# Correlation between two variables measured on a “strongly agree” to “strongly disagree” scale

The questions on a survey asked:

• Do you actively participate in a study group?
• Do you think the class is going too quickly?

For both, the responses are one of the following: strongly agree, agree, neutral, disagree, strongly disagree

So I want to analyze if there is a correlation between those who are in a study group and those who think the class is going to quickly.

So I have two columns in a data frame. The first column is labeled "group" and the second is "fast". I have converted the group variable into a numerical variable, like so: strongly agree = 5, agree = 4, neutral = 3, disagree = 2, strongly disagree = 1

So now I have a data frame with two columns, one full of numbers and the other still full of the original answers ("strongly agree", "agree", etc).

I have found the means of every option quickly, now I just need to see if there is a statistical significance, but I am clueless. How exactly should I calculate the p-value on this? I have tried several methods but the p-value seems wrong.

Sorry if this is easy stuff, I think I have made this way more complicated in my mind than it should be and I appreciate any help.

quickly <- CSExperiencesAllWithHeaders$CEQuickly groups <-CSExperiencesAllWithHeaders$CEStudyGroup

levels(groups) <- (c(levels(groups), 5, 4, 3, 2, 1))
groups[groups == "strongly agree"] <- 5
groups[groups == "agree"] <- 4
groups[groups == "neutral"] <- 3
groups[groups == "disagree"] <-2
groups[groups == "strongly disagree"] <- 1
groups[groups == ""] <- NA
groups[groups == "N/A"] <- NA
quickly[quickly == "N/A"] <- NA
quickly[quickly == ""] <- NA

groups <- factor(groups)
quickly <- factor(quickly)
analysis3 <- data.frame(groups,quickly)
analysis3 <- na.omit(analysis3)
analysis3$groups <- as.numeric(as.character(analysis3$groups))

sagree2 <- subset(analysis3, quickly  == "strongly agree")
agree2 <- subset(analysis3, quickly == "agree")
neutral2 <- subset(analysis3, quickly == "neutral")
disagree2 <- subset(analysis3, quickly == "disagree")
sdisagree2 <- subset(analysis3, quickly == "strongly disagree")

