Ex 8- Chi-squared Mapping Exercise

# Ex 8- Chi-squared Mapping Exercise - Geography 532...

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Geography 532 Name:________________________________ Geography of Environmental Health Dr. Paul Marr Exercise 8- Chi-Squared Map Analysis (10 pts) Introduction The Chi-Square ( χ 2 ) statistic is used to determine if there is a difference between observed values and expected values, therefore the null hypothesis is that the frequency of the observations found in the rows are independent of the frequency of observations found in the columns. The null hypothesis (h o ) would be “there is no difference between the observed and expected frequencies.” The alternative hypothesis (h a ) would therefore be “there is a difference between the observed and expected frequencies.” Remember that contingency tables test for differences but not the direction of the difference… that must either be implied from the data or determined using another statistical method. For this exercise we will use an alpha value ( α ) of 0.05 (or 5%). This number determines how “rare” the results have to be before we reject the null hypothesis. Procedure : 1. Construct a contingency table from the stratified data. 2. Determine both the row totals and column totals (sum across rows, sum across columns). 3. Calculate the expected frequencies. 4. Calculate the Chi-Square statistic. 5. Determine the Degrees of Freedom. 6. Compare the Chi-Square statistic to the critical value. 7. Write an appropriate statement of your findings. The equation for determining the expected frequencies ( f ’’ ij ) is: …where f ’’ ij is the expected frequency, R is the row, C is the column, and n total observations. The equation for calculating the Chi-Square ( χ 2 ) statistic is: …where f ij is the observed frequency and f ’’ ij is the expected frequency. The equation for the degrees of freedom ( v ) is: n C R f j i ij ) )( ( ' = ∑∑ = ' 2 ' 2 ) ( ij ij ij f f f χ ) 1 )( 1 ( = c r V

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An Example of Chi-Square Map Analysis In a neighborhood there is an elementary school 5 th grade class that has experienced a large number of childhood cancer cases. Of the 20 children in the class, ten developed some form of cancer. Parents noted that these children lived near two old factory sites and were concerned that pollutants found at these sites were making their children sick. One method of testing whether children living near the old factories were
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• Fall '12
• Paul Marr
• Geography, Frequency, Null hypothesis, Chi-square distribution, Pearson's chi-square test, cancer cases

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