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SOAN 3120
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Michelle Dumas
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Sociology and Anthropology

SOAN 3120

Michelle Dumas

Fall

Description

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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