Historical perspective

This page provides only a quick summary to provide context for discussions regarding equivalence.

In the 19th Century, Fisher developed the idea of Type I Error, based on the Normal Distribution, thus allows a probability estimate for whether the null hypothesis can be rejected. This allows decisions to be made in science and industry on whether a new product or process is better or worse than the current ones available. However, if the null hypothesis cannot be rejected, the researcher cannot draw any statistical conclusion, as a failure to reject null is not the same as an ability to accept null.

A generation later, Pearson added the idea of Type II Error and the statistical significance, so that both the ability to reject and accept the null hypothesis can be made. Although this method was widely used in the twentieth century, it was increasingly criticised because results of research are often nor reproducible because of difficulties in determining the population Standard Deviation.

To provide robustness to statistical conclusions, researchers increasingly used the 95% confidence interval of the difference, which is an intuitively easier to understand expression of the Type I Error, and to carry out power analysis, which makes no assumption about population parameters. The combination of these two approaches allows researchers to draw confident conclusions whether two sets of observations can be considered significantly different. However, the problem remains that a failure to demonstrate significant difference is not the same as to demonstrate similarity, and the ability to robustly demonstrate similarity is increasingly required, particularly in biomedical research.

An example is in cancer treatment. The current treatment may have severe side effects, and a new treatment may have much more acceptable side effects, but the researcher needs to know whether the effectiveness in controlling the cancer is the same, or at least not inferior to the current treatment.

The concept of equivalence

Given the random variations inherent in any set of observations, it is very unlikely to demonstrate two groups to have the same mean values. The term equivalence is therefore used to represent similarity. This is dependent on a pre-determined and arbitrarily assigned Critical Difference (CD) or Tolerance Limit (TL), a difference that can be considered as trivial in the practical sense. Using the 95% confidence interval of the difference to illustrate, the various conclusions that can be drawn are as shown in the diagram (Forest Plot) to the right. Assuming that the difference is that between group 1 and 2 (diff = mean₁ - mean₂)

• If the 95% CI does not intercept the null value, as shown in the 1^st and the 5^th lines in the diagram, then a significant difference exists. This is true whether the 95% CI is calculated using the one or two tail models.
• If the 95% CI is on the left (diff<null), intercepts the null, but does not intercept the positive Critical Difference (CD) value, as shown in the 2^nd line in the diagram, then group 1 is significantly not greater than group 2. This is true whether the 95% CI is calculated using the one or two tail models.
• If the 95% CI is on the right (diff>null), intercepts the null, but does not intercept the negative Critical Difference (CD) value, as shown in the 4^th line in the diagram, then group 1 is significantly not less than group 2. This is true whether the 95% CI is calculated using the one or two tail models.
• If the 95% CI is near the center, intercepts the null, but does not intercept either the negative positive Critical Difference (CD) value, as shown in the 3^rd line in the diagram, then the two groups is significantly equivalent. This is only true if the 95% CI is calculated using the two tail models.
• If the 95% CI intercepts both negative and positive Critical Difference values, as shown in the 6^th line in the diagram, then the data lack sufficient power to drawn statistical conclusions, usually because the variance is too large or the sample size not big enough. This is true whether the 95% CI is calculated using the one or two tail models.

One tail or two tail In most text books and published papers, statistics related to equivalence uses the one tail model. This is because most equivalence related research are concerned with non-inferiority, so that not significantly greater or not significantly less are the hypotheses to be tested. As the one tail model allows these conclusions and requires smaller sample size, this is the model to use. StatsToDo however provides calculations for both one and two tails in case any user requires them.

Sample size and power calculation

Sample size and power calculations for equivalence differ from those of significant differences in two ways.

Firstly, the decision is based not only on the relationship between the difference between the two groups and the null value, but also the positive and negative critical values.

Secondly, robustness is required for the conclusion of significant equivalence and not on significant difference. The Probability of Type I Error (α) is therefore relaxed, and the common values of 0.1 or 0.2 are used instead of 0.05 or 0.01. The Probability of Type II Error, in terms of power, is made more strict, so the power value of 0.9, 0.95, or 0.99 are used instead of 0.8

Statistical Decisions

Users should remember that good statistical practice requires that the hypothesis to be tested is defined at the planning stage, and statistical procedures are used to reject or support that hypothesis. A common malpractice of doing the statistical calculations first, then cherry pick the hypothesis according to how the numbers come together should be avoided. A study to test significant difference or equivalence, the direction of non-inferiority, whether the model should be one or two tail, must be determined at the planning stage before data collection and analysis.

Equivalence Between 2 Proportions

For equivalence to be validly established, the correct sample size must be estimated and used, and this requires 5 parameters.

• Probability of Type I Error (α). For equivalence, the value of 0.05 most commonly used, to be compatible with the 95% confidence interval. α of 0.1 and 0.2 are occasionally used in association with 90% and 80% confidence intervals of the difference.
• Power (1 - β). For equivalence, the value of 0.95 or 0.99 are often used
• The expected proportion around which the two proportions are to be compared.
• Critical Difference, the tolerated limit of difference, a difference in proportions which the researcher considers to be within measurement error or small enough to be trivial
• Ratio of sample sizes (φ = n_group2 / n_group1) to be used. In most clinical research the groups are of equal size (φ=1), but availability or clinical priority may require groups of unequal size. Please note the φ is calculated as n_group2 / n_group1).

From these parameters, the program calculates the sample size for each of the two groups, in the one and two tail models. For most non-inferiority studies, the sample size for the one tail model is used.

The two tail model is only required if the purpose of the study is to establish true equivalence, a confidence interval that is both significantly not less than the negative Critical Difference value, and significantly not greater than the positive Critical Difference value.

Analysis of data collected Once the data is collected, analysis requires the following information

• The numbers with positive and negative attributes in the two groups being compared
• The Probability of Type I Error (α) for calculations of confidence intervals and power estimation
• Critical Difference, the tolerated limit of difference, a difference in proportion which the researcher considers to be within measurement error or small enough to be trivial. This is also to be used for power estimation

The program summarizes the data

• The proportion with positive attributes in the two groups Prop = Pos / (Pos + Neg)
• The Difference in proportion between the two groups Diff = Prop₁ - Prop₂
• The Standard Error of the difference

The program then produce two analysis

• The confidence interval of the difference. 80% CI is presented if α=0.2, 90% CI if α=0.1, 95% CI if α=0.1, 99% CI if α=0.01
  • If the hypothesis is that group 1 is not less than group 2, then the first confidence interval, difference - 1.64 x SE→+∞ should be used
  • If the hypothesis is that group 1 is not more than group 2, then the second confidence interval, -∞→difference + 1.64 x SE should be used
  • If the hypothesis is true equivalence, that group 1 in neither less nor more than group 2, then the two tail confidence interval should be used
• The power for equivalence estimation from the data
  • If the hypothesis is that group 1 is not less than group 2, then the first one tail power calculation, (Power1!<) should be used
  • If the hypothesis is that group 1 is not more than group 2, then the second one tail power calculation, (Power1!>) should be used
  • If the hypothesis is true equivalence, that group 1 in neither less nor more than group 2, then the two tail power calculation (Power2) should be used

Please note that the two calculations produces different results. In most cases they lead to the same conclusions, but with data on the margin of statistical significant, the difference may lead to different conclusions. The reasons are as follow.

The confidence interval is the same as that calculated for comparing the difference between two proportions. This is offered as it is the most common parameter for making statistical decisions, particularly that associated with the 95% confidence interval (α=0.05). Such a decision allows the interpretation for significant difference, significant non inferiority, and equivalence.

The power calculation is based on a difference calculated using the Maximum Likelihood Model. It estimates the probability of detecting the non-inferiority or equivalence at the level of α, if it is truly present.

Most clinicians would be content to use the 95% confidence interval to decide whether equivalence exists or not. Statisticians however may wish for more nuance to determine the confidence of the decision, and use the power analysis.

Example

Please note the data in this example are artificially created to demonstrate the statistical procedure, and not based on any observations.

The current chemotherapeutic agent for a particular cancer is fairly effective, with a 1 year recurrence rate of 20% (0.2). However it is rather toxic, producing unacceptable side effects such as marrow depression, infections, and severe nausea.

A new agent has been produced, which has very little side effect, so that it would obviously be preferable, providing the cure rate is non-inferior. In statistical terms, the 1 year recurrence rate for the new agent should be significantly not higher than the old agent.

Sample size calculation

With variations in observation, we feel that a 20% (0.2) difference in recurrence rate is tolerable statistically, that we accept that the new treatment is non-inferior if the recurrence rate is less than 40% (0.4), so we set our critical difference to 0.2. We will use α=0.05 to follow the convention of 95% confidence interval, and power (1-β) of 0.9.