meansagree2 <- mean(sagree2$groups) meanagree2 <- mean(agree2$groups)
meanneutral2 <- mean(neutral2$groups) meandisagree2 <- mean(disagree2$groups)
meansdisagree2 <- mean(sdisagree2$groups) barplot(c(meansagree2, meanagree2, meanneutral2, meandisagree2, meansdisagree2), main = "Those Who Think Class is Too Quick: In Study Groups?", names.arg=c("Strongly Agree","Agree","Neutral","Disagree", "Strongly Disagree"), xlab = "Class too Quick?", ylab = "In a Study Group?")  all this code creates this data frame (I only took the top of the data frame since the real one is over 1000 columns):  groups quickly 1 5 'strongly disagree' 2 4 'strongly agree' 3 1 'disagree' 4 1 'disagree' 5 4 'strongly disagree' 6 2 'strongly disagree' 7 1 'neutral' 8 2 'disagree' 9 1 'strongly disagree' 10 2 'strongly disagree' 11 1 'strongly disagree' 12 2 'neutral' 13 5 'disagree' 14 2 'disagree' 15 4 'neutral' 16 2 'disagree' 17 5 'disagree' 18 5 'neutral' 19 4 'strongly disagree' 20 2 'strongly disagree' 21 3 'disagree' 22 1 'strongly disagree' 23 4 'strongly agree' 24 1 'strongly disagree' 26 5 'strongly disagree' 27 1 'strongly disagree' 28 5 'disagree' 29 5 'agree'  This is what I get when I use the dput function: structure(list(groups = c(5, 4, 1, 1, 4, 2, 1, 2, 1, 2, 1, 2, 5, 2, 4, 2, 5, 5, 4, 2, 3, 1, 4, 1, 5, 1, 5, 5, 5, 5), quickly = structure(c(5L, 4L, 2L, 2L, 5L, 5L, 3L, 2L, 5L, 5L, 5L, 3L, 2L, 2L, 3L, 2L, 2L, 3L, 5L, 5L, 2L, 5L, 4L, 5L, 5L, 5L, 2L, 1L, 2L, 3L), .Label = c("agree", "disagree", "neutral", "strongly agree", "strongly disagree"), class = "factor"), qui_fact = structure(c(5L, 1L, 4L, 4L, 5L, 5L, 3L, 4L, 5L, 5L, 5L, 3L, 4L, 4L, 3L, 4L, 4L, 3L, 5L, 5L, 4L, 5L, 1L, 5L, 5L, 5L, 4L, 2L, 4L, 3L), .Label = c("strongly agree", "agree", "neutral", "disagree", "strongly disagree"), class = "factor"), qui_num = c(5, 1, 4, 4, 5, 5, 3, 4, 5, 5, 5, 3, 4, 4, 3, 4, 4, 3, 5, 5, 4, 5, 1, 5, 5, 5, 4, 2, 4, 3)), .Names = c("groups", "quickly", "qui_fact", "qui_num"), na.action = structure(c(25L, 31L, 37L, 38L, 86L, 91L, 148L, 209L, 270L, 280L, 285L, 328L, 338L, 340L, 410L, 424L, 456L, 460L, 461L, 480L, 568L, 587L, 593L, 596L, 599L, 600L, 607L, 621L, 658L, 700L, 717L, 731L, 758L, 776L, 827L, 837L, 849L, 862L, 864L, 896L, 899L, 909L, 921L, 946L, 963L, 966L, 977L, 994L, 1007L, 1012L, 1074L, 1079L), .Names = c("25", "31", "37", "38", "86", "91", "148", "209", "270", "280", "285", "328", "338", "340", "410", "424", "456", "460", "461", "480", "568", "587", "593", "596", "599", "600", "607", "621", "658", "700", "717", "731", "758", "776", "827", "837", "849", "862", "864", "896", "899", "909", "921", "946", "963", "966", "977", "994", "1007", "1012", "1074", "1079"), class = "omit"), row.names = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L, 26L, 27L, 28L, 29L, 30L, 32L), class = "data.frame") • It occurs to me, you've set specific types here. Those numbers are supposed to be factors. You should probably enter dput(theDataFrame[1:30,] in R and paste the result into your question. That way people writing answers will have exactly what you have. After that, the only code you need to include here is what you've tried for correlations. – John Aug 26, 2013 at 6:46 ## 1 Answer As you have ordinal factors, means are not so useful. You could use a$\chi^2$test and/or Spearman correlation to find if the two values are correlated. Commands: chisq.test(analysis3$groups,analysis3$quickly) , and after converting your "quickly" strings to factors, reordering and extracting the levels to a numeric vector, you can apply Spearman correlation: analysis3$qui_fact<- as.factor(analysis3$quickly) levels(analysis$qui_fact) #(alphabetical levels)

analysis$qui_fact<- factor(analysis$qui_fact,levels(analysis$qui_fact)[c(4,1,3,2,5)]) #reorder as needed analysis$qui_num<- as.numeric(analysis$qui_fact) cor.test(analysis$groups,analysis$qui_num,alt="two.sided",method="spearman",conf.level=.99) • If you're going to do a$\chi^2$estimate why not just use Cramer's$\phi$which looks and functions like a correlation but is the standardized effect size for$\chi^2$? An advantage of$\phi$is that it only requires the same assumptions going into the relationship as the$\chi^2$did in the first place and nothing additional like a Spearman correlation. – John Aug 26, 2013 at 15:18 • Actually, the data is ordinal, so an ordinal test is in place, and Spearman is. I believe that with a lot of ties, or as a test of correlation, Kendall's$\tau$correlation might be better, see here.$\chi^2$throws away the order of the variables, so can be tested to see if this order is relevant. Aug 26, 2013 at 18:02 • I'm not saying Spearman is not good for ordinals (but the amount of ties in the whole dataset will be quite large). It's true that$\chi^2$won't demonstrate the ordinal correlation but that will come out in the descriptives. Also, it wasn't clear until your comment why you were doing both$\chi^2\$ and Spearman.
– John
Aug 26, 2013 at 19:14