and the number of degrees of freedom =k – 1.  Types of Chi-Square test:

1. Chi-Square test for Association or independence
2. Chi-Square test for Homogeneity of proportions
3. Chi-square test for Goodness of Fit
 Hypotheses for Chi-Square Tests:
Chi-Square test for Association or independence:
Ho: There is no association between the 2 variables. (The two variables are independent) Ha: There is an association between the 2 variables. (The variables are dependent) Chi-Square test for Homogeneity of proportions:

Ho: The proportions are equal ()
Ha: At least one proportion is different.
Chi-square test for Goodness of Fit
Ho: The data follow a specific distribution.
Ha: The data do not follow a specific distribution.
BIOSTATISTICS
Second Semester 2012 Page 2
dsbriones
Example 1. An obstetrician want to know whether the proportion of children born each day of the week is the same. She randomly selects 500 birth records and obtains the data shown below: Day
Frequency
Sunday
57
Monday
78
Tuesday
74
Wednesday
76
Thursday
71
Friday
81
Saturday
63
Is there reason to believe that the day of the week on which a child is born occurs with equal frequency at the =0.01 level of significance? Solution:
Ho: The...

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