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Chapter 4

SOAN 3120 Chapter Notes - Chapter 4: Standard Deviation, Txe, Dependent And Independent Variables


Department
Sociology and Anthropology
Course Code
SOAN 3120
Professor
Andrew Hathaway
Chapter
4

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Chapter 4 – Scatterplots and Correlation
4.1 – Explanatory and Response Variables
- A response variable measures an outcome of a study
oAka dependant variable
- An explanatory variable may explain or influence changes in a response variable
oAka independent variable or predictor variable
- The idea behind this language is that the response variable depends on the explanatory variable
- In many studies, the goal is to show that changes in one or more explanatory variables actually cause
changes in a response variable
oOther explanatory-response relationships do not involve direction causation
4.2 – Displaying Relationships: Scatterplots
- The most useful graph for displaying the relationship between two quantitative variables measured on the
same variables is a scatterplot
- The values of one variable appear on the horizontal axis, and the values of the other variable appear on
the vertical axis
- Each individual in the data appears as a point in the plot fixed by the values of both variables for that
individual
- Always plot the explanatory variable on the horizontal axis
oCall the explanatory variable x, and the response variable y
oIf there is none, either variable can go on the horizontal axis
4.3 – Interpreting Scatterplots
- Describe the overall pattern of the plot by its direction, form, and strength
oDirection indicates whether the overall pattern moves from lower left to upper right, from upper
right to lower left, or neither
oForm refers to the approximate functional form
Is it a roughly straight line? Is it curved?
oStrength refers to how closely the points in the plot follow the form
- Be careful not to confuse the ways we describe patterns for distributions of a single variable, such as
symmetric or skewed, with ways we describe patterns in scatterplots
- When discussing the direction of the relationship between two variables, use the word association
oAssociation and relationship are often treated as synonyms by statisticians
oTwo variables are positively associated when above-average values of one tend to accompany
above-average values of the other, and below-average values also tend to occur together
oTwo variables are negatively associated when above-average values of one tend to accompany
below-average values of the other, and vice versa
- It is wise to always ask what other variables may contribute to the relationship displayed in a scatterplot
4.4 – Adding Categorical Variables to Scatterplots
- To add a categorical variable to a scatterplot, use a different plot colour or symbol for each category
oEx. Provinces displayed with ‘o’ symbol, territories displayed with ‘+’ symbol
4.5 – Measuring Linear Association: Correlation
- Our eyes are not good judges of how strong a linear relationship is
oChanging the plotting scales or the amount of space around the cloud of points can fool us
- Instead, we measure using correlation
oCorrelation measures the direction and strength of the linear relationship between two
quantitative variables
oUsually written as r
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