Statistics II

1. The Spearman
Rank Order
Correlation
Coefficient
Desmond Ayim-Aboagye,
PhD
Association between two ordinally
scaled variables

2. The Spearman is also Pearson r
formula to rank-ordered data
– The Spearman rank order correlation coefficient, is used to examine the nature
of association found between two ordinally scaled variables.
– It is symbolized rs (occasionally p, or “rho”).

3. Difference
– The Pearson r is ideal for
measuring associations that are
linear (e.g., as X increases in value,
a corresponding increase in Y
occurs)
– The Spearman rs, when the
relationship is not linear.

4. Actors Judge 1’s
Ranking
Judge 2’s
Ranking D(diff) D²
Adam
Bill
Cara
Deena
Ernesto
Fran
Gerald
Helen
1
2
3
4
5
6
7
8
3
1
2
5
4
7
8
6
-2
1
1
-1
1
-1
-1
2
4
1
1
1
1
1
1
4
∑ 36 36 ∑D = 0 ∑D² =14
Table 14.8 Calculating Spearman rs Using Ordinal Data

5. Formula for Spearman rs:
Rs = 1-
6∑𝐷²
𝑁(𝑁2−1)

6. Calculating
– Rs = 1-
6∑𝐷²
𝑁(𝑁2−1)
– Rs = 1-
6(14)
8[ 82−1 ]
– Rs = 1-
84
8(64−1)
– Rs = 1-
84
8(63)
– Rs = 1-
84
504
– Rs = 1- .1667
– Rs = .83.

7. Rejecting or accepting
Hypothesis
– Table B. 10 in Appendix B
– As usual we perform a two-tailed test at the 0.05 level
– So we read the row for N = 8 [sample size] and locate the critical value of .738
– Is the observed rs of .83 greater than or equal to the rs critical value of .738.
Yes we can reject the null hypothesis of no difference, or:
– rs (8) = .83 ≥ rs critical (8) = .738; Reject H0.