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SOCY 211 (69)
Carl Keane (12)
Lecture

SOCY211 Week 8, Lecture 2

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Department
Sociology
Course
SOCY 211
Professor
Carl Keane
Semester
Winter

Description
ANALYSIS OF VARIANCE - Often referred to as a “Comparison of Means” test - Can be used when: Independent variable is measured at the nominal or ordinal level, and the Dependent Variable is measured at the interval/ratio level. - ANOVA - A lot of our independent variables vary- such as happiness - “Total Variation” = two components: (1) the distance, or deviation, of raw scores from their group mean - this is known as “Variation Within Groups,” and, (2) the distance, or deviation, of group means from one another - this is known as “Variation Between Groups.” - Education and income example - All have some overlap and within each group there will be some variations - When you compare between groups you always use the mean  Sum of Squares S =√ ∑(X – X)² N - We use all the values so that it is easier to compare - When we have groups we have different sums of squares but each type represents the sum of sum deviations from the mean  Total Sum of Squares  Within-Groups Sum of Squares  Between Groups Sum of Squares Happiness Measured on a Scale from 1 to 10 (example) Group A Group B Group C 8 x x 7 x x 5 x x 4 x x 24 X X N(A)=4 N(B)=4 N(C)=4 Total N=12 Mean(A) = 24/4 = 6 Total Mean (Hypothetically) = 5 - WITHIN-GROUP VARIATION/DEVIATION (Raw scores for each group member minus their group mean) e.g., Group A 8 – 6 = +2 1 7 – 6 = +1 5 – 6 = -1 4 – 6 = -2 - Then do the same for individuals in Groups B and C – subtracting their individual scores from their group means. - BETWEEN-GROUP VARIATION/DEVIATION (Means for each group minus the total mean) e.g., Group A: 6 – 5 = +1 - Then do the same for Groups B and C - TOTAL VARIATION/DEVIATION (Raw scores for each group member minus the total mean) e.g., Group A 8 – 5 = +3 7 – 5 = +2 5 – 5 = 0 4 – 5 = -1 - Then do the same for every member of Groups B and C. Mean Squares  Total Sum of Squares - measures variation of individual scores about the total mean  Within-Groups Sum of Squares - measures variation of individual scores about their group mean  Between-Groups Sum of Squares - measures variation of group means about the total mean F RATIO Between-Groups Mean Squares F = -------------------------------------- Within-Groups Mean Squares - Shows if our data is statistically significant - The stronger the relationship between the two variables, the larger the value of f (independent and dependent) - If there is a big difference between the variance then there is a relationship - If there is a weak association, the between group variance will be small SUMMARY Ratio of: Relationship B-G Variance/Mean Squares W-G Variance/Mean Squares Large B-G Mean Squares -------------------------- = Large F Ratio Strong Small W-G Mean Squares 2 Small B-G Mean Squares ------------------------- = Small F Ratio Weak Large W-G Mean Squares Medium B-G Mean Squares --------------------------- Moderate F Ratio Moderate Medium W-G Mean Squares Total Sum Within-Groups Between Groups = + of Squares Sum of Squares Sum of Squares So, Between-Groups Total Sum Within-Groups = - Sum of Squares of Squares Sum of Squares 2 - PRE measures of association with ANOVA is called ETA square (E ) - Makes use of the total sum of squares and group totals - Total sum of squares is total variation in dependent variable - Total sum of square is a measure of errors
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