-
Colurnn (a) lists Z scores frorn 0.{X} to 4.00. Only po*itive
scores are displaycdbut because rhe numal curve is syrnmetrical,
the areas feir rcgative score'E will bEexactly tlp same as
areasfupo*itive scores. Colurm tb) lists the proponion of thetotal
area between the Z gcwe md the meur. Figrne A.1 displays areas of
this type.Column (c) lisrs *re propertion of ttm uea bcymd the Z
wrare, a*d Figtrre A.2 dis-plays ttris type of rea.
FIGURE A1 Area Befixean llcanandZ
FlcUnE A2 ArwBefordZ
(b)Area
BelweenM66ntrdZ
(a)
z
{a)
z
(b)Area
BtweenMean ardZ
(c)A,rea
Beyondz
(c)Arq.a
Bepndz
0.00o.010.020.030.040.050.06o.070,oB0.090.100.r10.120_13ai40.150.160.170.180.19a.2a0.210.22
0.00000.0M00.00800"0120o.01600.01s9a.g23sa.o27g0.0319o035,90.0398
0.04380.04780"05170.05570.05960.06360.06754.47140.07530.07s30.08320.0871
0.50000.49609.49200.48800.48400.48010.4v814.47210.46814.4s414.46420.4562fr.45220"44830.44484.4404o.43544.43234.4286o.42474AN70.4168a.4129
4.230.244.254.260.274.280.290.300.310.320340.340.350.36o.370.380.390.406.418.424.434.44o.45
0.0910o.0s4B0.0987aia^a0.10640.11030.1 1
410.1179a.12174.12550.12930.13310.13680.1406o.14430.14800.15170.15540.15910.16280.16640.17000.1736
0.4090o.4t)520.4013439740.*136a38970.38590.3821a37ffi0.37450.3/070.36690.36320.35S40.35574s5200.34830.34460.340sas3v2033360.33008.3264
@ Ceftgag Leamiog 2013 O Cengage Learniflg 2013
-
ABEA UFJDER'IHE FIORMAI- ctJR'fE *7
(a)
z
(a)
0.460.470.480.490.50
(b)Area
BetweenMeffiardZ
(c)Area
Beyondz
(b)kea
Betweenli@nandZ
{c}Area
Beyondz
0.510.520.534.540.550.564.570.580.590.600.614.620.630.640.650.660.670.680.690.700.71a.720.730.740.750.760.774.780.790.800.814.820.830.840.850.864.870.880.890.900.91o.s20.93o.s40.950.960.970.980.991.00
o.17720,18084i844o.18790.19150.19500.19850.2019g.&34o.20ffio.21234.2157o.21ffi4.22244.22574.2291fr.2324o.23570.23894.24224.24544.24864.2517a.25490.25800.2611a.26424.2673o.27A34.2734o.27U4.27940.28234.28520.28810.29100.2939o.2s,670.2s50.30230.30510.30780.3't060.31330.31590.31860.92120.323843,2640.32890.33150.33400.33650.33890.3413
o.32280.31920.31560.31210"3085
0.30500.3015a.m10.2946o.2s,12a.28778.2M,30.28100.27764.27434.27490.26764.2643o.2611a.2576o.25464.25't44,24834.24514.24240,23890.23584.2327o.22970.22660.22360.2206a.21770.21480.21190.20s04.24610.20330.2005o.1s770.19494.1w20.18940.18670.1841
0.18't40_17884.17620.17364.17110.16850.16600.16350.16110.1587
1.011.421.031.041.051.061.071.SB1.091.101.111.'.tz1.131.14't.15''l.161.171.181.191.m1.211.221.231.241.251.261.271.281.291.301.3'l1.321.331.341.35t..,o1,371.381,391.44
1.411.421.431.441.451,461.471.481.491.50
1.511.521.531.il1"55
0.34380.34610.34850.3s80.35310.355443.5770.359x,4.ffi210.364d]0.36650.36860.37080.e729437490.3770a37W0.38100.38300.38490.38690.38880.39070.39250.3944o.39620.39800.3s970.40150.40320.40490.40664.40820.40s90.41150.41314.4147o.41624"41774.4192o.4247o.42224.42364.42510.42654.4279o.42gyz0.4306o.43194.4w24.43/.50.4i!570.43704.4w20.4394
o.1ffiz0.153S0.1515o.14920.1465o.1446o.14230.14010.1379o.1357
0.13350.1314aiN2o.12710.12510.12300.12100.1
1SO0.11700.11510.11310.11120.10930"10750i10560.10380.10200.10030.09850.0s680.09510.09&40.09180.0s10.08850.08690.ffi530.08380.08230.08080.07930.477&a.a7M9.47490.07354.472'lo.07080.06s4o.06810.06680.06550.06430.06300.06180.0606
-
3S APPENDIXA(al
z
(a) (b)Arp.g
Belweni#ean ard Z
(c)Area
Beyondz
(b)Ar6a
BetweenMeanard Z
{c}Aree
Bepndz