We looked the table in the previous panel. For α=0.05, power=0.9, Proportion = 0.2, and CD=0.2, we require 71 cases per group, assuming equal size groups (&phi=1)

Analysis of data

We randomly allocated patients to receive the two agents. Group 1 receive the new agent, and group 2 the old. At the end of data collection, we obtained the following results.

	Group 1 (new)	Group 2 (old)
Positive (recurrence)	16	14
Negative (no recurrence)	55	57
Total	71	71

The results of analysis are as shown in the next table to the right.

The recurrence rate for group 1 (new agent) is 22.5% (0.225) and for group 2 (old agent) is 19.7% (0.197). The difference is 2.8% (0.028). As the hypothesis to be tested is whether the new agent is non-inferior to old agent, so we choose the 95% confidence interval for one tail -∞→14.1% (0.141), which does not cross the positive Critical difference of 20%. We can therefore conclude that group 1 is significantly not greater than group 2, so the new agent is non-inferior to the old agent, in terms of one year recurrence rate.

Data					Summary				Confidence Intervals			Power Analysis
Pos1	Pos2	Neg1	Neg2	α	Prop1	Prop2	Diff	SEDiff	%CI	CI 1 tail	CI 2 tail	CD(tl)	Power1!<	Power1!>	Power2
16	14	55	57	0.05	0.225	0.197	0.028	0.069	95%CI	>-0.085 or <0.141	-0.106 to 0.162	0.2	0.95	0.8	0.70

The power estimation for group 1 not greater than group 2, using the one tail model, is 0.8, which is less than the 0.9 planned but still marginally acceptable statistically as having sufficient power. The same conclusion as that from the 95% confidence interval can be drawn, but with a little less confidence.

References

Rogers JL, Howard KI, Vessey JT. (1993) Using significance tests to evaluate equivalence between two experimental groups. Psychological Bulletin 113:553-565.

Jones B, Jarvis P, Lewis JA, Ebbutt AF. (1996) Trials to assess equivalence: the importance of rigorous methods. British Medical Journal 313:36-39

Hwang IK, Morikawa T. (1999) Design issues in noninferiority/equivalence trials. Drug Information Journal 33:1205-1218

Machin D, Campbell M, Fayers, P, Pinol A (1997) Sample Size Tables for Clinical Studies. Second Ed. Blackwell Science IBSN 0-86542-870-0 p. 100-104

Data Input for Sample Size is a table of 5 columns     Each row contains data from a separate study     Col 1 = Probability of Type I Error α for power analysis     Col 2 = Power (1 - β)     Col 3 = expected Proportion     Col 4 = Critical Difference, the tolerated limit of difference     Col 5 = φ ratio of sample sizegroup 2 / sample sizegroup 1 Data Input for Analysis is a table of 6 columns     Each row contains data from a separate study     Col 1 and 2 = Numbers with Positive Attributes in Group 1 & 2     Col 3 and 4 = Numbers with Negative Attributes in Group 1 & 2     Col 5 = Probability of Type I Error α for power analysis     Col 6 = Critical Difference, the tolerated limit of difference

Sample Size :     
Power Analysis :     

Table of sample size for equivalence between two proportions
Power=(1-β), β = Probability of Type II Error
α=Probability of Type I Error
π = Anticipated proportion
CD(tl) = Critical Difference (tolerance limit)
Cells contain sample size per group, assuming equal size groups

