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Correlation

Correlation is the broad class of statistical relationships involving dependence. Dependence is the relationship between two random variables or two sets of data. Examples of dependent phenomena include the correlation between the physical statures of parents and their offspring and the correlation between the demand for a product and its price. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. Correlation does not imply causation.

Rank correlation coefficients measure the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship. If, as the one variable increases, the other decreases, the rank correlation will be negative. It’s common to regard these rank correlation coefficients as alternatives to Pearson’s coefficient less sensitive to on-normality in distributions.  

The information given by a correlation coefficient is not enough to define the dependence structure. The correlation coefficient completely defines the dependence structure only in very particular cases.  For example, when the distribution is a multivariate normal distribution. Distance correlation and Brownian covariance were introduced to address the deficiency of Pearson’s correlation that it can be zero for dependent random variables; zero distance correlation and zero Brownian correlation imply independence. The correlation ratio is able to detect almost any functional dependency ad the entropy-based mutual information, total correlation and dual total correlation are capable of detecting even more general dependencies. 

Categories within Correlation

Pearson Product-Moment Correlation

Postings: 57

The Pearson product-moment correlation coefficient is a measure of the linear correlation between two variables X and Y, giving a value between +1 and −1 inclusive.

Partial Correlation

Postings: 5

Partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed.

Confounding Variable

Postings: 3

A confounding variable is an extraneous variable in a statistical model that correlates with both the dependent variable and the independent variable.

Conduct a Mann Whitney U test using real example

WEEK 6 PROBLEMS—30 POINTS 10 points each. Place answers in the following table: 1. 2. 3. 1. A company is evaluating the impact of a wellness program offered on-site as a means of reducing employee sick days. A total of 8 employees agree to participate in the evaluation which lasts 12 weeks. Their sick days

Dependent and Independent Variables and Formulating

I have to study correlated research. The title of the research study is Self-Efficacy and Quality of Life after Stroke. I need help with correlating self-efficacy and Quality of Life after Stroke with three variables. The variables are age, education level, and employment status. I also need help with forming research questions

Why Correlation Does Not Equal Causation

A major study finds that there is a correlation of. 85 between the number of cats owned and IQ in adults. Your aunt reads the study and decides that in order to increase her IQ she will adopt several cats. A. Based on the information above, will adopting cats increase her IQ? B. Explain your reasoning.

Situations with High and Low Correlation

A researcher wants to know the relationship between the height and weight of male students in school district. Correlation coefficients were obtained for (A) all male students between K-12 (B) male students between grades 2 and 5 and (C) all male students on high school varsity volleyball team. A. Which correlation was probab

The relationship between causation and correlation

A researcher finds that there is a correlation of 0.72 between the number of churches and the number of homicides in the city. A. In the study above, which is independent variable and which is the dependent variable? B. Fully explain why (a) is a trick question C. Give one possible example of a third (spurious) variabl

Correlation Analyses

For this case, we would like to investigate the impact of conflict on the quality of work. Research considers there to be two primary types of conflict (1) relationship conflict, (2) task conflict. Relationship conflict is the conflict that occurs between members of the group. This may invoke strong feelings of anger and frustra

Statistics: Chi-square Tests of Independence

The hypothesis that is considered for this study is that a higher rate/prevalence of pornography use is associated with decreased level of relationship satisfaction. Please run the appropriate tests to show whether pornography use leads to less relationship satisfaction, or whether the results do not prove it. Please provide a

Discussing relationship between correlation and causation

Here is when I used an informal type of correlation. In this case, "Does correlation imply causation?" Why or why not? A time when I used an informal type of correlation was to assume that there was a positive correlation between the number of hours studying and the grade that I receive in a course. Based on my experience, th

Statistics: correlation and causation

What is correlation? How is correlation used to understand the relationship between two variables? What is the difference between positive and negative (inverse) correlation? What is the correlation coefficient (r-value)? What values can the correlation coefficient (r-value) have and what do these values reveal about t

