Download Chapter 13 Inference for tables: Chi-square - gsa-lowe

Chapter 13 Inference for tables: Chi-square Procedures
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We are able to extend inference on proportions to more than two proportions by
enabling us to determine if a particular population distribution has changed from a
specified form.
The chi-squared test of independence allows us to test whether or not the
distribution of one variable has been influenced by another variable, based on the
information from a 2-way table.
The chi-squared distribution values start at 0, and then are all positive. The graph
is not symmetric(it is skewed right) and like the t-table depends on the number of
degrees of freedom. As the df increases the more bell-like and symmetric the
graph looks. The area under the curve is equal to 1.
The mode(or the high point) of a chi-squared distribution with m degrees of
freedom occurs over m-2( for a df>3)
Let’s look at -squared test of independence
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Ho: The variables are independent
Ha: The variables are not independent
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The table with the values is called the contingency table and its size is the # of
rows X # of columns.
We then find the probabilities of each cell which we will call the Expected
Frequency E: E=(row total)(column total)
Sample size
To calculate the Chi-squared test statistic: 2= O-E)2/E
To find df: (row-1)(column-1)
The P-value is the area to the right of the 2 under the density curve.
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Chi-Square: Goodness of fit test
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We are asking if a population follows a specified distribution.
Ho: The population fits the given distribution
Ha: The population does not fit the given distribution
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Expected Frequency E: E=(probability of population)(sample size)
To calculate the Chi-squared test statistic: 2= O-E)2/E
To find df: # of categories - 1
The P-value is the area to the right of the 2 under the density curve.