excel____T检验_公式

1、 成成组组设设计计的的两两样样本本均均数数比比较较的的 t t 检检验验编编号号样样 本本 甲甲样样 本本 乙乙例例 题题12600818363 34746344 4589710285 5548813186 6639015787 7456613188 8677916789 9577350991010234931631111121213131414151516161717181819192020合合计计X X5376446270合合计计X X方方3.03E+08 9.03E+08样样本本数数：1010自自由由度度：1818 均均数数：5376.44627均均方方差差：

2、14207014 6.89E+08 t t 值值: :0 0. .2 26 68 81 13 33 3 t t界界值值: :P=P= 0.05P=P= 0.01结结 论论单侧双侧单侧双侧1.7341.7342.1012.1012.5522.5522.8782.878单单侧侧检检验验结结果果：P P 0.050.05P=P= 0.3958230.395823双双侧侧检检验验结结果果：P P 0.050.05P=P= 0.7916450.791645t t界界值值表表N单侧0.05 双侧0.05 单侧0.01 双侧0.0116.31412.70631.82163.65722.924.3036.96

3、59.92532.3533.1824.5415.84142.1322.7763.7474.60452.0152.5713.3654.03261.9432.4473.1433.70771.8952.3652.9983.49981.862.3062.8963.35591.3832.2622.9213.25101.8122.2282.7643.169111.7962.2012.7183.106121.7822.1792.6813.055131.7712.162.653.012141.7612.1452.6242.977151.7532.1312.6022.947161.7462.122.5832.9

4、21171.742.112.5672.898181.7342.1012.5522.878191.7292.0932.5392.861201.7252.0862.5282.845211.7212.082.5182.831221.7172.0742.5082.819231.7142.0692.52.807241.7112.0642.4922.797251.7082.062.4852.787261.7062.0562.4792.779271.7032.0522.4732.771281.7012.0482.4672.763291.6992.0452.4622.756301.6972.0422.4572

5、.75311.6962.042.4532.744321.6942.0372.4492.738331.6922.0352.4452.733341.6912.0322.4412.728351.692.032.4382.724361.6882.0282.4342.719371.6872.0262.4312.715381.6862.0242.4292.712391.6852.0232.4262.708401.6842.0212.4232.704411.6752.0092.4032.678511.67122.392.66611.6671.9942.3812.648711.6641.992.3742.63

6、9811.6621.9872.3682.632911.661.9842.3642.6261911.6531.9722.3452.6014911.6481.9652.3342.5869911.6461.9622.332.5819999911.64491.962.32632.5758 成成组组设设计计的的两两样样本本几几何何均均数数比比较较的的 t t 检检验验例例题题编编号号样样本本甲甲LgXLgX样样本本乙乙LgXLgX1 1401.60206501.698972 2201.30103401.602063 3301.477121301.4771214 4251.39794351.5440685

7、 5101601.7781516 6151.176091701.8450987 7251.39794301.4771218 8301.477121201.301039 9401.60206251.397941010101701.8450981111151.176091351.5440681212301.477121251.39794131300141400151500161600171700181800191900202000合合计计X X29016.0845849018.90867合合计计X X方方820022.046392340030.15691样样本本数数：1212自自由由度度：2222

8、 均均数数： 24.16667 1.340381 40.83333 1.575722均均方方差差： 1191.667 0.486921 3391.667 0.362105 t t 值值: :2 2. .9 93 34 44 43 3 t t界界值值: :P=P= 0.05P=P= 0.01结结论论单侧双侧单侧双侧1.7171.7172.0742.0742.5082.5082.8192.819单单侧侧检检验验结结果果：P P 0.010.01P=P= 0.0038370.003837双双侧侧检检验验结结果果：P P 0.010.01P=P= 0.0076730.007673t t界界值值表表自由

9、度单侧0.05 双侧0.05 单侧0.01 双侧0.0116.31412.70631.82163.65722.924.3036.9659.92532.3533.1824.5415.84142.1322.7763.7474.60452.0152.5713.3654.03261.9432.4473.1433.70771.8952.3652.9983.49981.862.3062.8963.35591.3832.2622.9213.25101.8122.2282.7643.169111.7962.2012.7183.106121.7822.1792.6813.055131.7712.162.653.

