equally with a two sided z test or with a chi square test with 1 degree of

Equally with a two sided z test or with a chi square

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equally with a two-sided z test or with a chi-square test with 1 degree of freedom and get the same P -value. In fact, the two test statistics are related: X 2 = ( z ) 2
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An example (from Z to Chi^2) Consider the following two-way table of political ideology and gender Left Right Female 30 10 Male 20 40
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When is it safe to use a c 2 test? We can safely use the chi-square test when: The samples are simple random samples ( SRSs ). All individual expected counts are 1 or more (≥1). No more than 20% of expected counts are less than 5 (< 5). For a 2x2 table, this implies that all four expected counts should be 5 or more.
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Computations for two-way tables When analyzing relationships between two categorical variables, follow this procedure: 1. Calculate descriptive statistics that convey the important information in the table—usually column or row percents. 2. Find the expected counts and use them to compute the X 2 statistic. 3. Compare your X 2 statistic to the chi-square critical values from Table F to find the approximate P -value for your test. 4. Draw a conclusion about the association between the row and column variables.
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The chi-square statistic ( c 2 ) is a measure of how much the observed cell counts in a two-way table diverge from the expected cell counts. The formula for the c 2 statistic is: (summed over all r * c cells in the table) Where: Tip : First, calculate the c 2 components, (observed-expected) 2 /expected, for each cell of the table, and then sum them up to arrive at the c 2 statistic. Computing the chi-square statistic c 2 observed count - expected count 2 expected count
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Finding the P -value with Table F The χ 2 distributions are a family of distributions that can take only positive values, are skewed to the right, and are described by a specific degrees of freedom. Table F gives upper critical values for many χ 2 distributions.
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Example: Income and ideology (2) Is there a relation between family income and your political ideology?
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