1.561.571.581.591.601.611.621.631.641.651.66"t.671.681.691.701.711.721.731.741.751.761.771.781.791.801.811.82't.831.841.851.861.871.881.891.901.911.v21.931.941.951.961.971.981.992.002.012.O22.032.U2.A52.062.472,M2.092.10
0.44060.44180.44294.4441o.44520.446.34.4474a.44840.44950.45050.45154.45250.45350.45450.45540.45640.4573o.45420.45910.45S10.46080.46160.46250.46330.46410.46490.46564.46640.46714.4&780.4686o,46330.4699a.47ffia.47134.47194.4726o.47320.47389.47440.4750o.47560.4761o.4767D.4772
a.47780.47834.4788o.4w3q.47W0.48030.48080.48129.48170.4s21
0.05940.05820.05710.05590.otnl0.05370.05260.05160"05050.04950.0485a.04750.04650.04550.0446o.o4t!6O,MZ/0.0418o.o4m0.040J0.03920.03840.03750.0s70.03590.03510.08440.03it60.0s29a.93220.03140.0s70.030ra.aN40.42870.0281a.a2740.02686.W62a.42ffi0.02504"02440.02390.02334.42280.4u2o.aa70.o212a.aaJ7a.aNz0.01970"01s20.01880.01830.0179
2.112."t22.132.142.152.162.172.182.192.2A2.212"222.232.242.252.262.272.82.292,N2312.322.332.U2.352.362.372.3t2"392.402.412.422.432.442.452.462.472-482.492.542.5't2.522.532.il2.552.562.5V2.582.592.ffi2.612.622.632.642.65
0.4826o.4tl300.48340.48380-48420.48460.48500.48$ra.48570.4861
0.48640"4868a.4871o.4875Q.48780.48814.44844.44870.48900.48S0.48960.48S80.4so10.49040.49660.4s0s0.4s110.49130.49160.4918o.49244.49220.49254.49270.49290.4s314.49324.49340.4935o49380.49400.49410.4s430.4s450.49460.49480.4s4s0.4s51o.49520.49530.49550.49560.49570.4s590.4960
a.at740.01700.01660.01520.01580.01540.01500.01460.01430.01390.01360.01320.0129a.a125a.41220.01190.01160.01130.01100.0107
0.01040-01020.00990.0m60.00s40.00910_&)890.00870.00840.00820.00800.00780.00750.00730.007''0.00690.00680.00660.00640.00620.00600.00590.00570.00550.00540.00520.00510.0&*90.m480.00470.00450.00440.00430.00410.004tI
-
AHEAUNOERTHENOffMAI.CUEVE 38
(a){a} (b)Area
Betweeniran ffdZ
(c)Area
Bepndz
(b)Area
BetweenMenamdZ
(c)Area
Bq/ondz
2.66?'-672.682.692.702.712.722.732.742.752.762.772.782.792.802.812.822.832.U2.852.862.872.882.852.W2.912.922.532.942.352.962.972.982.W3.003.013.423.033.M3.053.063.O73.083.@3.103.113.12
0.4961o.4w20.4s630.496,10.4
650.496,60.49670.49680.4ss0.4s700.4971o.4s724.4s734.49740.4974o.49750.4976a.49770_4s770.49780.49794.49750.49800.49810.4s10.4w20.4s20.49830.4ffi40.49840.49850.4s50.49860.49860.4s860.49870.4sI70.49880.4gffi0.4s890.49890.49@0.49900.49ffi0.4w00.49910.4991
0.003s0.00380.00370.00360.00350.00340.0CI330,00320.00310.00.300.00290.00284.m.270.00260.0@60.00250.00240.00230.0023fr.w22o.aa214.w210.00200.m19o.001s0.00180.00180.00170.ffi160.00160.m150.00150.00140.00140.00140.00130.m130.00.t20.tr,120.00110.001
10.m110.00100.00100.00100.00090.0009
3.133,143.'t53.163.173.183.1S3.ffi3.213.223.233"243.253.263.273.283.8s.303.313.323.333.343.353.363.S73.383.3S3.403.413.423.433.443.453.463.473.483.493.503.603.703.80s.904.00
0.49310.49924.4w2a.4w20.4ss20.4s930-4w0.4s930.4sm0.4ssd0.4g940"49S40.4w40.49940.49S50.4s950.4ss0.49950,49ffi0.49s50.49360.49S60.4s96o.4s60.4s960.4ss60.4997o.4gg70.4w70.49s70.49976-45574.4*t74.4w70,49974.49970.49980.49980"49S80.49990.499s0.4ss9o.4gsx)
[email protected].(u)80.0CI080.00070.m7o.00070.00070.00060.00060,ffxl60,00060.ffn60.00050.00050.00050.@50.(m50"m50.00040.m40.00040"(ro40.00040.0m4o.ffiI0.00030.m030.000s0.00080.m030.00030.00frt0,[email protected]
0.0001
-
Use this table to find the crftical regiof, (step 3 of thc
five-step model) for tests ofsignificance with sample means whm the
sample size (iY; is small. First, choosean alpha level a*d a one-
or two-tailed test. Then, find degrees of freedorn to findthe f
scare &at mrks tke beginning of the critical regim.
