Friedman Test Calculator — Repeated Measures

The Friedman Test. The same subjects can experience several treatments while differing greatly in their raw levels. The Friedman test keeps each subject as a block and compares treatment orderings. Block alignment is the design. Row i in every treatment field must describe the same subject or matched set, with one comparable observation under every condition. Rank treatments separately inside each block from one through k. Never pool values across subjects, because a new rank scale begins on every row. Equal treatment values inside one block share their average rank. These midranks avoid arbitrary winners, while the tied group also enters the correction register. Sum each treatment's within-block ranks down its column. Dividing by the block count gives mean ranks that reveal which treatments repeatedly sit low or high. The uncorrected Q statistic increases as treatment rank sums separate. It scales the squared column sums and subtracts the common no-effect rank baseline. Ties reduce available ordering information. Divide Q by the standard tie factor; if every block is completely tied, that factor is zero and inference stops.

This page compares Q with the upper tail of a chi square distribution using treatment count minus one degrees of freedom. Larger Q is stronger evidence. That chi square reference is approximate. Fewer than ten blocks trigger a warning, but the calculator never switches automatically to exact tables or permutation inference. The omnibus null says there is no systematic treatment effect after blocking. Rejection means at least one treatment rank pattern differs, not that every pair differs. Blocks must be independent of one another. Observations within a block are intentionally related, but households, clusters, or repeated blocks need a design that represents that dependence. Meaningful within-block ordering is enough. Normality and equal raw spacing are not required, yet treatments must still be comparable inside every block. Adding the same constant to every treatment inside one block changes raw levels but not ranks. Between-block scale differences therefore cancel from the test. Kendall W equals Q divided by block count times treatment count minus one. It is a unitless rank-agreement effect, not raw variance explained or a confidence interval.

Now follow six blocks under three treatments at alpha point zero five. Five blocks rank treatment one highest, while the final block contains one tie. Rank each row independently. The first five rows use ordinary ranks, and block six gives treatments one and two the shared midrank one point five. That two-way tie contributes six to the tie register. The correction is one minus six over one hundred forty-four, or zero point nine five eight three. Treatment rank sums are sixteen point five, eight point five, and eleven. Their mean ranks are two point seven five, one point four two, and one point eight three. The uncorrected statistic is five point five eight three. After tie correction, Q is five point eight two six with two degrees of freedom. The upper-tail p-value is zero point zero five four three, narrowly above alpha. Fail to reject, while Kendall W is zero point four eight six and the small-block warning remains. This is not proof that all treatments are equivalent. The page provides no post hoc rows, so pairwise claims need separate paired tests and explicit multiplicity control.

For contrast, six blocks with the same treatment order every time give Q equal to twelve, p equal to zero point zero zero two four eight, and W equal to one. Lift one subject's three raw values by one hundred. Its within-block ranks stay one, three, and two, so every Friedman result remains unchanged. Partial and complete row ties both receive midranks. In this diagnostic, the tie factor is zero point six eight seven five and Q becomes zero point five four five. Validation requires three to twelve treatments, at least two aligned blocks, and equal field lengths. If every row is tied, the calculator stops instead of reporting zero evidence. A significant omnibus still names no pair. Use a preplanned paired follow up with multiplicity adjustment, and never manufacture post hoc rows the page does not calculate. Report block and treatment counts, alignment, within-block midranks, tie correction, Q, degrees of freedom, chi square approximation, p, alpha, warning, and Kendall W. Turn repeated measurements into one honest blocked rank comparison, preserve every subject row, and run the Friedman Test calculator free at Distri Scope dot com.