Hobbies And Interests
Spearman's Rho
Spearman's rho (the Greek letter) assumes only that the variables are ordinal scaled. Ordinal scaling means the numbers given for each variable are in the right order, but not necessarily equally spaced. For example, if you ask people how much they like President Obama and the choices were "Not at all," "A little bit," "Somewhat," "Pretty much," and "A great deal" and these choices were scored 1, 2, 3, 4 and 5, then the numbers are in the right order, but it's hard to say if the difference between "not at all" and "a little bit" is the same as the difference between "Pretty much" and "A great deal." To calculate Spearman's R, rank the data and compute the usual correlation between the ranks.
Kendall's Tau
Kendall's tau (the Greek letter) also assumes the data is ordinal, but it has a different meaning than Spearman's R. To understand Kendall's tau, you must first understand concordant and discordant pairs. A pair is any two subjects in the data set, for example, if you're dealing with people, a pair could be Bob and Joe. A pair of values is concordant if the subject who's higher on one variable is also higher on the other. A pair is discordant if the subject who's higher on one variable is lower on the other. Kendall's tau can be computed as (C-D)/(n*n-1/2), where C is the number of concordant pairs, D is the number of discordant pairs and n is the number of subjects.
Goodman-Kruskal Gamma
Goodman-Kruskal's gamma (the Greek letter) also assumes ordinal data. It's computed as (C-D)/(C+D) where C and D have the same meaning as in Section 2. Gamma is more appropriate when there are many tied observations. It's also somewhat easier to understand.
Chi-Square
Chi-square assumes only that data is nominal, which has no inherent order. For example, if you ask people about their ethnic group, and the choices are "White," "Black," "Latino," "Asian," and "Other," then there's no order to the responses. For this reason, some would say that Chi-square isn't really a measure of correlation, but it's certainly a measure of the relationship between two variables. To calculate Chi-square, the data must be in a contingency table. Label the rows and columns with numbers, then calculate the expected value in each cell (the row total times the column total divided by the grand total). Then, find the differences between the observed and expected frequencies in each cell, square them, divide them by the observed frequencies, and add all the quotients. Unlike the other measures, Chi-square can take on any positive number.