• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
The Analysis Factor

The Analysis Factor

Statistical Consulting, Resources, and Statistics Workshops for Researchers

  • Home
  • Our Programs
    • Membership
    • Online Workshops
    • Free Webinars
    • Consulting Services
  • About
    • Our Team
    • Our Core Values
    • Our Privacy Policy
    • Employment
    • Collaborate with Us
  • Statistical Resources
  • Contact
  • Blog
  • Login

Spearman correlation

The Difference Between Association and Correlation

by Karen Grace-Martin 1 Comment

What does it mean for two variables to be correlated?

Is that the same or different than if they’re associated or related?

This is the kind of question that can feel silly, but shouldn’t. It’s just a reflection of the confusing terminology used in statistics. In this case, the technical statistical term looks like, but is not exactly the same as, the way we mean it in everyday English. [Read more…] about The Difference Between Association and Correlation

Tagged With: association, Bivariate Statistics, Correlation, Cramer's V, Kendall's tau-b, point-biserial, Polychoric correlations, rank-biserial, Somer's D, Spearman correlation, Stuart's tau-c, tetrachoric

Related Posts

  • Member Training: Confusing Statistical Terms
  • How to Interpret the Width of a Confidence Interval
  • Six terms that mean something different statistically and colloquially
  • Effect Size Statistics: How to Calculate the Odds Ratio from a Chi-Square Cross-tabulation Table

R is Not So Hard! A Tutorial, Part 21: Pearson and Spearman Correlation

by guest contributer Leave a Comment

by David Lillis, Ph.D.

Let’s use R to explore bivariate relationships among variables.

Part 7 of this series showed how to do a nice bivariate plot, but it’s also useful to have a correlation statistic.

We use a new version of the data set we used in Part 20 of tourists from different nations, their gender, and number of children. Here, we have a new variable – the amount of money they spend while on vacation.

First, if the data object (A) for the previous version of the tourists data set is present in your R workspace, it is a good idea to remove it because it has some of the same variable names as the data set that you are about to read in. We remove A as follows:

rm(A)

Removing the object A ensures no confusion between different data objects that contain variables with similar names.

Now copy and paste the following array into R.

T <- structure(list(COUNTRY = structure(c(3L, 3L, 3L, 3L, 1L, 3L, 2L, 3L, 1L, 3L, 3L, 1L, 2L, 2L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 3L, 1L, 2L), .Label = c("AUS", "JAPAN", "USA"), class = "factor"),GENDER = structure(c(2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L), .Label = c("F", "M"), class = "factor"), CHILDREN = c(2L, 1L, 3L, 2L, 2L, 3L, 1L, 0L, 1L, 0L, 1L, 2L, 2L, 1L, 1L, 1L, 0L, 2L, 1L, 2L, 4L, 2L, 5L, 1L), SPEND = c(8500L, 23000L, 4000L, 9800L, 2200L, 4800L, 12300L, 8000L, 7100L, 10000L, 7800L, 7100L, 7900L, 7000L, 14200L, 11000L, 7900L, 2300L, 7000L, 8800L, 7500L, 15300L, 8000L, 7900L)), .Names = c("COUNTRY", "GENDER", "CHILDREN", "SPEND"), class = "data.frame", row.names = c(NA, -24L))

T
attach(T)

Do tourists with greater numbers of children spend more? Let’s calculate the correlation between CHILDREN and SPEND, using the cor() function.

R <- cor(CHILDREN, SPEND)
[1] -0.2612796

We have a weak correlation, but it’s negative! Tourists with a greater number of children tend to spend less rather than more!

(Even so, we’ll plot this in our next post to explore this unexpected finding).

We can round to any number of decimal places using the round() command.

round(R, 2)
[1] -0.26

The percentage of shared variance (100*r2) is:
100 * (R**2)
[1] 6.826704

To test whether your correlation coefficient differs from 0, use the cor.test() command.

cor.test(CHILDREN, SPEND)
Pearson's product-moment correlation
data: CHILDREN and SPEND
t = -1.2696, df = 22, p-value = 0.2175
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.6012997 0.1588609
sample estimates:
cor
-0.2612796

The cor.test() command returns the correlation coefficient, but also gives the p-value for the correlation. In this case, we see that the correlation is not significantly different from 0 (p is approximately 0.22).

