Bivariate Data

… a core topic in Quantitative Methods and Atlas104

BivariateDataTopic description

This topic examines ways to describe the relationship between two variables.

The treatment of this topic on the Atlas follows almost precisely that in Chapter IV, Describing Bivariate Data, of OnlineStatBook, Online Statistics Education – An Interactive Multimedia Course of Study, http://onlinestatbook.com/2/index.html, accessed 14 May 2016.

Topic learning outcome

Familiarity with ways of describing the relationship between two variables including following core concepts and terms.

[Note: Until Atlas pages are created for individual concepts in Quantitative Methods, the links in the concepts below point directly to the relevant pages in OnlineStatBook.]

Core concepts associated with this topic
Introduction to Bivariate Data

Values of the Pearson Correlation

Guessing Correlations Simulation

Properties of Pearson’s r

Computing Pearson’s r

Restriction of Range

Variance Sum Law II

Readings

Read and/or watch video for each of the concept pages above (top to bottom, starting in left column).

Read the Statistical Literacy exercises, Age and Sleep, and answer the questions.

Read the Angry Moods (AM) case study and complete following exercises:

  • What is the correlation between the Control-In and Control-Out scores? (relevant section)
  • Would you expect the correlation between the Anger-Out and Control-Out scores to be positive or negative? Compute this correlation. (relevant section & relevant section)

Read the Flatulence (F) case study and complete following exercise:

  • Is there a relationship between the number of male siblings and embarrassment in front of romantic interests? Create a scatterplot and compute r. (relevant section & relevant section)

Read the Stroop (S) case study and complete following exercise:

  • Create a scatterplot showing “colors” on the Y-axis and “words” on the X-axis. (relevant section)
  • Compute the correlation between “colors” and “words.” (relevant section)
  • Sort the data by color-naming time. Choose only the 20 fastest color-namers and create a scatterplot. (relevant section)
  • (a) What is the new correlation? (relevant section)
    (b) What is the technical term for the finding that this correlation is smaller than the correlation for the full dataset? (relevant section)

Read the Animal Research (AR) case study and answer the following question:

  • What is the overall correlation between the belief that animal research is wrong and belief that animal research is necessary? (relevant section)

Read the ADHD Treatment (AT) case study and complete the following exercises:

  • What is the correlation between the participants’ correct number of responses after taking the placebo and their correct number of responses after taking 0.60 mg/kg of MPH? (relevant section
Assessment questions

From http://onlinestatbook.com/2/describing_bivariate_data/ch4_exercises.html, accessed 14 May 2016.

AQ104.03.01. Describe the relationship between variables A and C. Think of things these variables could represent in real life. (relevant section)

AQ104.03.02. Make up a data set with 10 numbers that has a positive correlation. (relevant section & relevant section)

AQ104.03.03. Make up a data set with 10 numbers that has a negative correlation. (relevant section & relevant section)

AQ104.03.04. If the correlation between weight (in pounds) and height (in feet) is 0.58, find: AQ104.03.04.1 the correlation between weight (in pounds) and height (in yards); AQ104.03.04.2 the correlation between weight (in kilograms) and height (in meters) (relevant section)

AQ104.03.05. Would you expect the correlation between High School GPA and College GPA to be higher when taken from your entire high school class or when taken from only the top 20 students? Why? (relevant section)

AQ104.03.06. For a certain class, the relationship between the amount of time spent studying and the test grade earned was examined. It was determined that as the amount of time they studied increased, so did their grades. Is this a positive or negative association? (relevant section)

AQ104.03.07. For this same class, the relationship between the amount of time spent studying and the amount of time spent socializing per week was also examined. It was determined that the more hours they spent studying, the fewer hours they spent socializing. Is this a positive or negative association? (relevant section)

AQ104.03.08. For the following data:

A B
2
5
6
8
9
8
5
2
4
1

AQ104.03.08.1 Find the deviation scores for Variable A that correspond to the raw scores of 2 and 8.

AQ104.03.08.2 Find the deviation scores for Variable B that correspond to the raw scores of 5 and 4.

AQ104.03.08.3 Just from looking at these scores, do you think these variable A and B are positively or negatively correlated? AQ104.03.08.4 Why?

AQ104.03.08.5 Now calculate the correlation. Were you right?
(relevant section)

AQ104.03.09. Students took two parts of a test, each worth 50 points. Part A has a variance of 25, and Part B has a variance of 36. The correlation between the test scores is 0.8. AQ104.03.09.1 If the teacher adds the grades of the two parts together to form a final test grade, what would the variance of the final test grades be? AQ104.03.09.2 What would the variance of Part A – Part B be? (relevant section)

AQ104.03.10. True/False: The correlation in real life between height and weight is r=1. (relevant section)

AQ104.03.11. True/False: It is possible for variables to have r=0 but still have a strong association. (relevant section & relevant section)

12. True/False: Two variables with a correlation of 0.3 have a stronger linear relationship than two variables with a correlation of -0.7. (relevant section)

AQ104.03.13. True/False: After polling a certain group of people, researchers found a 0.5 correlation between the number of car accidents per year and the driver’s age. This means that older people get in more accidents. (relevant section)

AQ104.03.14. True/False: The correlation between R and T is the same as the correlation between T and R. (relevant section)

AQ104.03.15. True/False: To examine bivariate data graphically, the best choice is two side by side histograms. (relevant section)

AQ104.03.16. True/False: A correlation of r=1.2 is not possible. (relevant section)

Questions from Case Studies:

The following questions are from the Angry Moods (AM) case study.

AQ104.03.17. What is the correlation between the Control-In and Control-Out scores? (relevant section)

AQ104.03.18.1 Would you expect the correlation between the Anger-Out and Control-Out scores to be positive or negative? AQ104.03.18.2 Compute this correlation. (relevant section & relevant section)

The following question is from the Flatulence (F) case study.

AQ104.03.19.1 Is there a relationship between the number of male siblings and embarrassment in front of romantic interests? AQ104.03.19.2 Create a scatterplot and compute r. (relevant section & relevant section)

The following questions are from the Stroop (S) case study.

AQ104.03.20. Create a scatterplot showing “colors” on the Y-axis and “words” on the X-axis. (relevant section)

AQ104.03.21. Compute the correlation between “colors” and “words.” (relevant section)

AQ104.03.22.1 Sort the data by color-naming time. Choose only the 20 fastest color-namers and create a scatterplot. (relevant section)

AQ104.03.22.2 What is the new correlation? (relevant section)
AQ104.03.22.3 What is the technical term for the finding that this correlation is smaller than the correlation for the full dataset? (relevant section)

The following question is from the Animal Research (AR) case study.

AQ104.03.23. What is the overall correlation between the belief that animal research is wrong and belief that animal research is necessary? (relevant section)

The following question is from the ADHD Treatment (AT) case study.

AQ104.03.24. What is the correlation between the participants’ correct number of responses after taking the placebo and their correct number of responses after taking 0.60 mg/kg of MPH? (relevant section)

Page created by: Ian Clark, last modified on 16 May 2016.

Image: Fundamentals of Statistics, at http://www.statistics4u.info/fundstat_eng/cc_multivar_stat.html, accessed 14 May 2016.