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Chapter 13 Inference for tables: Chi-square Procedures 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 Ho: The variables are independent Ha: The variables are not independent 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. Chi-Square: Goodness of fit test 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 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.