stat tables

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)

0.0@90.m080.w80.(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,ffi030.00030.m020.m020.0@20.0001

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

3.093.002.922.852.792.742.702.662.632.@2.572.552.332.5'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 9.@7.72 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.