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# Soc%20005%20-%20Lecture%205 - Analyzing Categoric Data...

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SOCIOLOGY 005 Lecture 5 Analyzing Categoric Data Previous hypothesis tests have focused on the differences between means either between a sample and population or between two or more groups within a sample We can also test hypotheses with nominal and ordinal level data These data are often represented in contingency tables or cross-tabulations Analyzing Categoric Data Educational Mobility Ballet | Downward Static Upward | Total -----------+---------------------------------+---------- No | 83 785 150 | 1,018 | 71.55 83.87 66.96 | 79.78 -----------+---------------------------------+---------- Yes | 33 151 74 | 258 | 28.45 16.13 33.04 | 20.22 -----------+---------------------------------+---------- Total | 116 936 224 | 1,276 | 100.00 100.00 100.00 | 100.00 Contingency Table Cell - Contains the number of cases have joint values on two variables Marginals - Contain the row totals (row marginals) and column total (column marginals) Totals Independent Variable Outcomes Dependent Variable Outcomes Analyzing Categoric Data Educational Mobility Ballet | Downward Static Upward | Total -----------+---------------------------------+---------- No | 83 785 150 | 1,018 | 71.55 83.87 66.96 | 79.78 -----------+---------------------------------+---------- Yes | 33 151 74 | 258 | 28.45 16.13 33.04 | 20.22 -----------+---------------------------------+---------- Total | 116 936 224 | 1,276 | 100.00 100.00 100.00 | 100.00 Contingency Table Column Percentages

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Statistical Independence Statistical Independence For Contingency Tables, we say that when two variables are not significantly related to each other they are statistically independent In order to determine if two variables are independent, we need to calculate expected values for each cell and calculate a chi-square score for the table Expected values are hypothetical values which represent what a cell count would be if the two variables were statistically independent, that is, unrelated The Chi-Squared score is used to test the null hypothesis Analyzing Categoric Data Educational Mobility Ballet | Downward Static Upward | Total -----------+---------------------------------+---------- No | 83 785 150 | 1,018 | | -----------+---------------------------------+---------- Yes | 33 151 74 | 258 | | -----------+---------------------------------+---------- Total | 116 936 224 | 1,276 | | To calculate the expected value for each cell, we use the following equation: ˆ f ij = ( f i )( f j ) N 92.55 746.75 178.79 23.45 189.25 45.29 (1018)(116) 1276 (1018)(936) 1276 (1018)(224) 1276 (258)(224) 1276 (258)(936) 1276 (258)(116) 1276 Analyzing Categoric Data Once we calculate expected values for each cell, we need to calculate a chi-squared statistics in order to test the null hypothesis of statistical independence ! 2 = " ( f o # f e ) 2 f e ...with the following degrees of freedom: df = ( R ! 1)( C ! 1) Analyzing Categoric Data Educational Mobility Ballet | Downward Static Upward | Total -----------+---------------------------------+---------- No | 83 785 150 | 1,018 | | -----------+---------------------------------+---------- Yes | 33 151 74 | 258 | | -----------+---------------------------------+---------- Total | 116 936 224 | 1,276 | | 92.55 746.75 178.71 23.45 189.25 45.29 (83 - 92.55) 2 /92.55 = (-9.55) 2 /92.55 = .985 (785 - 746) 2 /746 = (38.25) 2 /746 = 1.96 (150 - 178.71) 2 /178.71 = (-28.71) 2 = 4.61 (33 - 23.45) 2 /23.45 = (9.55) 2 /23.45 = 3.88 (151 - 189.25) 2 /189.25 = (-38.25) 2 /189.25 = 7.73 (74 - 45.29) 2 /45.29 = (28.71) 2 /45.29 = 18.20 ! ( f o " f e ) 2 f e = 37.37 df = (2 ! 1)(3 ! 1) df = (1)(2) df = 2
Analyzing Categoric Data ! 2 = 37.37 df = 2 !" #\$#% #\$#&% #\$#’ #\$##% !"#\$% &"’(\$ )")!& *"#*+ & &"++% *"!*# +"(% %’"&+* ( *"#%& +"!\$# %%"!\$& %("#!# ) +"\$## %%"%\$! %!"(** %\$"#) % %%"’* %("#!! %&"’#) %)"*& * %("&+( %\$"\$\$+ %)"#%( %#"&\$# + %\$"’)* %)"’%! %#"\$*& (’"(*# , %&"&’* %*"&!& (’"’+ (%"+&& - %)"+%+ %+"’(! (%"))) (!"&#+ ’# %#"!’* (’"\$#! (!"(’+ (&"%## ’’ %+")*& (%"+( (\$"*(& ()"*&* ! 2 Critical Values Analyzing Categoric Data ! 2 Distribution Analyzing Categoric Data ! 2 Distribution ! 2 = 37.37 df = 2 Measures of Association If we reject the null hypothesis of statistical independence, we are likely interested on measuring the association between our variables Measures of association for contingency tables describe the strength of the covariation between pairs of discrete variables The measure of association that can be used is contingent on the number of rows and columns of a contingency table

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Measures of Association There are two types of measures of Association
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Soc%20005%20-%20Lecture%205 - Analyzing Categoric Data...

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