Lecture PowerPoint Slides Basic Practice of Statistics 7 th Edition

Why are we doing this stuff? Man vs. Earth (i.e., social media) Man vs. Earth What data can do to fight poverty UN Millenial goals ( ) Hans Rosling talk Official website Sustainable Development Goals ( ) Official website

Exams and solutions SA4 Questions on correlations readings?

Explanatory and Response Variables RESPONSE VARIABLE, EXPLANATORY VARIABLE A response variable measures an outcome of a study. An explanatory variable may explain or influence changes in a response variable.

Scatterplot Example: Make a scatterplot of the relationship between body weight and backpack weight for a group of hikers. Body weight (lb) Backpack weight (lb)

Interpreting Scatterplots To interpret a scatterplot, follow the basic strategy of data analysis from Chapters 1 and 2. Look for patterns and important departures from those patterns. HOW TO EXAMINE A SCATTERPLOT As in any graph of data, look for the overall pattern and for striking deviations from that pattern. You can describe the overall pattern of a scatterplot by the direction, form, and strength of the relationship. An important kind of departure is an outlier, an individual value that falls outside the overall pattern of the relationship.

Figure 4.7, The Basic Practice of Statistics, © 2015 W. H. Freeman

*blog.mrmeyer.com

Direction of Association POSITIVE ASSOCIATION, NEGATIVE ASSOCIATION Two 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. Two variables are negatively associated when above- average values of one tend to accompany below- average values of the other, and vice versa.

Measuring Linear Association  A scatterplot displays the strength, direction, and form of the relationship between two quantitative variables.  The correlation, r, measures the strength of the linear relationship between two quantitative variables. shorter form:

Facts about Correlation  Correlation makes no distinction between explanatory and response variables.  r has no units and does not change when we change the units of measurement of x, y, or both.  Positive r indicates positive association between the variables, and negative r indicates negative association.  The correlation r is always a number between – 1 and 1.

Figure 4.4, The Basic Practice of Statistics, © 2015 W. H. Freeman

Figure 4.5, The Basic Practice of Statistics, © 2015 W. H. Freeman

 Correlation Guessing Game Correlation Guessing Game

Be sure to double check grades; especially if you submitted late work or there was some other special circumstance Redemption option deadline (Friday) Correlation resources on Moodle Questions about SA4 (will discuss more later)

Entry Slip: Correlation (True/False) 1. Correlation requires that both variables be quantitative and that data be paired. 2. Correlation does not describe curved relationships between variables, no matter how strong the relationship is. 3. Correlation is resistant. r is not affected much by a few outlying observations. 4. Correlation is another way to say causation. 5. When two variables have a positive correlation, the r value is also positive.

Entry Slip: Correlation 1. Correlation requires that both variables be quantitative and that data be paired. 2. Correlation does not describe curved relationships between variables, no matter how strong the relationship is. 3. Correlation is not resistant. r can be highly affected by a few outlying observations. 4. Correlation does not imply causation (although it can be evidence in that direction). 5. When two variables have a positive correlation, the r value is also positive. (although the slope of the trendline usually does not equal r)

Anscombe’s Quartet

Correlation vs. Causation

Tyler Vigen’s Spurious Correlations Site

Joy of Stats: Correlation

Table 4.1, The Basic Practice of Statistics, © 2015 W. H. Freeman What do we do here?

Figure 4.2, The Basic Practice of Statistics, © 2015 W. H. Freeman

Let’s get some more meaningful data What can we do to increase reliability?

On a scale of 1-100… 1.How lonely are you these days? (100 is very lonely) 2.How much do you believe in a loving God? (100 strong belief in loving God) 3.How much do you believe that the Bible is true? (100 is completely true-every word) 4.How extroverted are you? (100 is pure extrovert) 5.How much do you believe in yourself? 6.How much do you feel supported by your friends? 7.How is your home life? (100 is very good) 8.How necessary is it for you to go to church? (100 very necessary) 9.How close are you to your parents?

Adding Categorical Variables Consider the relationship between mean SAT verbal score and percent of high-school grads taking SAT for each state. To add a categorical variable, use a different plot color or symbol for each category. Mean SAT Mathematics score and percent of high school graduates who take the test for only the Midwest (blue) and Northeast (red) states.

Let’s talk about S4

Categorical Variables Our textbook authors mention several times that you should only use quantitative variables for correlation (and regression). In general, this is true; however, there is a way to change a categorical variable so that it can be analyzed. - If it has only two categories (male/female, live/die, etc.), then you can just use 0 and 1 to represent the values. - With three or more categories, you have two options: - Collapse (i.e., change all ethnicities to either Hispanic or non-Hispanic) - Dummy coding (you will need k – 1 variables for k categories); ask me!

Discrete Strangeness