10、012141.7612.1452.6242.977151.7532.1312.6022.947161.7462.122.5832.921171.742.112.5672.898181.7342.1012.5522.878191.7292.0932.5392.861201.7252.0862.5282.845211.7212.082.5182.831221.7172.0742.5082.819231.7142.0692.52.807241.7112.0642.4922.797251.7082.062.4852.787261.7062.0562.4792.779271.7032.0522.4732

11、.771281.7012.0482.4672.763291.6992.0452.4622.756301.6972.0422.4572.75311.6962.042.4532.744321.6942.0372.4492.738331.6922.0352.4452.733341.6912.0322.4412.728351.692.032.4382.724361.6882.0282.4342.719371.6872.0262.4312.715381.6862.0242.4292.712391.6852.0232.4262.708401.6842.0212.4232.704411.6752.0092.

12、4032.678511.67122.392.66611.6671.9942.3812.648711.6641.992.3742.639811.6621.9872.3682.632911.661.9842.3642.6261911.6531.9722.3452.6014911.6481.9652.3342.5869911.6461.9622.332.5819999911.64491.962.32632.5758配配对对设设计计的的差差值值均均数数与与总总体体均均数数0 0比比较较的的t t检检验验例例题题编编号号治治疗疗前前治治疗疗后后差差值值d dd d 平平方方1 1355024501100

13、12100002 220002400-4001600003 330001800120014400004 4395032007505625005 5380032505503025006 637502700105011025007 7345025009509025008 830501750130016900009 900101000111100121200131300141400151500161600171700181800191900202000265502005065007370000样样本本数数：8 8 d d 均均数数：812.5812.5自自由由度度：7 7d d 标标准准差差 546

14、.2535546.2535 t t 值值: :4 4. .2 20 07 70 01 16 6 t t界界值值: :P=P= 0.05P=P= 0.01结结论论单侧双侧单侧双侧1.8951.8952.3652.3652.9982.9983.4993.499单单侧侧检检验验结结果果：P P 0.010.01P=P= 0.00200030.0020003双双侧侧检检验验结结果果：P P 0.010.01P=P= 0.00400050.0040005t t界界值值表表N单单侧侧0.050.05 双双侧侧0.050.05 单单侧侧0.010.01双双侧侧0.010.011 16.31412.70631

15、.82163.6572 22.924.3036.9659.9253 32.3533.1824.5415.8414 42.1322.7763.7474.6045 52.0152.5713.3654.0326 61.9432.4473.1433.7077 71.8952.3652.9983.4998 81.862.3062.8963.3559 91.3832.2622.9213.2510101.8122.2282.7643.16911111.7962.2012.7183.10612121.7822.1792.6813.05513131.7712.162.653.01214141.7612.1452

16、.6242.97715151.7532.1312.6022.94716161.7462.122.5832.92117171.742.112.5672.89818181.7342.1012.5522.87819191.7292.0932.5392.86120201.7252.0862.5282.84521211.7212.082.5182.83122221.7172.0742.5082.81923231.7142.0692.52.80724241.7112.0642.4922.79725251.7082.062.4852.78726261.7062.0562.4792.77927271.7032

17、.0522.4732.77128281.7012.0482.4672.76329291.6992.0452.4622.75630301.6972.0422.4572.7531311.6962.042.4532.74432321.6942.0372.4492.73833331.6922.0352.4452.73334341.6912.0322.4412.72835351.692.032.4382.72436361.6882.0282.4342.71937371.6872.0262.4312.71538381.6862.0242.4292.71239391.6852.0232.4262.70840

18、401.6842.0212.4232.70441411.6752.0092.4032.67851511.67122.392.6661611.6671.9942.3812.64871711.6641.992.3742.63981811.6621.9872.3682.63291911.661.9842.3642.6261911911.6531.9722.3452.6014914911.6481.9652.3342.5869919911.6461.9622.332.5819999919999911.64491.962.32632.5758 两两样样本本方方差差的的齐齐性性检检验验 方方差差不不齐齐时