		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.02	0.02	475	705	705	929	929	1149	645	909	909	1161	1161	1405	1033	1361	1361	1667	1667	1956
0.02	0.04	134	205	205	274	274	342	179	259	259	337	337	412	280	379	379	472	472	560
0.02	0.06	67	104	104	141	141	178	88	130	130	171	171	211	135	186	186	235	235	282
0.02	0.08	41	66	66	90	90	114	54	81	81	108	108	134	81	114	114	145	145	176
0.02	0.10	29	46	46	64	64	81	37	56	56	76	76	95	55	78	78	101	101	123
0.02	0.12	21	35	35	48	48	62	27	42	42	57	57	72	40	58	58	75	75	92
0.02	0.14	17	28	28	39	39	50	21	33	33	45	45	57	31	45	45	59	59	72
0.02	0.16	14	23	23	32	32	41	17	27	27	37	37	47	25	36	36	48	48	59
0.02	0.18	11	19	19	27	27	34	14	22	22	31	31	39	20	30	30	40	40	49
0.02	0.20	10	16	16	23	23	29	12	19	19	26	26	33	17	25	25	33	33	41
0.04	0.02	884	1294	1294	1692	1692	2081	1208	1682	1682	2132	2132	2565	1954	2545	2545	3093	3093	3611
0.04	0.04	232	344	344	452	452	559	315	443	443	566	566	684	504	664	664	812	812	953
0.04	0.06	109	164	164	217	217	270	147	209	209	269	269	328	233	310	310	383	383	451
0.04	0.08	65	99	99	132	132	164	87	125	125	162	162	198	136	183	183	228	228	270
0.04	0.10	44	67	67	90	90	113	58	85	85	111	111	136	90	123	123	154	154	183
0.04	0.12	32	50	50	67	67	84	42	62	62	81	81	100	65	89	89	112	112	134
0.04	0.14	25	38	38	52	52	66	32	48	48	63	63	78	49	68	68	86	86	103
0.04	0.16	20	31	31	42	42	53	26	38	38	50	50	63	39	54	54	69	69	83
0.04	0.18	16	25	25	35	35	44	21	31	31	42	42	52	31	44	44	56	56	68
0.04	0.20	14	21	21	29	29	37	17	26	26	35	35	44	26	37	37	47	47	57
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.06	0.02	1283	1873	1873	2445	2445	3003	1757	2439	2439	3086	3086	3709	2847	3700	3700	4488	4488	5233
0.06	0.04	328	482	482	632	632	777	448	625	625	794	794	957	723	944	944	1149	1149	1343
0.06	0.06	151	223	223	293	293	362	205	288	288	367	367	443	328	432	432	528	528	619
0.06	0.08	88	131	131	173	173	214	119	168	168	215	215	261	189	250	250	307	307	362
0.06	0.10	58	88	88	116	116	144	78	112	112	144	144	175	124	165	165	204	204	241
0.06	0.12	42	63	63	84	84	105	56	81	81	104	104	127	88	118	118	146	146	173
0.06	0.14	32	48	48	65	65	81	42	61	61	79	79	97	66	89	89	111	111	132
0.06	0.16	25	38	38	51	51	64	33	48	48	63	63	77	52	70	70	88	88	104
0.06	0.18	20	31	31	42	42	53	27	39	39	51	51	63	42	57	57	71	71	85
0.06	0.20	17	26	26	35	35	44	22	33	33	43	43	53	34	47	47	59	59	71
0.08	0.02	1667	2432	2432	3172	3172	3894	2284	3168	3168	4006	4006	4812	3705	4810	4810	5832	5832	6797
0.08	0.04	422	618	618	808	808	993	578	803	803	1018	1018	1224	934	1217	1217	1477	1477	1724
0.08	0.06	191	281	281	369	369	454	261	365	365	463	463	558	421	550	550	670	670	783
0.08	0.08	110	163	163	214	214	264	150	210	210	268	268	323	240	315	315	385	385	451
0.08	0.10	72	107	107	141	141	175	98	138	138	176	176	213	156	206	206	253	253	297
0.08	0.12	51	77	77	101	101	126	69	98	98	126	126	153	110	146	146	180	180	212
0.08	0.14	39	58	58	77	77	95	52	74	74	95	95	116	82	110	110	135	135	159
0.08	0.16	30	46	46	61	61	75	41	58	58	75	75	91	64	86	86	106	106	125
0.08	0.18	25	37	37	49	49	61	33	47	47	61	61	74	51	69	69	85	85	101
0.08	0.20	20	31	31	41	41	51	27	39	39	50	50	61	42	57	57	71	71	84
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.10	0.02	2034	2967	2967	3869	3869	4748	2789	3866	3866	4887	4887	5869	4525	5872	5872	7117	7117	8293
0.10	0.04	513	749	749	978	978	1201	702	975	975	1234	1234	1483	1137	1478	1478	1794	1794	2092
0.10	0.06	231	338	338	442	442	543	315	439	439	557	557	670	510	664	664	807	807	942
0.10	0.08	132	194	194	254	254	312	180	251	251	319	319	384	290	378	378	461	461	539
0.10	0.10	86	127	127	166	166	205	117	164	164	208	208	251	187	246	246	300	300	351
0.10	0.12	61	90	90	118	118	146	82	116	116	148	148	178	132	173	173	212	212	249
0.10	0.14	45	67	67	89	89	110	61	87	87	111	111	134	98	129	129	158	158	186
0.10	0.16	35	53	53	70	70	86	48	68	68	87	87	105	76	100	100	123	123	145
0.10	0.18	29	43	43	56	56	70	38	54	54	70	70	85	61	81	81	99	99	117
0.10	0.20	24	35	35	46	46	58	31	45	45	58	58	70	50	66	66	81	81	96
0.12	0.02	2385	3476	3476	4533	4533	5562	3270	4531	4531	5727	5727	6877	5305	6884	6884	8342	8342	9720
0.12	0.04	599	875	875	1141	1141	1401	821	1139	1139	1441	1441	1731	1331	1729	1729	2096	2096	2444
0.12	0.06	269	393	393	513	513	630	368	511	511	647	647	777	595	774	774	939	939	1096
0.12	0.08	153	224	224	293	293	360	209	290	290	368	368	443	337	439	439	534	534	623
0.12	0.10	99	145	145	190	190	234	135	188	188	239	239	288	217	284	284	346	346	404
0.12	0.12	70	102	102	134	134	166	95	133	133	169	169	203	152	199	199	243	243	284
0.12	0.14	52	77	77	100	100	124	70	99	99	126	126	152	113	148	148	181	181	212
0.12	0.16	40	60	60	78	78	97	55	77	77	98	98	118	87	115	115	140	140	164
0.12	0.18	32	48	48	63	63	78	44	61	61	78	78	95	69	92	92	112	112	132
0.12	0.20	27	39	39	52	52	64	36	50	50	64	64	78	57	75	75	92	92	108
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.14	0.02	2717	3961	3961	5164	5164	6336	3726	5162	5162	6524	6524	7835	6047	7844	7844	9505	9505	11074
0.14	0.04	682	994	994	1297	1297	1592	934	1295	1295	1638	1638	1968	1515	1967	1967	2384	2384	2779
0.14	0.06	305	445	445	581	581	713	417	579	579	733	733	881	676	878	878	1066	1066	1242
0.14	0.08	173	253	253	330	330	405	236	328	328	416	416	500	382	497	497	604	604	704
0.14	0.10	112	163	163	214	214	262	152	212	212	269	269	323	246	320	320	389	389	455
0.14	0.12	78	115	115	150	150	185	107	149	149	189	189	227	172	224	224	273	273	319
0.14	0.14	58	85	85	112	112	137	79	110	110	140	140	169	127	166	166	202	202	237
0.14	0.16	45	66	66	87	87	107	61	85	85	109	109	131	98	128	128	156	156	183
0.14	0.18	36	53	53	69	69	85	49	68	68	87	87	105	78	102	102	125	125	146
0.14	0.20	29	43	43	57	57	70	40	56	56	71	71	86	64	83	83	102	102	119
0.16	0.02	3032	4419	4419	5761	5761	7069	4158	5760	5760	7280	7280	8742	6748	8753	8753	10606	10606	12357
0.16	0.04	760	1108	1108	1445	1445	1773	1042	1444	1444	1825	1825	2192	1690	2193	2193	2658	2658	3097
0.16	0.06	339	495	495	646	646	792	465	644	644	815	815	979	753	978	978	1186	1186	1382
0.16	0.08	192	280	280	366	366	449	262	364	364	461	461	554	425	552	552	670	670	782
0.16	0.10	124	181	181	236	236	290	169	235	235	297	297	357	273	355	355	431	431	503
0.16	0.12	86	126	126	165	165	203	118	164	164	208	208	250	191	248	248	301	301	352
0.16	0.14	64	94	94	123	123	151	87	122	122	154	154	185	141	183	183	223	223	260
0.16	0.16	49	72	72	95	95	116	67	94	94	119	119	143	108	141	141	172	172	201
0.16	0.18	39	58	58	76	76	93	54	75	75	95	95	114	86	112	112	137	137	160
0.16	0.20	32	47	47	62	62	76	44	61	61	77	77	93	70	92	92	111	111	130
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.18	0.02	3329	4852	4852	6325	6325	7761	4565	6324	6324	7992	7992	9597	7409	9611	9611	11645	11645	13567
0.18	0.04	834	1215	1215	1585	1585	1945	1143	1584	1584	2002	2002	2404	1854	2406	2406	2916	2916	3398
0.18	0.06	372	542	542	707	707	867	509	706	706	893	893	1072	826	1072	1072	1299	1299	1514
0.18	0.08	210	306	306	399	399	490	287	399	399	504	504	606	466	605	605	733	733	855
0.18	0.10	135	197	197	257	257	316	185	256	256	324	324	390	299	388	388	471	471	549
0.18	0.12	94	138	138	180	180	221	129	179	179	226	226	272	208	271	271	329	329	383
0.18	0.14	70	102	102	133	133	163	95	132	132	167	167	201	154	200	200	243	243	283
