附录

标准正态累积分布表

图 1 标准正态分布表表示的是 \(X \leq x\) 概率，即阴影部分面积。

X	0.0	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0	0.5	0.504	0.508	0.512	0.516	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.5517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.591	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.648	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.67	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.695	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.719	0.7224
0.6	0.7257	0.7291	0.7324	0.7357	0.7389	0.7422	0.7454	0.7486	0.7517	0.7549
0.7	0.758	0.7611	0.7642	0.7673	0.7704	0.7734	0.7764	0.7794	0.7823	0.7852
0.8	0.7881	0.791	0.7939	0.7967	0.7995	0.8023	0.8051	0.8078	0.8106	0.8133
0.9	0.8159	0.8186	0.8212	0.8238	0.8264	0.8289	0.8315	0.834	0.8365	0.8389
1	0.8413	0.8438	0.8461	0.8485	0.8508	0.8531	0.8554	0.8577	0.8599	0.8621
1.1	0.8643	0.8665	0.8686	0.8708	0.8729	0.8749	0.877	0.879	0.881	0.883
1.2	0.8849	0.8869	0.8888	0.8907	0.8925	0.8944	0.8962	0.898	0.8997	0.9015
1.3	0.9032	0.9049	0.9066	0.9082	0.9099	0.9115	0.9131	0.9147	0.9162	0.9177
1.4	0.9192	0.9207	0.9222	0.9236	0.9251	0.9265	0.9279	0.9292	0.9306	0.9319
1.5	0.9332	0.9345	0.9357	0.937	0.9382	0.9394	0.9406	0.9418	0.9429	0.9441
1.6	0.9452	0.9463	0.9474	0.9484	0.9495	0.9505	0.9515	0.9525	0.9535	0.9545
1.7	0.9554	0.9564	0.9573	0.9582	0.9591	0.9599	0.9608	0.9616	0.9625	0.9633
1.8	0.9641	0.9649	0.9656	0.9664	0.9671	0.9678	0.9686	0.9693	0.9699	0.9706
1.9	0.9713	0.9719	0.9726	0.9732	0.9738	0.9744	0.975	0.9756	0.9761	0.9767
2	0.9772	0.9778	0.9783	0.9788	0.9793	0.9798	0.9803	0.9808	0.9812	0.9817
2.1	0.9821	0.9826	0.983	0.9834	0.9838	0.9842	0.9846	0.985	0.9854	0.9857
2.2	0.9861	0.9864	0.9868	0.9871	0.9875	0.9878	0.9881	0.9884	0.9887	0.989
2.3	0.9893	0.9896	0.9898	0.9901	0.9904	0.9906	0.9909	0.9911	0.9913	0.9916
2.4	0.9918	0.992	0.9922	0.9925	0.9927	0.9929	0.9931	0.9932	0.9934	0.9936
2.5	0.9938	0.994	0.9941	0.9943	0.9945	0.9946	0.9948	0.9949	0.9951	0.9952
2.6	0.9953	0.9955	0.9956	0.9957	0.9959	0.996	0.9961	0.9962	0.9963	0.9964
2.7	0.9965	0.9966	0.9967	0.9968	0.9969	0.997	0.9971	0.9972	0.9973	0.9974
2.8	0.9974	0.9975	0.9976	0.9977	0.9977	0.9978	0.9979	0.9979	0.998	0.9981
2.9	0.9981	0.9982	0.9982	0.9983	0.9984	0.9984	0.9985	0.9985	0.9986	0.9986
3	0.9987	0.9987	0.9987	0.9988	0.9988	0.9989	0.9989	0.9989	0.999	0.999

卡方分布临界值表

图 2 单侧卡方检验临界值

显著水平	0.5	0.25	0.1	0.05	0.01	0.005	0.001
自由度
1	0.455	1.323	2.706	3.841	6.635	7.879	10.828
2	1.386	2.773	4.605	5.991	9.21	10.597	13.816
3	2.366	4.108	6.251	7.815	11.345	12.838	16.266
4	3.357	5.385	7.779	9.488	13.277	14.86	18.467
5	4.351	6.626	9.236	11.07	15.086	16.75	20.515
6	5.348	7.841	10.645	12.592	16.812	18.548	22.458
7	6.346	9.037	12.017	14.067	18.475	20.278	24.322
8	7.344	10.219	13.362	15.507	20.09	21.955	26.124
9	8.343	11.389	14.684	16.919	21.666	23.589	27.877
10	9.342	12.549	15.987	18.307	23.209	25.188	29.588
11	10.341	13.701	17.275	19.675	24.725	26.757	31.264
12	11.34	14.845	18.549	21.026	26.217	28.3	32.909
13	12.34	15.984	19.812	22.362	27.688	29.819	34.528
14	13.339	17.117	21.064	23.685	29.141	31.319	36.123
15	14.339	18.245	22.307	24.996	30.578	32.801	37.697
16	15.338	19.369	23.542	26.296	32	34.267	39.252
17	16.338	20.489	24.769	27.587	33.409	35.718	40.79
18	17.338	21.605	25.989	28.869	34.805	37.156	42.312
19	18.338	22.718	27.204	30.144	36.191	38.582	43.82
20	19.337	23.828	28.412	31.41	37.566	39.997	45.315
21	20.337	24.935	29.615	32.671	38.932	41.401	46.797
22	21.337	26.039	30.813	33.924	40.289	42.796	48.268
23	22.337	27.141	32.007	35.172	41.638	44.181	49.728
24	23.337	28.241	33.196	36.415	42.98	45.559	51.179
25	24.337	29.339	34.382	37.652	44.314	46.928	52.62
26	25.336	30.435	35.563	38.885	45.642	48.29	54.052
27	26.336	31.528	36.741	40.113	46.963	49.645	55.476
28	27.336	32.62	37.916	41.337	48.278	50.993	56.892
29	28.336	33.711	39.087	42.557	49.588	52.336	58.301
30	29.336	34.8	40.256	43.773	50.892	53.672	59.703
31	30.336	35.887	41.422	44.985	52.191	55.003	61.098
32	31.336	36.973	42.585	46.194	53.486	56.328	62.487
33	32.336	38.058	43.745	47.4	54.776	57.648	63.87
34	33.336	39.141	44.903	48.602	56.061	58.964	65.247
35	34.336	40.223	46.059	49.802	57.342	60.275	66.619
36	35.336	41.304	47.212	50.998	58.619	61.581	67.985
37	36.336	42.383	48.363	52.192	59.893	62.883	69.346
38	37.335	43.462	49.513	53.384	61.162	64.181	70.703
39	38.335	44.539	50.66	54.572	62.428	65.476	72.055
40	39.335	45.616	51.805	55.758	63.691	66.766	73.402
41	40.335	46.692	52.949	56.942	64.95	68.053	74.745
42	41.335	47.766	54.09	58.124	66.206	69.336	76.084
43	42.335	48.84	55.23	59.304	67.459	70.616	77.419
44	43.335	49.913	56.369	60.481	68.71	71.893	78.75