19、时两两小小样样本本均均数数比比较较的的 tt 检检验验例例题题编编号号样样本本甲甲样样本本乙乙1 10.840.542 21.050.643 31.20.644 41.20.755 51.390.766 61.530.817 71.671.168 81.81.29 91.871.3410102.071.3511112.111.4812121.5613131.871414151516161717181819192020合合计计X X16.7314.1 方方差差不不齐齐时时两两小小样样本本均均数数比比较较的的 tt 检检验验标标准准差差： 0.421793 0.42215标标准准差差：1.79样样

20、本本数数：1113样样本本数数：10自自由由度度：2222自自由由度度：58 均均数数： 1.520909 1.084615 均均数数：6.21标标准准误误： 0.016174 0.013708标标准准误误：0.32041两两样样本本方方差差的的齐齐性性检检验验两两样样本本方方差差的的齐齐性性检检验验分分子子=0 0. .4 42 22 21 15 5分分母母= 0 0. .4 42 21 17 79 93 3分分子子=1 1. .7 79 9F F 值值= = 1.0016931.001693F F 值值= = 10.2171610.21716自自由由度度：1210自自由由度度：9V分分子子

21、=1212V分分母母= = 1010V分分子子=10100.050.050.010.010.050.05F 界界 值值= 3.623.62F 界界 值值= 2.452.45检检验验结结果果方方差差齐齐性性好好检检验验结结果果方方差差不不齐齐 tt 值值: :2 2. .5 52 23 39 91 1TT0.05=2 2. .2 20 05 55 52 21 1 tt值值: : 3 3. .2 27 71 17 74 42 2t0.05 v12.228t0.05 v22.179t0.05 v12.262P 0.050.05结结论论P 0.050.05t t界界值值表表N单单侧侧0.050.05双

22、双侧侧0.050.05单单侧侧0.010.01双双侧侧0.010.0116.31412.70631.82163.65722.924.3036.9659.92532.3533.1824.5415.84142.1322.7763.7474.60452.0152.5713.3654.03261.9432.4473.1433.70771.8952.3652.9983.49981.862.3062.8963.35591.3832.2622.9213.25101.8122.2282.7643.169111.7962.2012.7183.106121.7822.1792.6813.055131.7712.1

23、62.653.012141.7612.1452.6242.977151.7532.1312.6022.947161.7462.122.5832.921171.742.112.5672.898181.7342.1012.5522.878191.7292.0932.5392.861201.7252.0862.5282.845211.7212.082.5182.831221.7172.0742.5082.819231.7142.0692.52.807241.7112.0642.4922.797251.7082.062.4852.787261.7062.0562.4792.779271.7032.05

24、22.4732.771281.7012.0482.4672.763291.6992.0452.4622.756301.6972.0422.4572.75311.6962.042.4532.744321.6942.0372.4492.738331.6922.0352.4452.733341.6912.0322.4412.728351.692.032.4382.724361.6882.0282.4342.719371.6872.0262.4312.715381.6862.0242.4292.712391.6852.0232.4262.708401.6842.0212.4232.704411.675

25、2.0092.4032.678511.67122.392.66611.6671.9942.3812.648711.6641.992.3742.639811.6621.9872.3682.632911.661.9842.3642.6261911.6531.9722.3452.6014911.6481.9652.3342.5869911.6461.9622.332.5819999911.64491.962.32632.5758F F界界值值表表（P=0.05)P=0.05)分子自由度分母自由度1234561647.79799.5864.16899.58921.85937.11238.513939.

