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Lesson 1  Introduction to Statistical Research Methods 
Lesson 2  Visualizing Data 
Lesson 3  Central Tendency 
Lesson 4  Variability 
Lesson 5  Standardizing 
Lesson 6  Normal Distribution 
Lesson 7  Sampling Distributions 
Lesson 8  Estimation 
Lesson 9  Hypothesis Testing 
Lesson 10  tTests for Dependent Samples 
Lesson 11  tTests for Independent Samples 
Lesson 12  Intro to OneWay ANOVA 
Lesson 13  OneWay ANOVA: Test significance of differences 
Lesson 14  Correlation 
Lesson 15  Linear Regression 
Lesson 16  ChiSquared Tests 
Afterward  
Index 
So far, we’ve been working with one variable. We used ztests to see if a value of a certain variable (e.g., a value of 6’1” from the variable “height”) differed significantly from the mean value for that variable. We used ttests to do the same thing, but using samples to approximate populations. And we used ANOVA to look at values of the same variable, but in different groups.
In this lesson, we’ll analyze the relationship between two variables from the same sample (e.g., height and weight, which come from the same people; population and amount of pollution, which come from the same cities; number of students and number of teachers, which come from the same schools). In statistics, this relationship is called the correlation.
Mathematician Hans Rosling has a great video where he visualizes relationships between variables in cool new ways.
Let’s analyze some real data so you can get a good sense of how we can use correlations to draw conclusions. The data below lists the first few rows of the following variables: [Link to full data]
 population US state population in millions
 pop_density Population density per sq. km.
 tax_rate State tax rate
 spending State and local spending as percent of gross state product
 debt State and local debt as percent of gross state product
 rsg Real state growth in percent
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