Spearman Rank Correlation Calculator

Spearman Rank Correlation is evaluated from X1, Y1 and X2. The calculation reports Spearman rs, Number of Pairs and Interpretation.

Results

Thanks — we’ve logged this for review.

About the Spearman Rank Correlation Calculator

Spearman Rank Correlation is treated here as a quantitative relation between X1, Y1, X2 and Y2 and Spearman rs, Number of Pairs and Interpretation.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
2. Compute d = rank(X) - rank(Y) for each pair
3. rs = 1 - (6Sigmad^2) / (n(n^2-1))

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

2. Compute d = rank(X) - rank(Y) for each pair
3. rs = 1 - (6Sigmad^2) / (n(n^2-1))

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Income rank vs. happiness rank: 5 respondents

Inputs

x1: 1 y1: 2 x2: 2 y2: 3 x3: 3 y3: 1 x4: 4 y4: 5 x5: 5 y5: 4
Spearman rs: 0.9515. Number of Pairs: 10. Interpretation: Very strong positive correlation

With X1 = 1, Y1 = 2, X2 = 2 and Y2 = 3 as the stated inputs, the result is Spearman rs = 0.9515, Number of Pairs = 10 and Interpretation = Very strong positive correlation. Each value corresponds to the declared output fields.

Example 2: Study hours rank vs. grade rank: 7 students

Inputs

x1: 1 y1: 2 x2: 3 y2: 1 x3: 2 y3: 3 x4: 6 y4: 5 x5: 5 y5: 6 x6: 4 y6: 4 x7: 7 y7: 7
Spearman rs: 0.9515. Number of Pairs: 10. Interpretation: Very strong positive correlation

With X1 = 1, Y1 = 2, X2 = 3 and Y2 = 1 as the stated inputs, the result is Spearman rs = 0.9515, Number of Pairs = 10 and Interpretation = Very strong positive correlation. Each value corresponds to the declared output fields.

Example 3: Customer wait time rank vs. satisfaction rank: 8 customers

Inputs

x1: 8 y1: 1 x2: 6 y2: 3 x3: 7 y3: 2 x4: 4 y4: 5 x5: 5 y5: 4 x6: 2 y6: 6 x7: 3 y7: 7 x8: 1 y8: 8
Spearman rs: -0.0061. Number of Pairs: 10. Interpretation: Very weak or no correlation

With X1 = 8, Y1 = 1, X2 = 6 and Y2 = 3 as the stated inputs, the result is Spearman rs = -0.0061, Number of Pairs = 10 and Interpretation = Very weak or no correlation. Each value corresponds to the declared output fields.

Example 4: City rank by cost of living vs. rank by quality of life: 6 cities

Inputs

x1: 6 y1: 2 x2: 5 y2: 1 x3: 4 y3: 4 x4: 3 y4: 3 x5: 2 y5: 5 x6: 1 y6: 6
Spearman rs: 0.6. Number of Pairs: 10. Interpretation: Moderate positive correlation

With X1 = 6, Y1 = 2, X2 = 5 and Y2 = 1 as the stated inputs, the result is Spearman rs = 0.6, Number of Pairs = 10 and Interpretation = Moderate positive correlation. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate rank correlation for ordinal or non-normal data
  • Non-parametric alternative to Pearson r
  • Measure monotonic relationships with outliers