0.18	0.16	54	78	78	102	102	126	73	102	102	129	129	155	118	154	154	187	187	218
0.18	0.18	43	62	62	82	82	100	58	81	81	102	102	123	94	122	122	148	148	173
0.18	0.20	35	51	51	66	66	82	47	66	66	83	83	100	76	99	99	121	121	141
0.20	0.02	3608	5258	5258	6855	6855	8410	4948	6854	6854	8662	8662	10401	8031	10417	10417	12621	12621	14704
0.20	0.04	903	1316	1316	1716	1716	2106	1238	1716	1716	2168	2168	2604	2009	2607	2607	3159	3159	3680
0.20	0.06	402	586	586	765	765	938	551	764	764	966	966	1160	894	1160	1160	1406	1406	1639
0.20	0.08	227	331	331	431	431	530	311	431	431	545	545	654	504	654	654	793	793	924
0.20	0.10	146	213	213	277	277	340	200	277	277	350	350	420	323	420	420	509	509	593
0.20	0.12	102	148	148	193	193	237	139	193	193	244	244	293	225	292	292	354	354	413
0.20	0.14	75	109	109	143	143	175	102	142	142	180	180	216	166	215	215	261	261	305
0.20	0.16	58	84	84	110	110	135	79	109	109	138	138	166	127	165	165	201	201	234
0.20	0.18	46	67	67	87	87	107	62	87	87	110	110	132	101	131	131	159	159	186
0.20	0.20	37	54	54	71	71	87	51	71	71	89	89	107	82	106	106	129	129	151
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.22	0.02	3869	5638	5638	7350	7350	9018	5306	7350	7350	9288	9288	11153	8612	11171	11171	13534	13534	15767
0.22	0.04	968	1411	1411	1839	1839	2257	1328	1839	1839	2324	2324	2791	2154	2794	2794	3386	3386	3945
0.22	0.06	431	628	628	819	819	1005	591	818	818	1034	1034	1242	958	1243	1243	1507	1507	1755
0.22	0.08	243	354	354	462	462	566	333	461	461	583	583	700	540	700	700	849	849	989
0.22	0.10	156	227	227	296	296	363	213	296	296	374	374	449	346	449	449	544	544	634
0.22	0.12	109	158	158	206	206	253	149	206	206	260	260	313	241	312	312	379	379	441
0.22	0.14	80	117	117	152	152	187	109	152	152	192	192	230	177	230	230	279	279	325
0.22	0.16	61	90	90	117	117	143	84	116	116	147	147	177	136	176	176	214	214	249
0.22	0.18	49	71	71	93	93	114	67	92	92	117	117	140	108	140	140	169	169	197
0.22	0.20	40	58	58	75	75	92	54	75	75	95	95	114	87	113	113	137	137	160
0.24	0.02	4112	5993	5993	7812	7812	9585	5640	7812	7812	9872	9872	11853	9154	11873	11873	14385	14385	16758
0.24	0.04	1029	1499	1499	1954	1954	2398	1411	1954	1954	2469	2469	2965	2289	2969	2969	3598	3598	4191
0.24	0.06	458	667	667	869	869	1067	627	869	869	1098	1098	1319	1018	1321	1321	1600	1600	1864
0.24	0.08	258	376	376	490	490	601	353	489	489	619	619	743	573	743	743	901	901	1050
0.24	0.10	165	241	241	314	314	385	226	314	314	396	396	476	367	476	476	577	577	672
0.24	0.12	115	168	168	218	218	268	158	218	218	276	276	331	255	331	331	401	401	468
0.24	0.14	85	123	123	161	161	197	116	161	161	203	203	244	188	244	244	295	295	344
0.24	0.16	65	95	95	123	123	151	89	123	123	156	156	187	144	187	187	226	226	264
0.24	0.18	52	75	75	98	98	120	70	97	97	123	123	148	114	148	148	179	179	209
0.24	0.20	42	61	61	79	79	97	57	79	79	100	100	120	92	120	120	145	145	169
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.26	0.02	4337	6321	6321	8239	8239	10109	5948	8239	8239	10412	10412	12502	9655	12523	12523	15172	15172	17676
0.26	0.04	1085	1581	1581	2061	2061	2528	1488	2060	2060	2604	2604	3126	2414	3131	3131	3794	3794	4420
0.26	0.06	482	703	703	916	916	1124	662	916	916	1158	1158	1390	1073	1392	1392	1687	1687	1965
0.26	0.08	272	396	396	516	516	633	372	516	516	652	652	782	604	784	784	949	949	1106
0.26	0.10	174	254	254	330	330	405	239	330	330	417	417	501	387	502	502	608	608	708
0.26	0.12	121	176	176	230	230	282	166	230	230	290	290	348	269	349	349	422	422	492
0.26	0.14	89	130	130	169	169	207	122	169	169	213	213	256	198	256	256	310	310	362
0.26	0.16	68	99	99	129	129	159	94	129	129	163	163	196	151	196	196	238	238	277
0.26	0.18	54	79	79	102	102	125	74	102	102	129	129	155	120	155	155	188	188	219
0.26	0.20	44	64	64	83	83	102	60	83	83	105	105	126	97	126	126	152	152	177
0.28	0.02	4544	6622	6622	8633	8633	10592	6232	8633	8633	10909	10909	13099	10117	13121	13121	15897	15897	18520
0.28	0.04	1136	1656	1656	2158	2158	2648	1558	2159	2159	2728	2728	3275	2530	3281	3281	3975	3975	4630
0.28	0.06	505	736	736	960	960	1177	693	960	960	1212	1212	1456	1124	1458	1458	1767	1767	2058
0.28	0.08	284	414	414	540	540	662	390	540	540	682	682	819	633	820	820	994	994	1158
0.28	0.10	182	265	265	346	346	424	250	346	346	437	437	524	405	525	525	636	636	741
0.28	0.12	127	184	184	240	240	294	174	240	240	303	303	364	281	365	365	442	442	515
0.28	0.14	93	135	135	176	176	216	128	176	176	223	223	267	207	268	268	325	325	378
0.28	0.16	71	104	104	135	135	166	98	135	135	171	171	205	158	205	205	248	248	289
0.28	0.18	56	82	82	107	107	131	77	107	107	135	135	162	125	162	162	196	196	229
0.28	0.20	46	66	66	86	86	106	63	87	87	109	109	131	101	131	131	159	159	185
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.30	0.02	4733	6898	6898	8992	8992	11032	6492	8992	8992	11363	11363	13644	10538	13668	13668	16559	16559	19290
0.30	0.04	1184	1725	1725	2248	2248	2758	1623	2248	2248	2841	2841	3411	2635	3417	3417	4139	4139	4822
0.30	0.06	526	767	767	999	999	1226	722	999	999	1262	1262	1516	1171	1519	1519	1840	1840	2143
0.30	0.08	296	431	431	562	562	689	406	562	562	710	710	852	659	854	854	1035	1035	1205
0.30	0.10	190	276	276	360	360	441	260	360	360	454	454	545	422	547	547	662	662	771
0.30	0.12	132	192	192	250	250	306	181	250	250	315	315	379	293	380	380	460	460	535
0.30	0.14	97	141	141	183	183	225	133	183	183	232	232	278	215	279	279	338	338	393
0.30	0.16	74	108	108	140	140	172	102	140	140	177	177	213	165	213	213	258	258	301
0.30	0.18	59	85	85	111	111	136	80	111	111	140	140	168	130	169	169	204	204	237
0.30	0.20	48	69	69	90	90	110	65	90	90	113	113	136	105	136	136	165	165	192
0.32	0.02	4905	7147	7147	9317	9317	11431	6727	9317	9317	11774	11774	14137	10919	14162	14162	17157	17157	19988
0.32	0.04	1226	1787	1787	2329	2329	2857	1682	2329	2329	2943	2943	3534	2730	3540	3540	4289	4289	4996
0.32	0.06	545	794	794	1035	1035	1269	747	1035	1035	1308	1308	1570	1213	1573	1573	1906	1906	2220
0.32	0.08	307	447	447	582	582	714	420	582	582	735	735	883	682	885	885	1072	1072	1248
0.32	0.10	196	286	286	372	372	456	269	372	372	470	470	565	437	566	566	685	685	798
0.32	0.12	136	198	198	258	258	317	187	259	259	326	326	392	303	393	393	476	476	554
0.32	0.14	100	146	146	190	190	232	137	190	190	240	240	287	223	289	289	349	349	407
0.32	0.16	77	111	111	145	145	178	105	145	145	183	183	220	171	221	221	267	267	311
0.32	0.18	61	88	88	114	114	140	83	115	115	145	145	173	135	174	174	211	211	245
0.32	0.20	49	71	71	93	93	113	67	93	93	117	117	140	109	141	141	171	171	198
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.34	0.02	5058	7371	7371	9608	9608	11788	6937	9608	9608	12142	12142	14579	11260	14604	14604	17693	17693	20612
0.34	0.04	1264	1842	1842	2401	2401	2946	1734	2402	2402	3035	3035	3644	2815	3650	3650	4422	4422	5152
0.34	0.06	562	819	819	1067	1067	1309	771	1067	1067	1348	1348	1619	1251	1622	1622	1965	1965	2289
0.34	0.08	316	460	460	600	600	736	433	600	600	758	758	910	704	912	912	1105	1105	1287
0.34	0.10	202	294	294	384	384	470	277	384	384	485	485	582	450	583	583	706	706	823
0.34	0.12	140	204	204	266	266	326	193	266	266	336	336	404	313	405	405	490	490	571
0.34	0.14	103	150	150	195	195	239	141	196	196	247	247	296	230	297	297	360	360	419