26、1739.2539.339.33317.4416.0415.4415.114.8814.73412.2210.659.989.69.369.2510.018.437.767.397.156.9868.817.266.66.235.995.8278.076.545.895.525.295.1287.576.065.425.054.824.6597.215.715.084.724.484.32106.945.464.834.474.244.07116.725.264.634.284.043.88126.555.14.474.123.893.73136.414.974.3543.773.6146.3

27、4.864.243.893.663.5156.24.774.153.83.583.41166.124.694.083.733.53.34176.044.624.013.663.443.28185.984.563.953.613.383.22195.924.513.93.563.333.17205.874.463.863.513.293.13215.834.423.823.483.253.09225.794.383.783.443.223.05235.754.353.753.413.183.02245.724.323.723.383.152.99255.694.293.693.353.132.9

28、7265.664.273.673.333.12.94275.634.243.653.313.082.92285.614.223.633.293.062.9295.594.23.613.273.042.88305.574.183.593.253.032.87405.424.053.463.132.92.74605.293.933.343.012.792.631205.153.83.232.892.672.52999999995.023.693.122.792.572.410.56504.340.006272分分母母=0 0. .5 56 649V分分母母= = 49490.010.01TT0.0

29、5=0.05=2 2. .2 25 57 71 14 43 3t0.05 v22.009结结论论 方方差差不不齐齐时时两两小小样样本本均均数数比比较较的的 tt 检检验验两两样样本本方方差差的的齐齐性性检检验验78910121520948.22956.66963.29968.63976.71984.87993.139.3639.3739.3939.439.4139.4339.4514.6214.5414.4714.4214.3414.2514.179.078.988.98.848.758.668.566.856.766.686.626.526.436.335.75.65.525.465.375

30、.275.174.994.94.824.764.674.574.474.534.434.364.34.24.144.24.14.033.963.873.773.673.953.853.783.723.623.523.423.763.663.593.533.433.333.233.613.513.443.373.283.183.073.483.393.313.253.153.052.953.383.293.213.153.052.952.843.293.23.123.062.962.862.763.223.123.052.992.892.792.683.163.062.982.922.822.7

31、22.623.13.012.932.872.772.672.563.052.962.882.822.722.622.513.012.912.842.772.682.572.462.972.872.82.732.642.532.422.932.842.762.72.62.52.392.92.812.732.672.572.472.362.872.782.72.642.542.442.332.852.752.682.612.512.412.32.822.732.652.592.492.392.282.82.712.632.572.472.362.252.782.692.612.552.452.34

32、2.232.762.672.592.532.432.322.212.752.652.572.512.412.312.22.622.532.452.392.292.182.072.512.412.332.272.172.061.942.392.32.222.162.051.941.822.292.192.112.051.941.831.713060 999999991001.411009.81018.2639.4639.4839.514.0813.9913.98.468.368.266.236.126.025.074.964.854.364.254.143.893.783.673.563.453

33、.333.313.23.083.1232.882.962.852.722.842.722.62.732.612.492.642.522.42.572.452.322.52.382.252.442.322.192.392.272.132.352.222.092.312.182.042.272.1422.242.111.972.212.081.942.182.051.912.162.031.882.1321.852.111.981.832.091.961.812.071.941.791.941.81.641.821.671.481.691.531.311.571.391 t t 检检验验数数据据区

34、区域域编编号号 样样本本甲甲样样本本乙乙1 17162 28183 38174 49195 57206 612207 77218 813229 915191010141811111617121217221313172314141824151518251616192617172019181815251919122520201328212114232222152423231423242412242525172226261421272711342828122929133030153131103232113333934348353520363610373711383814393915404012414

35、113424213 样样本本数数据据例例 题题甲甲样样本本乙乙样样本本样样本本数数：4227均均 数数： 13.04762 22.03704标标准准差差： 3.547259 3.887668自自由由度度：6722.03704标标准准误误： 0.299596 0.5597761S2= 12.58304 15.11396S大大2 2/S/S小小2 2= =1.201137齐齐性性检检验验：1Sc2= 13.56519Sx1-x2 = 0.908513方方差差齐齐性性检检验验：方差齐性好。 t t 值值: :9 9. .8 89 94 46 65 54 4P=P= 0.05P=P= 0.01t界界值值: :单侧双侧单侧双侧1.6671.6671.9941.9942.3812.3812.7792.779单单侧侧检检验验结结果果：P P 0.010.01结结 论论：两两样样本本均均数数的的差差别别有有极极显显著著性性意意义义。 双双侧侧检检验验结结果果：P P 0.010.050.05结结 论论： 两两样样本本均均数数的的差差别别没没有有极极显显著著性