Median of Pairwise Slopes Calculator
Calculates the Theil–Sen median of nonvertical pairwise slopes for paired data. The worked condition keeps the method and source values visible for an independent check.
Enter the source values during an independent check
Median pairwise slope
The quantity this page defines in the worked condition
Calculates the Theil–Sen median of nonvertical pairwise slopes for paired data. The displayed relationship is median((yj−yi)/(xj−xi)), and each symbol is tied to a labeled field. The page-specific quantity is median pairwise slope.
The example has a median pairwise slope of approximately 1.0625. This example is a numerical check, not proof that the model describes every dataset. The chosen median pairwise slope convention remains attached to the source record. Before reusing this result, write down the observed scale, model boundary, and convention behind the displayed value. That record separates a changed dataset from a changed definition and gives the next analyst a clear route back to the original calculation.
A related measure is hodges lehmann location.
Where the method applies before reporting
Pairs with equal X are omitted; the robust slope resists a single response outlier but does not establish a causal trend. The page-specific quantity is median pairwise slope.
The unit of analysis, time order, sample boundary, and treatment of ties or missing values remain outside the answer unless they are entered. Keep those choices beside this robust result. The chosen median pairwise slope convention remains attached to the source record. Before reusing this result, write down the observed scale, model boundary, and convention behind the displayed value. That record separates a changed dataset from a changed definition and gives the next analyst a clear route back to the original calculation.
Keeping a reproducible record under the stated model
Check scales and domains before evaluating median of pairwise slopes. Counts, probabilities, rates, windows, and squared units are not interchangeable merely because a field accepts a number.
If one input changes, predict the direction of the result from the formula first. That catches reversed groups, invalid windows, and parameterization errors. The chosen median pairwise slope convention remains attached to the source record.
What the statistic can support when the sample changes
Recalculate one intermediate quantity from median((yj−yi)/(xj−xi)) and work back from the displayed answer. The source values should be enough for another analyst to reproduce median of pairwise slopes.
Use a boundary case when possible: equal values, a probability near zero, a window of two, or a rate of zero. Expected limiting behavior is often more informative than another decimal place. The chosen median pairwise slope convention remains attached to the source record.
The reference quantity during an independent review
The number answers one statistical question. It does not establish causation, model fit, representativeness, or a useful decision threshold by itself. The page-specific quantity is median pairwise slope.
Practical meaning depends on the measurement scale and consequences. State the comparison or benchmark before presenting median of pairwise slopes as evidence.
Evidence beside the calculation at the chosen parameters
Pairs with equal X are omitted; the robust slope resists a single response outlier but does not establish a causal trend. Outliers, dependence, extrapolation, seasonality, or a mismatched convention can change the appropriate method. The page-specific quantity is median pairwise slope.
Choose an alternative because the design or data require it, not because its result is more favorable. Preserve the selected convention in the report. The chosen median pairwise slope convention remains attached to the source record.
Questions about the method before reporting
For this result, what should be checked before reusing this result?
Keep the inputs, units, method name, exclusions, and unrounded output together. The reported quantity here is median pairwise slope.
When inputs change, why might another program return a different number?
Parameterization, interpolation, tie rules, window placement, and rounding can differ. The reported quantity here is median pairwise slope.