Of course we have only a few values of the variable CHILDREN, and this fact will influence the correlation. Just how many values of CHILDREN do we have? Can we use the levels() command directly? (Recall that the term “level” has a few meanings in statistics, once of which is the values of a categorical variable, aka “factor“).

levels(CHILDREN)
NULL

R does not recognize CHILDREN as a factor. In order to use the levels() command, we must turn CHILDREN into a factor temporarily, using as.factor().

levels(as.factor(CHILDREN))
[1] "0" "1" "2" "3" "4" "5"

So we have six levels of CHILDREN. CHILDREN is a discrete variable without many values, so a Spearman correlation can be a better option. Let’s see how to implement a Spearman correlation:

cor(CHILDREN, SPEND, method ="spearman")
[1] -0.3116905

We have obtained a similar but slightly different correlation coefficient estimate because the Spearman correlation is indeed calculated differently than the Pearson.

Why not plot the data? We will do so in our next post.

*****

See our full R Tutorial Series and other blog posts regarding R programming.

About the Author: David Lillis has taught R to many researchers and statisticians. His company, Sigma Statistics and Research Limited, provides both on-line instruction and face-to-face workshops on R, and coding services in R. David holds a doctorate in applied statistics.

Bookmark and Share

Tagged With: as.factor(), cor(), cor.test(), levels, Pearson Correlation, R, round(), Spearman correlation

Related Posts

  • R is Not So Hard! A Tutorial, Part 22: Creating and Customizing Scatter Plots
  • R Graphics: Plotting in Color with qplot Part 2
  • Doing Scatterplots in R
  • R Graphics: Multiple Graphs and par(mfrow=(A,B))

Member Training: Measures of Association: Beyond Pearson’s Correlation

by Karen Grace-Martin Leave a Comment

There are dozens of measures of association. Even just correlations come in many flavors: Pearson, Spearman, biserial, tetrachoric, squared multiple, to name a few.

And there are many measures beyond correlation.

You probably learned many of these way back in intro stat, then promptly forgot about them. That may be reasonable, but they do pop up as important within the context of other, more complicated statistical methods. A strong foundation in the measures of association makes those other methods much easier to understand.

In this webinar, we’re going to re-examine many of these measures, see how they fit together (or don’t), and talk about when each one is useful.


Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

Not a Member? Join!

About the Instructor

Karen Grace-Martin helps statistics practitioners gain an intuitive understanding of how statistics is applied to real data in research studies.

She has guided and trained researchers through their statistical analysis for over 15 years as a statistical consultant at Cornell University and through The Analysis Factor. She has master’s degrees in both applied statistics and social psychology and is an expert in SPSS and SAS.

Not a Member Yet?

It’s never too early to set yourself up for successful analysis with support and training from expert statisticians. Just head over and sign up for Statistically Speaking. You'll get access to this training webinar, 100+ other stats trainings, a pathway to work through the trainings that you need — plus the expert guidance you need to build statistical skill with live Q&A sessions and an ask-a-mentor forum.

Tagged With: measures of association, Pearson Correlation, Spearman correlation

Related Posts

  • Member Training: The Multi-Faceted World of Residuals
  • R is Not So Hard! A Tutorial, Part 21: Pearson and Spearman Correlation
  • Member Training: Introduction to SPSS Software Tutorial
  • Member Training: R for Menu Users Software Tutorial

Primary Sidebar

This Month’s Statistically Speaking Live Training

  • Member Training: Analyzing Pre-Post Data

Upcoming Free Webinars

Poisson and Negative Binomial Regression Models for Count Data

Upcoming Workshops

  • Analyzing Count Data: Poisson, Negative Binomial, and Other Essential Models (Jul 2022)
  • Introduction to Generalized Linear Mixed Models (Jul 2022)

Copyright © 2008–2022 The Analysis Factor, LLC. All rights reserved.
877-272-8096   Contact Us

The Analysis Factor uses cookies to ensure that we give you the best experience of our website. If you continue we assume that you consent to receive cookies on all websites from The Analysis Factor.
Continue Privacy Policy
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled
Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.
Non-necessary
Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.
SAVE & ACCEPT