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Sociology and Anthropology
SOAN 3120
Michelle Dumas

September 13, 2012 Chapter 3 and Chapter 8 The relationship between two variables = correlation The positive slope implies a positive correlation.  / The negative slope implies a negative correlation.  \ No relationship between education income. (Flat Slope) – no relationship - Scatterplots play an important role when exploring the relationship between two quantitative variables o They allow us to identify problem cases, the form of the relationship (whether it is linear or not) and have a preliminary estimate of the strength of the relationship - only when the relationship is linear does it make sense to use the correlation coefficient o the correlation coefficient is a good summary measure of the direction and strength of a linear relationship  it ranges from -1 (perfect negative linear relationship) and +1 (perfect positive linear relationship) and 0 means no linear relationship  it does not tell us the slope of the line - if the line goes from top to bottom, it’s a negative (-0.8, -0.3, etc.) - if the line goes from bottom to top, it’s positive (0.9, 0.5, etc) - if the dots are all over, it’s 0 - if its pretty close to creating a straight line from top to bottom, it’s a positive, probably 0.5 (and vice versa for negative) - if it’s nearly creating a straight line from top to bottom, it’s a positive probably 0.9 (and vice versa for positive) - what to do with “outliers” (the unusual)? o Is part of the data but unusual o Is a coding error – you may have to remove that one random one, it may change the results dramatically - The issue of causality o How do we know which variable causes the other?  Correlation does not mean causation  We infer a causal relationship based on the understanding of the temporal relationship between the variables - Variable Classification o Independent variables (cause) (x-axis) (horizontal) o Dependent variables (effect variables) (y-axis) (vertical) - Sometimes identifying a causal order can be problematic o Relationship between education and motivation o Educational attainment (1-23) o Motivational scale (1-100) o High score implies greater motivation  Education  motivation  Education  motivation  Education   motivation o Address the issue:  Good theorizing (how have other researchers done it? What are their justifications?)  Advanced statistics - How do we know if the relationship is statistically significant? (in other words, is it meaningful? Is it real, or could it just occur by chance?) o The higher correlation the stronger the relationship (steep and tightly compact slope in terms of the dots around the line) o Computer statistical software programs generate significance tests  Likelihood – probability (chance)  education increases income  given the data, the probability that changes in education do not cause changes in income is approximately p = .01 (1 in 100) (the p value gives us an idea, what’s the change the probability is due to change … the p is probability – if the probability is low, then it’s unlikely the relationship is due to chance.) o Common Thresholds (multiply the probability by 100)  P = .05 (5% chance. .. multiply the probability by 100)  P = .01  P = .001 - Statistics does not equal mathematics o We never use the word prove – we prove something beyond a reasonable doubt  The issue of control – still a chance we could be wrong – we could have just had a bizarre sample  Statistical control - The relationship between the length of big toe and income is spuri
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