Measures the strength of a monotonic (not necessarily linear) relationship - and is used when data are ranked or not normally distributed.
In short: Spearman's rank correlation coefficient measures how well the ranks of two variables agree, so it suits relationships that are consistently increasing or decreasing but not necessarily linear. Rank each data set, enter the ranks in two lists and run linear regression on them. The value of r for the ranks is Spearman's coefficient.
When you'd use this
Data are given as ranks rather than raw numbers, e.g. judges' placings.
The relationship looks monotonic (consistently increasing or decreasing) but not necessarily a straight line.
The raw data has an outlier that would distort a normal (Pearson) correlation coefficient.
A question specifically asks for Spearman's r_s rather than Pearson's r.
At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared
TI-84 Plus CE
Casio fx-CG50 and fx-CG100
TI-Nspire CX
Key sequence
STAT → CALC → 4:LinReg(ax+b) on the two rank lists; the r value is rₛ (Spearman's rank correlation).
Enter rank lists, then CALC → REG → X → linear regression; the displayed r is rₛ.
Run Linear Regression (menu → Statistics → Stat Calculations → Linear Regression) on the two rank lists; r = rₛ.
On a TI-84 Plus CE
Rank each data set from 1 (smallest) to n (largest). For tied values, assign the mean of the tied ranks.
The GDC does not have a dedicated Spearman button - use the linear regression r on the RANKS instead of the raw data.
Enter the ranks of x in one list and the ranks of y in another list.
STAT → CALC → 4:LinReg(ax+b) on the two rank lists; the r value is rₛ (Spearman's rank correlation).
Alternatively, compute rₛ = 1 − (6 Σd²) / (n(n²−1)) by hand, where d = difference in ranks.
Tip: rₛ = ±1 means a perfect monotonic relationship; rₛ = 0 means no monotonic trend. Unlike Pearson r, Spearman is not thrown off by outliers or a non-linear but still monotonic pattern.
On a Casio fx-CG50 and fx-CG100
Rank each data set from 1 (smallest) to n (largest). For tied values, assign the mean of the tied ranks.
The GDC does not have a dedicated Spearman button - use the linear regression r on the RANKS instead of the raw data.
Enter the ranks of x in one list and the ranks of y in another list.
Enter rank lists, then CALC → REG → X → linear regression; the displayed r is rₛ.
Alternatively, compute rₛ = 1 − (6 Σd²) / (n(n²−1)) by hand, where d = difference in ranks.
Tip: rₛ = ±1 means a perfect monotonic relationship; rₛ = 0 means no monotonic trend. Unlike Pearson r, Spearman is not thrown off by outliers or a non-linear but still monotonic pattern.
On a TI-Nspire CX
Rank each data set from 1 (smallest) to n (largest). For tied values, assign the mean of the tied ranks.
The GDC does not have a dedicated Spearman button - use the linear regression r on the RANKS instead of the raw data.
Enter the ranks of x in one list and the ranks of y in another list.
Run Linear Regression (menu → Statistics → Stat Calculations → Linear Regression) on the two rank lists; r = rₛ.
Alternatively, compute rₛ = 1 − (6 Σd²) / (n(n²−1)) by hand, where d = difference in ranks.
Tip: rₛ = ±1 means a perfect monotonic relationship; rₛ = 0 means no monotonic trend. Unlike Pearson r, Spearman is not thrown off by outliers or a non-linear but still monotonic pattern.
Here's a real IB-style question that uses exactly this technique.
MediumCalculatorPaper 2[3 marks]
Two judges rank 5 competitors. Judge A's ranks are 1, 2, 3, 4, 5 and Judge B's ranks for the same competitors are 2, 1, 4, 3, 5. Find Spearman's rank correlation coefficient.
r_s = 0.8
Mark it
Correct3 / 3 marks
Worked solution & mark scheme:
M1 Find d for each pair and square it
A1 r_s = 0.8
Common questions
When would I need to find Spearman's rank correlation coefficient in IB Maths?
Measures the strength of a monotonic (not necessarily linear) relationship - and is used when data are ranked or not normally distributed. Data are given as ranks rather than raw numbers, e.g. judges' placings. The relationship looks monotonic (consistently increasing or decreasing) but not necessarily a straight line.
How do I find Spearman's rank correlation coefficient on a TI-84 Plus CE?
1. Rank each data set from 1 (smallest) to n (largest). For tied values, assign the mean of the tied ranks. 2. The GDC does not have a dedicated Spearman button - use the linear regression r on the RANKS instead of the raw data. 3. Enter the ranks of x in one list and the ranks of y in another list. 4. STAT → CALC → 4:LinReg(ax+b) on the two rank lists; the r value is rₛ (Spearman's rank correlation). 5. Alternatively, compute rₛ = 1 − (6 Σd²) / (n(n²−1)) by hand, where d = difference in ranks.
How do I find Spearman's rank correlation coefficient on a Casio fx-CG50 and fx-CG100?
1. Rank each data set from 1 (smallest) to n (largest). For tied values, assign the mean of the tied ranks. 2. The GDC does not have a dedicated Spearman button - use the linear regression r on the RANKS instead of the raw data. 3. Enter the ranks of x in one list and the ranks of y in another list. 4. Enter rank lists, then CALC → REG → X → linear regression; the displayed r is rₛ. 5. Alternatively, compute rₛ = 1 − (6 Σd²) / (n(n²−1)) by hand, where d = difference in ranks.
How do I find Spearman's rank correlation coefficient on a TI-Nspire CX?
1. Rank each data set from 1 (smallest) to n (largest). For tied values, assign the mean of the tied ranks. 2. The GDC does not have a dedicated Spearman button - use the linear regression r on the RANKS instead of the raw data. 3. Enter the ranks of x in one list and the ranks of y in another list. 4. Run Linear Regression (menu → Statistics → Stat Calculations → Linear Regression) on the two rank lists; r = rₛ. 5. Alternatively, compute rₛ = 1 − (6 Σd²) / (n(n²−1)) by hand, where d = difference in ranks.
What should I watch out for when I find Spearman's rank correlation coefficient?
rₛ = ±1 means a perfect monotonic relationship; rₛ = 0 means no monotonic trend. Unlike Pearson r, Spearman is not thrown off by outliers or a non-linear but still monotonic pattern.
How are marks awarded when I find Spearman's rank correlation coefficient in an IB exam?
In the worked example on this page (3 marks, Paper 2), the marks are: M1: Find d for each pair and square it; A1: r_s = 0.8.