0.34	0.16	79	115	115	149	149	183	108	150	150	189	189	226	176	227	227	275	275	320
0.34	0.18	62	91	91	118	118	144	86	118	118	149	149	178	139	179	179	217	217	253
0.34	0.20	51	73	73	95	95	117	69	95	95	120	120	144	112	145	145	176	176	204
0.36	0.02	5193	7567	7567	9864	9864	12103	7122	9865	9865	12466	12466	14968	11561	14994	14994	18166	18166	21163
0.36	0.04	1298	1891	1891	2465	2465	3025	1780	2466	2466	3116	3116	3741	2890	3748	3748	4540	4540	5289
0.36	0.06	577	840	840	1095	1095	1343	791	1095	1095	1384	1384	1661	1284	1665	1665	2017	2017	2349
0.36	0.08	324	472	472	615	615	755	445	616	616	778	778	934	722	936	936	1134	1134	1321
0.36	0.10	208	302	302	394	394	483	285	394	394	497	497	597	462	599	599	725	725	844
0.36	0.12	144	210	210	273	273	335	198	273	273	345	345	414	321	415	415	503	503	586
0.36	0.14	106	154	154	200	200	245	145	201	201	253	253	304	236	305	305	369	369	430
0.36	0.16	81	118	118	153	153	187	111	153	153	193	193	232	180	233	233	282	282	328
0.36	0.18	64	93	93	121	121	148	88	121	121	153	153	183	142	184	184	223	223	259
0.36	0.20	52	75	75	97	97	119	71	98	98	123	123	148	115	149	149	180	180	209
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.38	0.02	5310	7738	7738	10087	10087	12376	7283	10087	10087	12747	12747	15306	11822	15333	15333	18576	18576	21640
0.38	0.04	1327	1934	1934	2521	2521	3093	1820	2521	2521	3186	3186	3825	2955	3832	3832	4642	4642	5408
0.38	0.06	590	859	859	1120	1120	1373	809	1120	1120	1415	1415	1699	1313	1703	1703	2062	2062	2402
0.38	0.08	332	483	483	629	629	772	455	630	630	795	795	955	738	957	957	1159	1159	1350
0.38	0.10	212	309	309	402	402	493	291	403	403	508	508	610	472	612	612	741	741	863
0.38	0.12	147	214	214	279	279	342	202	279	279	353	353	423	328	425	425	514	514	598
0.38	0.14	108	157	157	205	205	251	148	205	205	259	259	310	241	312	312	377	377	439
0.38	0.16	83	120	120	156	156	191	113	157	157	198	198	237	184	238	238	288	288	335
0.38	0.18	65	95	95	123	123	151	90	124	124	156	156	187	145	188	188	227	227	264
0.38	0.20	53	77	77	100	100	122	73	100	100	126	126	151	118	152	152	184	184	214
0.40	0.02	5409	7882	7882	10275	10275	12607	7419	10276	10276	12985	12985	15591	12043	15619	15619	18922	18922	22044
0.40	0.04	1352	1970	1970	2568	2568	3150	1854	2568	2568	3245	3245	3896	3010	3904	3904	4729	4729	5509
0.40	0.06	601	875	875	1140	1140	1399	824	1141	1141	1441	1441	1730	1338	1734	1734	2100	2100	2447
0.40	0.08	338	492	492	641	641	786	463	641	641	810	810	972	752	975	975	1181	1181	1375
0.40	0.10	216	314	314	410	410	502	296	410	410	518	518	621	481	623	623	755	755	879
0.40	0.12	150	218	218	284	284	348	206	284	284	359	359	431	334	432	432	523	523	609
0.40	0.14	110	160	160	208	208	255	151	209	209	263	263	316	245	317	317	384	384	447
0.40	0.16	84	122	122	159	159	195	116	159	159	201	201	241	188	243	243	293	293	341
0.40	0.18	67	96	96	125	125	153	91	126	126	159	159	190	148	191	191	231	231	269
0.40	0.20	54	78	78	101	101	124	74	102	102	128	128	153	120	155	155	187	187	217
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.42	0.02	5490	8001	8001	10429	10429	12796	7530	10430	10430	13180	13180	15825	12223	15853	15853	19206	19206	22374
0.42	0.04	1372	1999	1999	2606	2606	3197	1882	2607	2607	3293	3293	3954	3055	3962	3962	4800	4800	5591
0.42	0.06	610	888	888	1157	1157	1420	836	1158	1158	1463	1463	1756	1358	1760	1760	2132	2132	2483
0.42	0.08	343	499	499	650	650	798	470	651	651	822	822	987	763	989	989	1198	1198	1395
0.42	0.10	219	319	319	416	416	510	301	416	416	525	525	630	488	633	633	766	766	892
0.42	0.12	152	221	221	288	288	353	209	289	289	364	364	437	339	439	439	531	531	618
0.42	0.14	112	162	162	211	211	259	153	212	212	267	267	320	249	322	322	390	390	453
0.42	0.16	85	124	124	161	161	198	117	162	162	204	204	245	190	246	246	298	298	346
0.42	0.18	67	98	98	127	127	156	93	128	128	161	161	193	150	194	194	235	235	273
0.42	0.20	55	79	79	103	103	126	75	103	103	130	130	156	122	157	157	190	190	220
0.44	0.02	5553	8093	8093	10549	10549	12943	7616	10549	10549	13331	13331	16007	12364	16035	16035	19427	19427	22631
0.44	0.04	1388	2022	2022	2636	2636	3234	1904	2636	2636	3331	3331	4000	3090	4008	4008	4855	4855	5655
0.44	0.06	617	898	898	1171	1171	1436	846	1171	1171	1479	1479	1776	1373	1780	1780	2156	2156	2512
0.44	0.08	347	505	505	658	658	807	476	658	658	831	831	998	772	1001	1001	1212	1212	1411
0.44	0.10	222	323	323	420	420	515	304	421	421	531	531	638	494	640	640	775	775	902
0.44	0.12	154	224	224	291	291	357	211	292	292	368	368	442	343	444	444	537	537	625
0.44	0.14	113	164	164	214	214	262	155	214	214	270	270	324	252	326	326	394	394	458
0.44	0.16	86	125	125	163	163	200	119	164	164	206	206	247	192	249	249	301	301	350
0.44	0.18	68	99	99	128	128	157	94	129	129	163	163	195	152	196	196	237	237	276
0.44	0.20	55	80	80	104	104	127	76	104	104	131	131	157	123	159	159	192	192	223
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.46	0.02	5598	8158	8158	10634	10634	13048	7678	10635	10635	13439	13439	16136	12464	16165	16165	19584	19584	22815
0.46	0.04	1399	2039	2039	2657	2657	3260	1919	2658	2658	3358	3358	4032	3115	4040	4040	4894	4894	5701
0.46	0.06	622	905	905	1180	1180	1447	853	1180	1180	1491	1491	1790	1384	1795	1795	2174	2174	2532
0.46	0.08	350	509	509	663	663	813	479	663	663	838	838	1006	778	1009	1009	1221	1221	1423
0.46	0.10	224	325	325	424	424	519	307	424	424	536	536	643	498	645	645	781	781	909
0.46	0.12	155	226	226	294	294	360	213	294	294	371	371	445	345	447	447	541	541	630
0.46	0.14	114	165	165	215	215	264	156	216	216	272	272	326	254	328	328	397	397	462
0.46	0.16	87	126	126	164	164	201	119	165	165	208	208	249	194	251	251	303	303	353
0.46	0.18	69	100	100	129	129	159	94	130	130	164	164	196	153	198	198	239	239	278
0.46	0.20	56	80	80	105	105	128	76	105	105	132	132	158	124	160	160	193	193	225
0.48	0.02	5625	8198	8198	10686	10686	13110	7715	10686	10686	13504	13504	16214	12524	16243	16243	19679	19679	22925
0.48	0.04	1406	2049	2049	2670	2670	3276	1928	2671	2671	3374	3374	4051	3130	4059	4059	4918	4918	5728
0.48	0.06	625	910	910	1186	1186	1454	857	1186	1186	1498	1498	1799	1391	1803	1803	2184	2184	2544
0.48	0.08	351	511	511	666	666	817	482	667	667	842	842	1011	782	1014	1014	1227	1227	1429
0.48	0.10	225	327	327	426	426	522	308	426	426	538	538	646	500	648	648	785	785	913
0.48	0.12	156	227	227	295	295	362	214	296	296	373	373	447	347	449	449	544	544	633
0.48	0.14	114	166	166	216	216	265	157	217	217	273	273	328	255	330	330	399	399	464
0.48	0.16	88	127	127	165	165	202	120	166	166	209	209	250	195	252	252	305	305	355
0.48	0.18	69	100	100	130	130	159	95	131	131	165	165	197	154	199	199	240	240	279
0.48	0.20	56	81	81	105	105	128	77	106	106	133	133	159	124	161	161	194	194	226
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.50	0.02	5634	8211	8211	10703	10703	13131	7728	10703	10703	13526	13526	16240	12544	16269	16269	19710	19710	22962
0.50	0.04	1408	2052	2052	2674	2674	3281	1932	2675	2675	3380	3380	4058	3135	4066	4066	4925	4925	5738
0.50	0.06	626	911	911	1188	1188	1457	858	1188	1188	1501	1501	1802	1393	1806	1806	2188	2188	2548
0.50	0.08	352	512	512	667	667	818	482	668	668	843	843	1012	783	1015	1015	1229	1229	1432
0.50	0.10	225	327	327	426	426	523	309	427	427	539	539	647	501	649	649	786	786	915
