excel____T檢驗(yàn)_公式

1、 成成組組設(shè)設(shè)計(jì)計(jì)的的兩兩樣樣本本均均數(shù)數(shù)比比較較的的 t t 檢檢驗(yàn)驗(yàn)編編號號樣樣 本本 甲甲樣樣 本本 乙乙例例 題題12600818363 34746344 4589710285 5548813186 6639015787 7456613188 8677916789 9577350991010234931631111121213131414151516161717181819192020合合計(jì)計(jì)X X5376446270合合計(jì)計(jì)X X方方3.03E+08 9.03E+08樣樣本本數(shù)數(shù)：1010自自由由度度：1818 均均數(shù)數(shù)：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結(jié)結(jié) 論論單側(cè)雙側(cè)單側(cè)雙側(cè)1.7341.7342.1012.1012.5522.5522.8782.878單單側(cè)側(cè)檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果：P P 0.050.05P=P= 0.3958230.395823雙雙側(cè)側(cè)檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果：P P 0.050.05P=P= 0.7916450.791645t t界界值值表表N單側(cè)0.05 雙側(cè)0.05 單側(cè)0.01 雙側(cè)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 成成組組設(shè)設(shè)計(jì)計(jì)的的兩兩樣樣本本幾幾何何均均數(shù)數(shù)比比較較的的 t t 檢檢驗(yàn)驗(yàn)例例題題編編號號樣樣本本甲甲LgXLgX樣樣本本乙乙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合合計(jì)計(jì)X X29016.0845849018.90867合合計(jì)計(jì)X X方方820022.046392340030.15691樣樣本本數(shù)數(shù)：1212自自由由度度：2222

8、 均均數(shù)數(shù)： 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結(jié)結(jié)論論單側(cè)雙側(cè)單側(cè)雙側(cè)1.7171.7172.0742.0742.5082.5082.8192.819單單側(cè)側(cè)檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果：P P 0.010.01P=P= 0.0038370.003837雙雙側(cè)側(cè)檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果：P P 0.010.01P=P= 0.0076730.007673t t界界值值表表自由

9、度單側(cè)0.05 雙側(cè)0.05 單側(cè)0.01 雙側(cè)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配配對對設(shè)設(shè)計(jì)計(jì)的的差差值值均均數(shù)數(shù)與與總總體體均均數(shù)數(shù)0 0比比較較的的t t檢檢驗(yàn)驗(yàn)例例題題編編號號治治療療前前治治療療后后差差值值d dd d 平平方方1 1355024501100

13、12100002 220002400-4001600003 330001800120014400004 4395032007505625005 5380032505503025006 637502700105011025007 7345025009509025008 830501750130016900009 900101000111100121200131300141400151500161600171700181800191900202000265502005065007370000樣樣本本數(shù)數(shù)：8 8 d d 均均數(shù)數(shù)：812.5812.5自自由由度度：7 7d d 標(biāo)標(biāo)準(zhǔn)準(zhǔn)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結(jié)結(jié)論論單側(cè)雙側(cè)單側(cè)雙側(cè)1.8951.8952.3652.3652.9982.9983.4993.499單單側(cè)側(cè)檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果：P P 0.010.01P=P= 0.00200030.0020003雙雙側(cè)側(cè)檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果：P P 0.010.01P=P= 0.00400050.0040005t t界界值值表表N單單側(cè)側(cè)0.050.05 雙雙側(cè)側(cè)0.050.05 單單側(cè)側(cè)0.010.01雙雙側(cè)側(cè)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 兩兩樣樣本本方方差差的的齊齊性性檢檢驗(yàn)驗(yàn) 方方差差不不齊齊時(shí)

19、時(shí)兩兩小小樣樣本本均均數(shù)數(shù)比比較較的的 tt 檢檢驗(yàn)驗(yàn)例例題題編編號號樣樣本本甲甲樣樣本本乙乙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合合計(jì)計(jì)X X16.7314.1 方方差差不不齊齊時(shí)時(shí)兩兩小小樣樣本本均均數(shù)數(shù)比比較較的的 tt 檢檢驗(yàn)驗(yàn)標(biāo)標(biāo)準(zhǔn)準(zhǔn)差差： 0.421793 0.42215標(biāo)標(biāo)準(zhǔn)準(zhǔn)差差：1.79樣樣

20、本本數(shù)數(shù)：1113樣樣本本數(shù)數(shù)：10自自由由度度：2222自自由由度度：58 均均數(shù)數(shù)： 1.520909 1.084615 均均數(shù)數(shù)：6.21標(biāo)標(biāo)準(zhǔn)準(zhǔn)誤誤： 0.016174 0.013708標(biāo)標(biāo)準(zhǔn)準(zhǔn)誤誤：0.32041兩兩樣樣本本方方差差的的齊齊性性檢檢驗(yàn)驗(yàn)兩兩樣樣本本方方差差的的齊齊性性檢檢驗(yàn)驗(yàn)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檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果方方差差齊齊性性好好檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果方方差差不不齊齊 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結(jié)結(jié)論論P(yáng) 0.050.05t t界界值值表表N單單側(cè)側(cè)0.050.05雙

22、雙側(cè)側(cè)0.050.05單單側(cè)側(cè)0.010.01雙雙側(cè)側(cè)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結(jié)結(jié)論論 方方差差不不齊齊時(shí)時(shí)兩兩小小樣樣本本均均數(shù)數(shù)比比較較的的 tt 檢檢驗(yàn)驗(yàn)兩兩樣樣本本方方差差的的齊齊性性檢檢驗(yàn)驗(yàn)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 檢檢驗(yàn)驗(yàn)數(shù)數(shù)據(jù)據(jù)區(qū)

34、區(qū)域域編編號號 樣樣本本甲甲樣樣本本乙乙1 17162 28183 38174 49195 57206 612207 77218 813229 915191010141811111617121217221313172314141824151518251616192617172019181815251919122520201328212114232222152423231423242412242525172226261421272711342828122929133030153131103232113333934348353520363610373711383814393915404012414

35、113424213 樣樣本本數(shù)數(shù)據(jù)據(jù)例例 題題甲甲樣樣本本乙乙樣樣本本樣樣本本數(shù)數(shù)：4227均均 數(shù)數(shù)： 13.04762 22.03704標(biāo)標(biāo)準(zhǔn)準(zhǔn)差差： 3.547259 3.887668自自由由度度：6722.03704標(biāo)標(biāo)準(zhǔn)準(zhǔn)誤誤： 0.299596 0.5597761S2= 12.58304 15.11396S大大2 2/S/S小小2 2= =1.201137齊齊性性檢檢驗(yàn)驗(yàn)：1Sc2= 13.56519Sx1-x2 = 0.908513方方差差齊齊性性檢檢驗(yàn)驗(yàn)：方差齊性好。 t t 值值: :9 9. .8 89 94 46 65 54 4P=P= 0.05P=P= 0.01t界界值值: :單側(cè)雙側(cè)單側(cè)雙側(cè)1.6671.6671.9941.9942.3812.3812.7792.779單單側(cè)側(cè)檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果：P P 0.010.01結(jié)結(jié) 論論：兩兩樣樣本本均均數(shù)數(shù)的的差差別別有有極極顯顯著著性性意意義義。 雙雙側(cè)側(cè)檢檢驗(yàn)驗(yàn)結(jié)結(jié)果果：P P 0.010.050.05結(jié)結(jié) 論論： 兩兩樣樣本本均均數(shù)數(shù)的的差差別別沒沒有有極極顯顯著著性