Nonparametric Tests

Jonckheere-Terpstra Test Table: Exact Critical Values of J

Exact critical values for the Jonckheere-Terpstra test for an ordered trend across groups, such as increasing dose.

k = 3 to 6 groups
Exact values
Unequal sizes in calculator

Jonckheere-Terpstra Table

Jump to a value of k below. Rows: subjects per group · Columns: one-tailed α · Cells: critical J. Reject H₀ if J ≥ the cell.

k = 3 groups

k = 3 groups
One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	10	11	12	—	—	—
3	20	22	23	25	25	27
4	34	36	38	40	42	45
5	51	54	57	60	62	66
6	71	75	79	83	86	92
7	95	100	105	110	114	121
8	121	128	134	140	145	154
9	152	160	166	174	180	190
10	185	194	202	212	218	230

k = 4 groups

k = 4 groups
One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	18	19	21	22	23	24
3	37	40	42	44	45	48
4	63	67	70	73	76	81
5	95	100	105	110	114	120
6	134	141	147	154	158	167
7	179	188	196	204	210	222
8	231	242	251	262	269	283
9	290	302	313	326	334	351
10	354	369	382	397	407	427

k = 5 groups

k = 5 groups
One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	28	30	32	33	35	37
3	59	62	65	69	71	75
4	100	106	110	116	119	126
5	153	160	167	174	179	189
6	216	226	235	244	251	264
7	290	303	313	325	334	350
8	375	390	403	418	428	449
9	470	488	504	522	534	558
10	576	597	615	636	650	679

k = 6 groups

k = 6 groups
One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	40	43	45	47	49	52
3	85	90	94	98	101	107
4	147	154	160	167	171	181
5	224	234	242	252	259	272
6	317	330	342	354	363	381
7	427	443	457	474	484	507
8	552	572	589	609	623	650
9	693	717	738	761	777	810
10	850	878	902	930	949	987

Tip: click any value to highlight its row and column.

How to read this table

Order the groups by the hypothesised trend (for example placebo, low, middle, high dose).
For every pair of groups i < j, count the pairs of observations where the value in the later group is larger (ties count ½). J is the sum of these counts.
Reject H₀ in favour of an increasing trend if J is greater than or equal to the table value. For unequal group sizes, use the calculator.

Worked example

A study gives placebo, low dose and high dose to 5 patients each, and the counts of increasing pairs sum to J = 56. In the k = 3 table, row 5, α = 0.05 gives 54, so there is a significant increasing trend at the 5% level.

Click the underlined links to highlight the value in the table.

Calculator

For values between the rows and columns of the table. Results update as you type.

Formula and how the values were computed

J = Σ_i<j U_ij · E(J) = (N² − Σnᵢ²)/4 · Var(J) = (N²(2N + 3) − Σnᵢ²(2nᵢ + 3))/72

Under H₀ the J statistic is distributed as a sum of independent Mann-Whitney statistics, and its exact distribution is the normalised q-multinomial coefficient, computed exactly. Each entry is the smallest J with P(J ≥ j) ≤ α.

Frequently asked questions

Why not just use Kruskal-Wallis?

Kruskal-Wallis tests for any difference and ignores the order of the groups. When the alternative is a monotone trend, Jonckheere-Terpstra is considerably more powerful.

Is this a test of dose-response?

Yes, it is a common nonparametric test of a monotone dose-response. For binary outcomes the Cochran-Armitage trend test plays the same role.

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	10	11	12	—	—	—
3	20	22	23	25	25	27
4	34	36	38	40	42	45
5	51	54	57	60	62	66
6	71	75	79	83	86	92
7	95	100	105	110	114	121
8	121	128	134	140	145	154
9	152	160	166	174	180	190
10	185	194	202	212	218	230

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	18	19	21	22	23	24
3	37	40	42	44	45	48
4	63	67	70	73	76	81
5	95	100	105	110	114	120
6	134	141	147	154	158	167
7	179	188	196	204	210	222
8	231	242	251	262	269	283
9	290	302	313	326	334	351
10	354	369	382	397	407	427

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	28	30	32	33	35	37
3	59	62	65	69	71	75
4	100	106	110	116	119	126
5	153	160	167	174	179	189
6	216	226	235	244	251	264
7	290	303	313	325	334	350
8	375	390	403	418	428	449
9	470	488	504	522	534	558
10	576	597	615	636	650	679

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	40	43	45	47	49	52
3	85	90	94	98	101	107
4	147	154	160	167	171	181
5	224	234	242	252	259	272
6	317	330	342	354	363	381
7	427	443	457	474	484	507
8	552	572	589	609	623	650
9	693	717	738	761	777	810
10	850	878	902	930	949	987

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	10	11	12	—	—	—
3	20	22	23	25	25	27
4	34	36	38	40	42	45
5	51	54	57	60	62	66
6	71	75	79	83	86	92
7	95	100	105	110	114	121
8	121	128	134	140	145	154
9	152	160	166	174	180	190
10	185	194	202	212	218	230

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	18	19	21	22	23	24
3	37	40	42	44	45	48
4	63	67	70	73	76	81
5	95	100	105	110	114	120
6	134	141	147	154	158	167
7	179	188	196	204	210	222
8	231	242	251	262	269	283
9	290	302	313	326	334	351
10	354	369	382	397	407	427

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	28	30	32	33	35	37
3	59	62	65	69	71	75
4	100	106	110	116	119	126
5	153	160	167	174	179	189
6	216	226	235	244	251	264
7	290	303	313	325	334	350
8	375	390	403	418	428	449
9	470	488	504	522	534	558
10	576	597	615	636	650	679

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	40	43	45	47	49	52
3	85	90	94	98	101	107
4	147	154	160	167	171	181
5	224	234	242	252	259	272
6	317	330	342	354	363	381
7	427	443	457	474	484	507
8	552	572	589	609	623	650
9	693	717	738	761	777	810
10	850	878	902	930	949	987

Jonckheere-Terpstra Test Table: Exact Critical Values of J

Jonckheere-Terpstra Table

k = 3 groups

k = 4 groups

k = 5 groups

k = 6 groups

How to read this table

Worked example

Calculator

Formula and how the values were computed

Frequently asked questions

Related calculators and tutorials

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	10	11	12	—	—	—
3	20	22	23	25	25	27
4	34	36	38	40	42	45
5	51	54	57	60	62	66
6	71	75	79	83	86	92
7	95	100	105	110	114	121
8	121	128	134	140	145	154
9	152	160	166	174	180	190
10	185	194	202	212	218	230

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	18	19	21	22	23	24
3	37	40	42	44	45	48
4	63	67	70	73	76	81
5	95	100	105	110	114	120
6	134	141	147	154	158	167
7	179	188	196	204	210	222
8	231	242	251	262	269	283
9	290	302	313	326	334	351
10	354	369	382	397	407	427

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	28	30	32	33	35	37
3	59	62	65	69	71	75
4	100	106	110	116	119	126
5	153	160	167	174	179	189
6	216	226	235	244	251	264
7	290	303	313	325	334	350
8	375	390	403	418	428	449
9	470	488	504	522	534	558
10	576	597	615	636	650	679

One-tailed α → n per group ↓	0.1	0.05	0.025	0.01	0.005	0.001
2	40	43	45	47	49	52
3	85	90	94	98	101	107
4	147	154	160	167	171	181
5	224	234	242	252	259	272
6	317	330	342	354	363	381
7	427	443	457	474	484	507
8	552	572	589	609	623	650
9	693	717	738	761	777	810
10	850	878	902	930	949	987