Leve* d Significanee for One-TailedTestDegrees
dFreedqn(dfl
.01 .005 .0005Lerd of Significance for Trro-Tailsd Tsst
1
2J4567Is
1011121314t5't6171819202122232425262728N304,o60paq
Sourca:T&le lll of Fishs and Yates. Statistical Tables for
Biotagicat, Agricutturat and Medica!Flg,earch, publishd by Longman
Group Ltd., Lffidsn (1924), 6th edition (previously publishedby
Oliver & Boyd Ltd., Edinburgh). Beprinted by permission of
Addison Wesley Longman Ltd,
.425.05.10
.@1-01'.o2.05.10.N3.4781.8861.6381.5331.4761.4441.4151.3971.3831.3721.3631.3561.3501.e451.U11.3371.3331.330'1.3281.325't.3231.3211.3191.3181.3161.3151.3141.313"1.311
1.310't.3031.2S61.2891.282
6.3142.982.3532.1322.4151.9431.8951.8601.8331.8121.7961.7821.7711.7611.7531.7461.7401.741.7251.7251.721't.7171.7141.7111"7081.7ffi1.7431.7011.6991.6971.6841.6711.6581.645
12.7064.3033.1822.7762.5712.4472.ffis2-3062.2622"2282.2A12.1792.1602.'t452.',t312J2A2.1102.1012.O932.4862.0802.0742.652"4642"0642.0562.4522.U&2.0452.A422.A212.AAA1.9801.S60
31.8216.S654.5413.7473.3653.r432.W82.8962.8212.7U2.7182.6812.6502.6242.6022.5832.5872_5
22.5392.5282-5182.5082,5002.4922.4852.4792.4732.4672.4622.4572.4%2,3942.3582-3%,
63.657 636.61S9.S25 31.5S85.841 12.5414.ffi4 8.6104.032
5,8593.707 s"ssg3.4W 5.4053.355 5.0413.250 4.7813.16S 4.ffi73.106
4.4373.055 4.3183.A12 4"2212.977 4.1402.947 4.A732"9/2.1 ,f
.0152.898 3"9652.878 3.9222.861 3.8832_&45 3.8502"831
3_8192.819 3.7522.807 3.76?2.797 4.7452.787 3.7252.779 3.7A72.771
3.6S02.763 3.6742.7ffi 3.65S2.750 3.M62.704 3.5512.66A 3.4602.617
3.3732.576 3.291
-
Use this table to find the critical regi*n (step 3 of the
five-srep rnodel) for analysisof variance tests. Choose an alpha
level of eith6 O.O5 or 0,01 and then find thedegrees of, freedom to
find the F ratio that rnarks the beginning of the criticalregion.
\Ialues of n, and /r2 represent the dcgrees of freedom associated
with thebetween and within estimates of variance, respectively.
