Hello Nitu,

No, not necessarily. Both correlations measure the strength of linear association. Pearson correlation measures strength of linear association between two sets of scores, whereas Spearman correlation measures strength of linear association between two sets of ranked scores. Both tend to be somewhat close, both in sign and magnitude, with many data sets.

In point of fact, a Spearman correlation is nothing but the Pearson formula applied to ranked data (this automatically adjusts for tied scores, which ordinarily is an additional worry when computing the Spearman correlation using the traditional textbook formula).

Here's an example of when the two methods will diverge in magnitude.

Let X = 1..10 (e.g., 10 cases, having values 1, 2, ... 10)

Let Y = 1..10.

Rp = Rs = 1.0

Now, let Y = X^3

Rp = .928, Rs = 1.000

Now, let Y = X^5

Rp = .839

Rs = 1.000

The more the plot of X and Y values diverges from linear in form (even though the rank order between X and Y remains unchanged), the greater the disparity in magnitude between the two types of correlations. More generally, the greater the difference in distributional shapes of X and Y, the more likely it is that computed values of Rs and Rp will differ.

Good luck with your work!

Thank you sir for your detailed explanation. Sir my data was based on likert scales ( affective construct like temper, anxiety, motivation, emotional stability)which was correlated with achievement scores. I want to ask you two more questions that can the data obtained from likert scales in educational setting should be always treated as ordinal level data or there are means to get it qualified to interval level even? Second at ordinal level measurement also there are instances when parametric statistics has been applied for e.g in attitude scales. Is it totally a wrong procedure. Thank you sir

Thank you very much Prof David Morse for the detailed explanation.

Hello again Nitu,

To answer your additional questions:

1. Purists would say "yes," pragmatists would say "not necessarily."

2. Yes, plenty of published examples exist.

However, do recall that Rensis Likert's work made two very important points. First, his choice of successive integers as score values (e.g., 1, 2, ... k where k is the number of response options) was because it was far easier to apply this method of quantification than were the more intensive (for the time) scaling methods available. Further, he found that the supposedly more exact scaled score values correlated at about the mid-.90s with the successive integer values.

Second, Likert was concerned with using the summed score across multiple items having to do with the same target concept/construct/phenomenon, and not with individual scores from individual items. Since then, some folks have taken the perspective that these summated scores tend to behave a lot more like continuous/metric variable measures than discrete/ordinal variable measures.

Good luck with your work!

Reference: Likert, R. (1932). A technique for the measurement of attitudes. Archives of Psychology, 22(140), 1-55.

Thank You so much Sir once again for another detailed answer.