0.50	0.12	156	227	227	295	295	362	214	296	296	374	374	448	348	450	450	545	545	634
0.50	0.14	115	166	166	217	217	265	157	217	217	274	274	328	255	330	330	400	400	465
0.50	0.16	88	127	127	165	165	203	120	166	166	209	209	251	195	252	252	305	305	355
0.50	0.18	69	100	100	130	130	159	95	131	131	165	165	197	154	199	199	241	241	280
0.50	0.20	56	81	81	105	105	129	77	106	106	133	133	159	125	161	161	194	194	226
0.52	0.02	5625	8198	8198	10686	10686	13110	7715	10686	10686	13504	13504	16214	12524	16243	16243	19679	19679	22925
0.52	0.04	1406	2049	2049	2670	2670	3276	1928	2671	2671	3374	3374	4051	3130	4059	4059	4918	4918	5728
0.52	0.06	625	910	910	1186	1186	1454	857	1186	1186	1498	1498	1799	1391	1803	1803	2184	2184	2544
0.52	0.08	351	511	511	666	666	817	482	667	667	842	842	1011	782	1014	1014	1227	1227	1429
0.52	0.10	225	327	327	426	426	522	308	426	426	538	538	646	500	648	648	785	785	913
0.52	0.12	156	227	227	295	295	362	214	296	296	373	373	447	347	449	449	544	544	633
0.52	0.14	114	166	166	216	216	265	157	217	217	273	273	328	255	330	330	399	399	464
0.52	0.16	88	127	127	165	165	202	120	166	166	209	209	250	195	252	252	305	305	355
0.52	0.18	69	100	100	130	130	159	95	131	131	165	165	197	154	199	199	240	240	279
0.52	0.20	56	81	81	105	105	128	77	106	106	133	133	159	124	161	161	194	194	226
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.54	0.02	5598	8158	8158	10634	10634	13048	7678	10635	10635	13439	13439	16136	12464	16165	16165	19584	19584	22815
0.54	0.04	1399	2039	2039	2657	2657	3260	1919	2658	2658	3358	3358	4032	3115	4040	4040	4894	4894	5701
0.54	0.06	622	905	905	1180	1180	1447	853	1180	1180	1491	1491	1790	1384	1795	1795	2174	2174	2532
0.54	0.08	350	509	509	663	663	813	479	663	663	838	838	1006	778	1009	1009	1221	1221	1423
0.54	0.10	224	325	325	424	424	519	307	424	424	536	536	643	498	645	645	781	781	909
0.54	0.12	155	226	226	294	294	360	213	294	294	371	371	445	345	447	447	541	541	630
0.54	0.14	114	165	165	215	215	264	156	216	216	272	272	326	254	328	328	397	397	462
0.54	0.16	87	126	126	164	164	201	119	165	165	208	208	249	194	251	251	303	303	353
0.54	0.18	69	100	100	129	129	159	94	130	130	164	164	196	153	198	198	239	239	278
0.54	0.20	56	80	80	105	105	128	76	105	105	132	132	158	124	160	160	193	193	225
0.56	0.02	5553	8093	8093	10549	10549	12943	7616	10549	10549	13331	13331	16007	12364	16035	16035	19427	19427	22631
0.56	0.04	1388	2022	2022	2636	2636	3234	1904	2636	2636	3331	3331	4000	3090	4008	4008	4855	4855	5655
0.56	0.06	617	898	898	1171	1171	1436	846	1171	1171	1479	1479	1776	1373	1780	1780	2156	2156	2512
0.56	0.08	347	505	505	658	658	807	476	658	658	831	831	998	772	1001	1001	1212	1212	1411
0.56	0.10	222	323	323	420	420	515	304	421	421	531	531	638	494	640	640	775	775	902
0.56	0.12	154	224	224	291	291	357	211	292	292	368	368	442	343	444	444	537	537	625
0.56	0.14	113	164	164	214	214	262	155	214	214	270	270	324	252	326	326	394	394	458
0.56	0.16	86	125	125	163	163	200	119	164	164	206	206	247	192	249	249	301	301	350
0.56	0.18	68	99	99	128	128	157	94	129	129	163	163	195	152	196	196	237	237	276
0.56	0.20	55	80	80	104	104	127	76	104	104	131	131	157	123	159	159	192	192	223
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.58	0.02	5490	8001	8001	10429	10429	12796	7530	10430	10430	13180	13180	15825	12223	15853	15853	19206	19206	22374
0.58	0.04	1372	1999	1999	2606	2606	3197	1882	2607	2607	3293	3293	3954	3055	3962	3962	4800	4800	5591
0.58	0.06	610	888	888	1157	1157	1420	836	1158	1158	1463	1463	1756	1358	1760	1760	2132	2132	2483
0.58	0.08	343	499	499	650	650	798	470	651	651	822	822	987	763	989	989	1198	1198	1395
0.58	0.10	219	319	319	416	416	510	301	416	416	525	525	630	488	633	633	766	766	892
0.58	0.12	152	221	221	288	288	353	209	289	289	364	364	437	339	439	439	531	531	618
0.58	0.14	112	162	162	211	211	259	153	212	212	267	267	320	249	322	322	390	390	453
0.58	0.16	85	124	124	161	161	198	117	162	162	204	204	245	190	246	246	298	298	346
0.58	0.18	67	98	98	127	127	156	93	128	128	161	161	193	150	194	194	235	235	273
0.58	0.20	55	79	79	103	103	126	75	103	103	130	130	156	122	157	157	190	190	220
0.60	0.02	5409	7882	7882	10275	10275	12607	7419	10276	10276	12985	12985	15591	12043	15619	15619	18922	18922	22044
0.60	0.04	1352	1970	1970	2568	2568	3150	1854	2568	2568	3245	3245	3896	3010	3904	3904	4729	4729	5509
0.60	0.06	601	875	875	1140	1140	1399	824	1141	1141	1441	1441	1730	1338	1734	1734	2100	2100	2447
0.60	0.08	338	492	492	641	641	786	463	641	641	810	810	972	752	975	975	1181	1181	1375
0.60	0.10	216	314	314	410	410	502	296	410	410	518	518	621	481	623	623	755	755	879
0.60	0.12	150	218	218	284	284	348	206	284	284	359	359	431	334	432	432	523	523	609
0.60	0.14	110	160	160	208	208	255	151	209	209	263	263	316	245	317	317	384	384	447
0.60	0.16	84	122	122	159	159	195	116	159	159	201	201	241	188	243	243	293	293	341
0.60	0.18	67	96	96	125	125	153	91	126	126	159	159	190	148	191	191	231	231	269
0.60	0.20	54	78	78	101	101	124	74	102	102	128	128	153	120	155	155	187	187	217
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.62	0.02	5310	7738	7738	10087	10087	12376	7283	10087	10087	12747	12747	15306	11822	15333	15333	18576	18576	21640
0.62	0.04	1327	1934	1934	2521	2521	3093	1820	2521	2521	3186	3186	3825	2955	3832	3832	4642	4642	5408
0.62	0.06	590	859	859	1120	1120	1373	809	1120	1120	1415	1415	1699	1313	1703	1703	2062	2062	2402
0.62	0.08	332	483	483	629	629	772	455	630	630	795	795	955	738	957	957	1159	1159	1350
0.62	0.10	212	309	309	402	402	493	291	403	403	508	508	610	472	612	612	741	741	863
0.62	0.12	147	214	214	279	279	342	202	279	279	353	353	423	328	425	425	514	514	598
0.62	0.14	108	157	157	205	205	251	148	205	205	259	259	310	241	312	312	377	377	439
0.62	0.16	83	120	120	156	156	191	113	157	157	198	198	237	184	238	238	288	288	335
0.62	0.18	65	95	95	123	123	151	90	124	124	156	156	187	145	188	188	227	227	264
0.62	0.20	53	77	77	100	100	122	73	100	100	126	126	151	118	152	152	184	184	214
0.64	0.02	5193	7567	7567	9864	9864	12103	7122	9865	9865	12466	12466	14968	11561	14994	14994	18166	18166	21163
0.64	0.04	1298	1891	1891	2465	2465	3025	1780	2466	2466	3116	3116	3741	2890	3748	3748	4540	4540	5289
0.64	0.06	577	840	840	1095	1095	1343	791	1095	1095	1384	1384	1661	1284	1665	1665	2017	2017	2349
0.64	0.08	324	472	472	615	615	755	445	616	616	778	778	934	722	936	936	1134	1134	1321
0.64	0.10	208	302	302	394	394	483	285	394	394	497	497	597	462	599	599	725	725	844
0.64	0.12	144	210	210	273	273	335	198	273	273	345	345	414	321	415	415	503	503	586
0.64	0.14	106	154	154	200	200	245	145	201	201	253	253	304	236	305	305	369	369	430
0.64	0.16	81	118	118	153	153	187	111	153	153	193	193	232	180	233	233	282	282	328
0.64	0.18	64	93	93	121	121	148	88	121	121	153	153	183	142	184	184	223	223	259
0.64	0.20	52	75	75	97	97	119	71	98	98	123	123	148	115	149	149	180	180	209
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.66	0.02	5058	7371	7371	9608	9608	11788	6937	9608	9608	12142	12142	14579	11260	14604	14604	17693	17693	20612
0.66	0.04	1264	1842	1842	2401	2401	2946	1734	2402	2402	3035	3035	3644	2815	3650	3650	4422	4422	5152
0.66	0.06	562	819	819	1067	1067	1309	771	1067	1067	1348	1348	1619	1251	1622	1622	1965	1965	2289
