Introduction to Sociological Research_Kupchik_Date__050510

# Introduction to Sociological Research_Kupchik_Date__050510...

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ANOVA – Analysis of Variance Testing Hypothesis with multiple group means (ANOVA) Why analysis of variance (ANOVA)? o To compare means across more than 2 groups We have a continuous (interval or ratio level) dependent variable, and more than 2 groups Exactly like a t-test for independent sample, but for more than 2 groups The logic of ANOVA o When we compare means across groups, we need to think of how the scores vary: There is the total variance for the sample Then there is the between-group variance (groups different means) And there is the within-group variance (say there are 500 people across the country in different parts. Break down into 4 groups. How are people in northeast different from south, west, and Midwest? That is the variance between groups. How are people in the Northeast different from each other?) o Total variance = between variance + within variance o We compare the differences across the groups to the differences within groups o Just like with a t-test, where we compare the difference between scores to the standard error TOTAL VARIANCE Total variance (1) o Total variance measure how each case varies from the mean: Total variance : s 2 = (Σ (x1- ) 2 ) / n-1 o = o First we calculate the sum of squares : SS total = Σ i Σ k (x ik - grand ) 2 grand – overall mean of all 500 cases Σ i – means start at first case (each ind. case) Σ k – means do it for each group K- number of groups Total variance (2) o Then we find the degrees of freedom DF total = n-1 o And then we divide the sum of squares by the degrees of freedom, for the mean squares total MS total = ( Σ i Σ k (x ik - grand ) 2 ) / (n-1) VARIANCE BETWEEN GROUPS Between group variance (1) o Tells us how the groups vary-how strong an effect our independent variable has

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o First, sum of squares between SS between = Σn k ( k - grand ) 2 k – each group’s average tells us how the group averages from total case’s average Between group variance (2) o Then, df between =k-1 (k=# of groups) o And, mean squares between MS between = (Σn k ( k - grand ) 2 ) / (k-1) VARIANCE WITHIN GROUP Within group variance (1) o How widely dispersed each group is o First, SS within = Σ i Σ k (x ik - k ) 2 Within group variance (2) o The df within =n-k o And, mean squares within = MS within = i Σ k (x ik - k ) 2 ) / (n-k) Calculating sum of squares o SS total = SS between + SS within o This means you only need to know 2 of the 3 o For example: SS between = SS total - SS within Comparing variances o Finally, we do an F-test F-distribution is a different distribution, like t- or z-distribution It is for a ratio See Appendix E-5, pp727-728 (n1= degrees of freedom between) (n2= degrees of freedom within) F = (SS between /DF between ) / (SS within /DF within ) = variance between groups / variance within groups ON PAGE 727, up in top left corner of table, it says N-2 then N-1. 728 is correct
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## This note was uploaded on 08/30/2010 for the course SOCI 301 taught by Professor Kupchick during the Spring '09 term at University of Delaware.

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Introduction to Sociological Research_Kupchik_Date__050510...

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