Decision Statistics: Correlation and Causation

Describe a time in your life that you used correlation to make a decision. Use a paragraph to explain. What was the result? Explain Did you wrongly feel that correlation was the same as causation? Based on the previous question you just answered. Why or why not - (I

Determining Sample Correlation Coefficients

1. The following statistics were calculated from pairs of observations where X represents the independent variable and Y represents the dependent variable. Σx = 511 Σy = 314 Σxy = 19,064 Σx^2 = 34,234.5 Σy^2 = 13,036 n = 8 Determine the least squares line. Determine the sample correlation coefficient between

Correlation in Cost Variables

The attachment for the question contains the top 100 hotel restaurants in the United States and the variables state, city, restaurant, hotel, cost (estimated price of dinner including one drink and tip), and ranking (1 to 100, with the 1 top rated restaurant). Which Five Number Summary is correct for the Cost variable? A.

Statistics: Correlation Between Two Events

Research has shown that the people often see a correlation between two events when one does not really exist. Why do you think this happens? Can you think of at least two situations in which this should not occur and at least two situations in which it is more likely to occur?

Correlation misreported as causation

Hello, I'm working on a paper and want to include something like this in it. Can you please help me with this? What are your thoughts? This is not the actual assignment, simply something I found and want to include in my paper. Correlation is sometimes misreported as causation. When two variables systematically change, the

Using Excel to Find Correlations

Use Excel to do a correlation between the following variables: 1) X - 2,5,5,6,6,7,8,9 2) Y - 1,2,2,3,4,4,5,5 A drug company is measuring levels of oxygenation in patients after receiving a test medication. As the researcher, you are interested in whether Group I, which received the medication, has the same oxygenation level

Various Statistics Questions

1. Of the following four research questions, which one are appropriate for the chi-square test? a.The difference between the average scores of two math classes. b.The difference between the number of children who passed the math test in Class 1 and the number of children who passed the math test in class 2. c. The number of

Interpret the relationship between two variables

The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000) 1 12 10.

Interpreting the relationship between two variables

Calculate, test, and interpret the relationship between two variables using the correlation coefficient Given the following sample observations, draw a scatter diagram on a separate piece of paper. X: -8 -18 14 5 18 Y: 57 257 140 9 348 (1) Compute the correlation coefficient. (Round your answer to 3 d

Relationship Between Variables Using the Correlation Coefficient

Calculate, test, and interpret the relationship between two variables using the correlation coefficient. The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to d

Bardi Correlation Coefficient

Bardi Trucking Company, located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate,

Interpreting Tables

I need help interpreting these tables. I have started on them but I do no think they are correct. The solutions would be very helpful for my studies. Problem 1. Below is a tabulation of the demographic data from the Frequency distribution of a survey done by Ms. Sandra Jones. Her sample consisted of 148 of a total of 3,700

Coefficient of Correlation, etc.

Use the data provided. (Also see attachment.) a. Plot the data; determine the least-squares line for the data and overlay it on the plot. b. Test the hypothesis (at ? = 0.05) that X contributes no information for predicting Y. What are your conclusions? c. Find a 95% confidence interval for ?1. d. Determine the coefficie

Analyzing a Linear Correlation between Two Variables

Question: Construct a scatter-plot, find the value of the linear correlation coefficient r, and find the critical values of r, using alpha = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. Scenario: Crickets and temperature One classic application of

Correlation Calculation

A researcher collects the following data from five high-school students: GPA SAT 2.00 960 3.00 1000 4.00 1300 1.00 650 3.54 1280 What is the correlation between high-school GPA and SAT scores? Report the appropriate null and research hypotheses and the critical value (alpha = 0.05). In addition, provide your

Finding and Testing the Correlation Coefficient

A sociologist is interested in the relation between x=number of job changes and y=annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information: x (number of job changes) 0 7 6 2 8 6 8 7 0 0 y

Statistics Possibilities

For each of the following summaries, first indicate what the usual interpretation would be, then indicate whether there are any other possibilities. a. r = 1. b. r = 0.85. c. r = 0. d. r= -0.15. e. r = -1.