0.66	0.08	316	460	460	600	600	736	433	600	600	758	758	910	704	912	912	1105	1105	1287
0.66	0.10	202	294	294	384	384	470	277	384	384	485	485	582	450	583	583	706	706	823
0.66	0.12	140	204	204	266	266	326	193	266	266	336	336	404	313	405	405	490	490	571
0.66	0.14	103	150	150	195	195	239	141	196	196	247	247	296	230	297	297	360	360	419
0.66	0.16	79	115	115	149	149	183	108	150	150	189	189	226	176	227	227	275	275	320
0.66	0.18	62	91	91	118	118	144	86	118	118	149	149	178	139	179	179	217	217	253
0.66	0.20	51	73	73	95	95	117	69	95	95	120	120	144	112	145	145	176	176	204
0.68	0.02	4905	7147	7147	9317	9317	11431	6727	9317	9317	11774	11774	14137	10919	14162	14162	17157	17157	19988
0.68	0.04	1226	1787	1787	2329	2329	2857	1682	2329	2329	2943	2943	3534	2730	3540	3540	4289	4289	4996
0.68	0.06	545	794	794	1035	1035	1269	747	1035	1035	1308	1308	1570	1213	1573	1573	1906	1906	2220
0.68	0.08	307	447	447	582	582	714	420	582	582	735	735	883	682	885	885	1072	1072	1248
0.68	0.10	196	286	286	372	372	456	269	372	372	470	470	565	437	566	566	685	685	798
0.68	0.12	136	198	198	258	258	317	187	259	259	326	326	392	303	393	393	476	476	554
0.68	0.14	100	146	146	190	190	232	137	190	190	240	240	287	223	289	289	349	349	407
0.68	0.16	77	111	111	145	145	178	105	145	145	183	183	220	171	221	221	267	267	311
0.68	0.18	61	88	88	114	114	140	83	115	115	145	145	173	135	174	174	211	211	245
0.68	0.20	49	71	71	93	93	113	67	93	93	117	117	140	109	141	141	171	171	198
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.70	0.02	4733	6898	6898	8992	8992	11032	6492	8992	8992	11363	11363	13644	10538	13668	13668	16559	16559	19290
0.70	0.04	1184	1725	1725	2248	2248	2758	1623	2248	2248	2841	2841	3411	2635	3417	3417	4139	4139	4822
0.70	0.06	526	767	767	999	999	1226	722	999	999	1262	1262	1516	1171	1519	1519	1840	1840	2143
0.70	0.08	296	431	431	562	562	689	406	562	562	710	710	852	659	854	854	1035	1035	1205
0.70	0.10	190	276	276	360	360	441	260	360	360	454	454	545	422	547	547	662	662	771
0.70	0.12	132	192	192	250	250	306	181	250	250	315	315	379	293	380	380	460	460	535
0.70	0.14	97	141	141	183	183	225	133	183	183	232	232	278	215	279	279	338	338	393
0.70	0.16	74	108	108	140	140	172	102	140	140	177	177	213	165	213	213	258	258	301
0.70	0.18	59	85	85	111	111	136	80	111	111	140	140	168	130	169	169	204	204	237
0.70	0.20	48	69	69	90	90	110	65	90	90	113	113	136	105	136	136	165	165	192
0.72	0.02	4544	6622	6622	8633	8633	10592	6232	8633	8633	10909	10909	13099	10117	13121	13121	15897	15897	18520
0.72	0.04	1136	1656	1656	2158	2158	2648	1558	2159	2159	2728	2728	3275	2530	3281	3281	3975	3975	4630
0.72	0.06	505	736	736	960	960	1177	693	960	960	1212	1212	1456	1124	1458	1458	1767	1767	2058
0.72	0.08	284	414	414	540	540	662	390	540	540	682	682	819	633	820	820	994	994	1158
0.72	0.10	182	265	265	346	346	424	250	346	346	437	437	524	405	525	525	636	636	741
0.72	0.12	127	184	184	240	240	294	174	240	240	303	303	364	281	365	365	442	442	515
0.72	0.14	93	135	135	176	176	216	128	176	176	223	223	267	207	268	268	325	325	378
0.72	0.16	71	104	104	135	135	166	98	135	135	171	171	205	158	205	205	248	248	289
0.72	0.18	56	82	82	107	107	131	77	107	107	135	135	162	125	162	162	196	196	229
0.72	0.20	46	66	66	86	86	106	63	87	87	109	109	131	101	131	131	159	159	185
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.74	0.02	4337	6321	6321	8239	8239	10109	5948	8239	8239	10412	10412	12502	9655	12523	12523	15172	15172	17676
0.74	0.04	1085	1581	1581	2061	2061	2528	1488	2060	2060	2604	2604	3126	2414	3131	3131	3794	3794	4420
0.74	0.06	482	703	703	916	916	1124	662	916	916	1158	1158	1390	1073	1392	1392	1687	1687	1965
0.74	0.08	272	396	396	516	516	633	372	516	516	652	652	782	604	784	784	949	949	1106
0.74	0.10	174	254	254	330	330	405	239	330	330	417	417	501	387	502	502	608	608	708
0.74	0.12	121	176	176	230	230	282	166	230	230	290	290	348	269	349	349	422	422	492
0.74	0.14	89	130	130	169	169	207	122	169	169	213	213	256	198	256	256	310	310	362
0.74	0.16	68	99	99	129	129	159	94	129	129	163	163	196	151	196	196	238	238	277
0.74	0.18	54	79	79	102	102	125	74	102	102	129	129	155	120	155	155	188	188	219
0.74	0.20	44	64	64	83	83	102	60	83	83	105	105	126	97	126	126	152	152	177
0.76	0.02	4112	5993	5993	7812	7812	9585	5640	7812	7812	9872	9872	11853	9154	11873	11873	14385	14385	16758
0.76	0.04	1029	1499	1499	1954	1954	2398	1411	1954	1954	2469	2469	2965	2289	2969	2969	3598	3598	4191
0.76	0.06	458	667	667	869	869	1067	627	869	869	1098	1098	1319	1018	1321	1321	1600	1600	1864
0.76	0.08	258	376	376	490	490	601	353	489	489	619	619	743	573	743	743	901	901	1050
0.76	0.10	165	241	241	314	314	385	226	314	314	396	396	476	367	476	476	577	577	672
0.76	0.12	115	168	168	218	218	268	158	218	218	276	276	331	255	331	331	401	401	468
0.76	0.14	85	123	123	161	161	197	116	161	161	203	203	244	188	244	244	295	295	344
0.76	0.16	65	95	95	123	123	151	89	123	123	156	156	187	144	187	187	226	226	264
0.76	0.18	52	75	75	98	98	120	70	97	97	123	123	148	114	148	148	179	179	209
0.76	0.20	42	61	61	79	79	97	57	79	79	100	100	120	92	120	120	145	145	169
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.78	0.02	3869	5638	5638	7350	7350	9018	5306	7350	7350	9288	9288	11153	8612	11171	11171	13534	13534	15767
0.78	0.04	968	1411	1411	1839	1839	2257	1328	1839	1839	2324	2324	2791	2154	2794	2794	3386	3386	3945
0.78	0.06	431	628	628	819	819	1005	591	818	818	1034	1034	1242	958	1243	1243	1507	1507	1755
0.78	0.08	243	354	354	462	462	566	333	461	461	583	583	700	540	700	700	849	849	989
0.78	0.10	156	227	227	296	296	363	213	296	296	374	374	449	346	449	449	544	544	634
0.78	0.12	109	158	158	206	206	253	149	206	206	260	260	313	241	312	312	379	379	441
0.78	0.14	80	117	117	152	152	187	109	152	152	192	192	230	177	230	230	279	279	325
0.78	0.16	61	90	90	117	117	143	84	116	116	147	147	177	136	176	176	214	214	249
0.78	0.18	49	71	71	93	93	114	67	92	92	117	117	140	108	140	140	169	169	197
0.78	0.20	40	58	58	75	75	92	54	75	75	95	95	114	87	113	113	137	137	160
0.80	0.02	3608	5258	5258	6855	6855	8410	4948	6854	6854	8662	8662	10401	8031	10417	10417	12621	12621	14704
0.80	0.04	903	1316	1316	1716	1716	2106	1238	1716	1716	2168	2168	2604	2009	2607	2607	3159	3159	3680
0.80	0.06	402	586	586	765	765	938	551	764	764	966	966	1160	894	1160	1160	1406	1406	1639
0.80	0.08	227	331	331	431	431	530	311	431	431	545	545	654	504	654	654	793	793	924
0.80	0.10	146	213	213	277	277	340	200	277	277	350	350	420	323	420	420	509	509	593
0.80	0.12	102	148	148	193	193	237	139	193	193	244	244	293	225	292	292	354	354	413
0.80	0.14	75	109	109	143	143	175	102	142	142	180	180	216	166	215	215	261	261	305
0.80	0.16	58	84	84	110	110	135	79	109	109	138	138	166	127	165	165	201	201	234
0.80	0.18	46	67	67	87	87	107	62	87	87	110	110	132	101	131	131	159	159	186
0.80	0.20	37	54	54	71	71	87	51	71	71	89	89	107	82	106	106	129	129	151
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.82	0.02	3329	4852	4852	6325	6325	7761	4565	6324	6324	7992	7992	9597	7409	9611	9611	11645	11645	13567
0.82	0.04	834	1215	1215	1585	1585	1945	1143	1584	1584	2002	2002	2404	1854	2406	2406	2916	2916	3398
0.82	0.06	372	542	542	707	707	867	509	706	706	893	893	1072	826	1072	1072	1299	1299	1514
