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Chapter 4

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

by OC506543

School

University of GuelphDepartment

Sociology and AnthropologyCourse Code

SOAN 3120Professor

Andrew HathawayChapter

4This

**preview**shows half of the first page. to view the full**2 pages of the document.**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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