P=.05n1n1 2412
1
2345b7II
10
11121314151617181S2A
21222324252627ZA293040
161.418.5110.137.716.615.9SEEO5.325.124.96l.u4.754.674.@4-A4.494.454.4"14.384.354.324.304.284.264.244.224.214.244.184.17
4.084.003.523.84
19S.519.009.556.945795.144.744.464.264ia3.983.883.803.743.683.633.593.554.523,493.473.443.423.443.383.373.353.343,333.323.233.153.W2.99
215.719.169.286.535.414.764.354.A73.863.71
3.593.4S3.413.343.293.243.203.163.133.103.073.053.033.012.992.982.%2.952.932.522.U2.762.682.ffi
224.619.259.126.3S5.194.534.123.U3.633.483.363.263.183.113.063.012.562.932.902.W2.842.822.8A2.782.762.742.732.712.702.692.61
2.522.452.37
230.219.30s.016.265.054.39&.w3.693.483.333.203.113,A22"982.902.8.52.812.772.742.71
2.682-682.642.622.ffi2.592.572.562.542.53
2.452.372.29
2.21
234.O19.338.946.164.954.283.873.58e37.a-tz
[email protected]'l2.492.472.462.442.4e2.42
2.342.252.17
2.09
238.919.378.846.044.824.153.733.443.233"07,OE2"852.772.7A2.U2.552.552.512.482.452.422.4A2.382,362.342.322.302.292.282.27
2.182JA2.A21.94
243.51S.418.745.914,684.003.573.283.O72.51
2.792.62,642.532.482.422.Sg2.U2.312.282.252"232.242.182.162.152.132.122.142.092.001.92'r.83
1.75
249.0 254.319;45 19.508.64 B.s35.77 5.634.53 4.363.84 3.673.41
3.233j2 2.932.90 2.712.74 2.542.61 2.402.50 z.ffi2,42 2.212.95
2.132.N 2.A72.24 2.012.1$ 1.962.'t5 1.922.11 1.882.08 't.842.45
1.812.03 1.782.AO 1.761.98 1.731.96 1.711.S5 1.6S1.S3 1.671.S1
1.651"90 1.M1.89 1.621 .79 1.511.70 1.3S60
1m!
1"61 1.251.52 1.00
-
ofsrElBuTloiloFF 404
p=.01n1nzI ?4t2
'l 40522 54.493 U.124 21"245 16.266 13.747 1?.25I 11.26I 10.5610
10.0411 9.6512 9.3313 9.0714 8.8615 8.6816 8.5317 8.4018 8.2819
8.18zfl &1021 8.0222 V.94n 7.8824 7.8225 7.7726 7.7227 7.68n
7.64n 7.6030 7.5640 7.3'.160 7.08
ea 6.85I 6.M
4999 5403s9.01 99.1730.81 29.4618.00 16.6913.27 12.4610.92
9.789.55 8.458.65 7.5S8.42 6.397.56 6.55
7 -20 6.226.93 5,S56.70 5.746.s1 5.566.36 5.426.23 5.256.11
5.185.01 5.095.93 5.015.85 4.945.78 4.875.72 4.825.66 4.765.61
4.725.57 4.685.53 4.U5.49 4.W5.45 4.575.42 4.U5.39 4.515.18
4.314.S8 4.134.75 3-954.6fi 3.78
5625 576499.25 99.3028.71 2&.2415.98 15.5211.39 10"979.'t5
8.757.85 7.ffi7.U 6.636.42 6.065.Sg 5.645.67 5.325.41 5,065.20
4.865.03 4,ffi4.89 4,.564.77 4.444.67 4.344.ffi 4.254.50 4.174.43
4.104.37 4.A44.31 3.SS4.26 3.944.22 3.904.18 3.864.14 3.824.11
3.784.87 3.754.44 3.734.42 3.703.83 3.513.65 3.343.48 9j73.32
3.82
5859 5S81ss"33 99.3627.91 n.4915.21 14.8010.67 1A.278.47 8.10v1s
6.846.37 6.005.80 5.475.3S 5.065.07 4.744.82 4.504.62 4.304.46
4.144.32 4.004.20 3.894.10 3'794.U 3.713.S4 3.633.87 3.563.81
3.513.76 3.453.71 3.413.67 3.S3"63 3.S23.59 3.253.56 3.263.53
3.253.50 3.203.47 3)73.29 2.W3.12 2.822.% z.ffi2.W 2.$1
2.50 2.122.e4 1.952.18 1.79
6106 62e4 636699.42 s9.46 WL5027,45 26.60 26.1214.37 13.93
13.,t69.89 9.47 [email protected] 7.31 6.886.17 6.07 5.655,67 6.28 4.865.11
4.73 4.314.71 4.33 3-914.44 4.A2 3.604.J6 3.78 3.363.36 3.5S
3.163.80 3.43 3.003.67 3.29 2.8V3.55 3.18 2.753.45 3.08 2.653. 7
3.00 2.573"30 2.92 2.493.23 2.86 2.423.17 2.8A 2363.12 2.75
2"313.47 2.70 2.263.0iI z.ffi 2.212.* 2.62 2.172.96 2.58 zie2.93
2.45 2.102.W 2.52 2.M2.87 2.49 2.A32.84 2.47 2.O12.66 2.29 1.80
1.601.381-00
Srurca Thh V ol Frsher and Yates. Stafbtbd Tfutsg lor Eldryica4
Agtitrufuxd and hfedhd fu#ffih, puHisted by Longrnan Grwp
Ltd.,London (1974), 6th edition (prevkNsly puuished by Oliver and
Boyd Ltd., Edinburgh). Reprinted by pemission of Pearson Education
Ltd.