0.82	0.08	210	306	306	399	399	490	287	399	399	504	504	606	466	605	605	733	733	855
0.82	0.10	135	197	197	257	257	316	185	256	256	324	324	390	299	388	388	471	471	549
0.82	0.12	94	138	138	180	180	221	129	179	179	226	226	272	208	271	271	329	329	383
0.82	0.14	70	102	102	133	133	163	95	132	132	167	167	201	154	200	200	243	243	283
0.82	0.16	54	78	78	102	102	126	73	102	102	129	129	155	118	154	154	187	187	218
0.82	0.18	43	62	62	82	82	100	58	81	81	102	102	123	94	122	122	148	148	173
0.82	0.20	35	51	51	66	66	82	47	66	66	83	83	100	76	99	99	121	121	141
0.84	0.02	3032	4419	4419	5761	5761	7069	4158	5760	5760	7280	7280	8742	6748	8753	8753	10606	10606	12357
0.84	0.04	760	1108	1108	1445	1445	1773	1042	1444	1444	1825	1825	2192	1690	2193	2193	2658	2658	3097
0.84	0.06	339	495	495	646	646	792	465	644	644	815	815	979	753	978	978	1186	1186	1382
0.84	0.08	192	280	280	366	366	449	262	364	364	461	461	554	425	552	552	670	670	782
0.84	0.10	124	181	181	236	236	290	169	235	235	297	297	357	273	355	355	431	431	503
0.84	0.12	86	126	126	165	165	203	118	164	164	208	208	250	191	248	248	301	301	352
0.84	0.14	64	94	94	123	123	151	87	122	122	154	154	185	141	183	183	223	223	260
0.84	0.16	49	72	72	95	95	116	67	94	94	119	119	143	108	141	141	172	172	201
0.84	0.18	39	58	58	76	76	93	54	75	75	95	95	114	86	112	112	137	137	160
0.84	0.20	32	47	47	62	62	76	44	61	61	77	77	93	70	92	92	111	111	130
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.86	0.02	2717	3961	3961	5164	5164	6336	3726	5162	5162	6524	6524	7835	6047	7844	7844	9505	9505	11074
0.86	0.04	682	994	994	1297	1297	1592	934	1295	1295	1638	1638	1968	1515	1967	1967	2384	2384	2779
0.86	0.06	305	445	445	581	581	713	417	579	579	733	733	881	676	878	878	1066	1066	1242
0.86	0.08	173	253	253	330	330	405	236	328	328	416	416	500	382	497	497	604	604	704
0.86	0.10	112	163	163	214	214	262	152	212	212	269	269	323	246	320	320	389	389	455
0.86	0.12	78	115	115	150	150	185	107	149	149	189	189	227	172	224	224	273	273	319
0.86	0.14	58	85	85	112	112	137	79	110	110	140	140	169	127	166	166	202	202	237
0.86	0.16	45	66	66	87	87	107	61	85	85	109	109	131	98	128	128	156	156	183
0.86	0.18	36	53	53	69	69	85	49	68	68	87	87	105	78	102	102	125	125	146
0.86	0.20	29	43	43	57	57	70	40	56	56	71	71	86	64	83	83	102	102	119
0.88	0.02	2385	3476	3476	4533	4533	5562	3270	4531	4531	5727	5727	6877	5305	6884	6884	8342	8342	9720
0.88	0.04	599	875	875	1141	1141	1401	821	1139	1139	1441	1441	1731	1331	1729	1729	2096	2096	2444
0.88	0.06	269	393	393	513	513	630	368	511	511	647	647	777	595	774	774	939	939	1096
0.88	0.08	153	224	224	293	293	360	209	290	290	368	368	443	337	439	439	534	534	623
0.88	0.10	99	145	145	190	190	234	135	188	188	239	239	288	217	284	284	346	346	404
0.88	0.12	70	102	102	134	134	166	95	133	133	169	169	203	152	199	199	243	243	284
0.88	0.14	52	77	77	100	100	124	70	99	99	126	126	152	113	148	148	181	181	212
0.88	0.16	40	60	60	78	78	97	55	77	77	98	98	118	87	115	115	140	140	164
0.88	0.18	32	48	48	63	63	78	44	61	61	78	78	95	69	92	92	112	112	132
0.88	0.20	27	39	39	52	52	64	36	50	50	64	64	78	57	75	75	92	92	108
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.90	0.02	2034	2967	2967	3869	3869	4748	2789	3866	3866	4887	4887	5869	4525	5872	5872	7117	7117	8293
0.90	0.04	513	749	749	978	978	1201	702	975	975	1234	1234	1483	1137	1478	1478	1794	1794	2092
0.90	0.06	231	338	338	442	442	543	315	439	439	557	557	670	510	664	664	807	807	942
0.90	0.08	132	194	194	254	254	312	180	251	251	319	319	384	290	378	378	461	461	539
0.90	0.10	86	127	127	166	166	205	117	164	164	208	208	251	187	246	246	300	300	351
0.90	0.12	61	90	90	118	118	146	82	116	116	148	148	178	132	173	173	212	212	249
0.90	0.14	45	67	67	89	89	110	61	87	87	111	111	134	98	129	129	158	158	186
0.90	0.16	35	53	53	70	70	86	48	68	68	87	87	105	76	100	100	123	123	145
0.90	0.18	29	43	43	56	56	70	38	54	54	70	70	85	61	81	81	99	99	117
0.90	0.20	24	35	35	46	46	58	31	45	45	58	58	70	50	66	66	81	81	96
0.92	0.02	1667	2432	2432	3172	3172	3894	2284	3168	3168	4006	4006	4812	3705	4810	4810	5832	5832	6797
0.92	0.04	422	618	618	808	808	993	578	803	803	1018	1018	1224	934	1217	1217	1477	1477	1724
0.92	0.06	191	281	281	369	369	454	261	365	365	463	463	558	421	550	550	670	670	783
0.92	0.08	110	163	163	214	214	264	150	210	210	268	268	323	240	315	315	385	385	451
0.92	0.10	72	107	107	141	141	175	98	138	138	176	176	213	156	206	206	253	253	297
0.92	0.12	51	77	77	101	101	126	69	98	98	126	126	153	110	146	146	180	180	212
0.92	0.14	39	58	58	77	77	95	52	74	74	95	95	116	82	110	110	135	135	159
0.92	0.16	30	46	46	61	61	75	41	58	58	75	75	91	64	86	86	106	106	125
0.92	0.18	25	37	37	49	49	61	33	47	47	61	61	74	51	69	69	85	85	101
0.92	0.20	20	31	31	41	41	51	27	39	39	50	50	61	42	57	57	71	71	84
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.94	0.02	1283	1873	1873	2445	2445	3003	1757	2439	2439	3086	3086	3709	2847	3700	3700	4488	4488	5233
0.94	0.04	328	482	482	632	632	777	448	625	625	794	794	957	723	944	944	1149	1149	1343
0.94	0.06	151	223	223	293	293	362	205	288	288	367	367	443	328	432	432	528	528	619
0.94	0.08	88	131	131	173	173	214	119	168	168	215	215	261	189	250	250	307	307	362
0.94	0.10	58	88	88	116	116	144	78	112	112	144	144	175	124	165	165	204	204	241
0.94	0.12	42	63	63	84	84	105	56	81	81	104	104	127	88	118	118	146	146	173
0.94	0.14	32	48	48	65	65	81	42	61	61	79	79	97	66	89	89	111	111	132
0.94	0.16	25	38	38	51	51	64	33	48	48	63	63	77	52	70	70	88	88	104
0.94	0.18	20	31	31	42	42	53	27	39	39	51	51	63	42	57	57	71	71	85
0.94	0.20	17	26	26	35	35	44	22	33	33	43	43	53	34	47	47	59	59	71
0.96	0.02	884	1294	1294	1692	1692	2081	1208	1682	1682	2132	2132	2565	1954	2545	2545	3093	3093	3611
0.96	0.04	232	344	344	452	452	559	315	443	443	566	566	684	504	664	664	812	812	953
0.96	0.06	109	164	164	217	217	270	147	209	209	269	269	328	233	310	310	383	383	451
0.96	0.08	65	99	99	132	132	164	87	125	125	162	162	198	136	183	183	228	228	270
0.96	0.10	44	67	67	90	90	113	58	85	85	111	111	136	90	123	123	154	154	183
0.96	0.12	32	50	50	67	67	84	42	62	62	81	81	100	65	89	89	112	112	134
0.96	0.14	25	38	38	52	52	66	32	48	48	63	63	78	49	68	68	86	86	103
0.96	0.16	20	31	31	42	42	53	26	38	38	50	50	63	39	54	54	69	69	83
0.96	0.18	16	25	25	35	35	44	21	31	31	42	42	52	31	44	44	56	56	68
0.96	0.20	14	21	21	29	29	37	17	26	26	35	35	44	26	37	37	47	47	57
		Power=0.9						Power=0.95						Power=0.99
		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05		α=0.2		α=0.1		α=0.05
π	CD(tl)	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail	1 tail	2 tail
0.98	0.02	475	705	705	929	929	1149	645	909	909	1161	1161	1405	1033	1361	1361	1667	1667	1956
0.98	0.04	134	205	205	274	274	342	179	259	259	337	337	412	280	379	379	472	472	560
0.98	0.06	67	104	104	141	141	178	88	130	130	171	171	211	135	186	186	235	235	282
0.98	0.08	41	66	66	90	90	114	54	81	81	108	108	134	81	114	114	145	145	176
0.98	0.10	29	46	46	64	64	81	37	56	56	76	76	95	55	78	78	101	101	123
0.98	0.12	21	35	35	48	48	62	27	42	42	57	57	72	40	58	58	75	75	92
0.98	0.14	17	28	28	39	39	50	21	33	33	45	45	57	31	45	45	59	59	72
0.98	0.16	14	23	23	32	32	41	17	27	27	37	37	47	25	36	36	48	48	59
0.98	0.18	11	19	19	27	27	34	14	22	22	31	31	39	20	30	30	40	40	49
0.98	0.20	10	16	16	23	23	29	12	19	19	26	26	33	17	25	25	33	33	41