正态分布的不同输出

Question

我正在测试正态分布，但是不同的测试给了我不同的输出，我不知道我应该相信/使用哪个输出。

另一个问题是，我不知道是否应该使用固定效应模型或stadard模型，而不需要检查正常分布。固定效应模型是我以后必须使用的模型，所以我认为更重要的是知道这个模型是怎么回事，还是我错了？

代码如下：

FORMULAR.PLM.BASELINE <- StockPrice.WINS ~ EPS.WINS + BookValuePS.WINS + ESGscore.WINS + ggroup

MOD.FE <- plm(FORMULAR.PLM.BASELINE, data = PD.Datensatz_final, model = "within", effect = "twoways")
summary(MOD.FE)

VEC.Residuals.FE <- residuals(MOD.FE)

# The strange thing is that there are different outcomes influenced by the test I use. How do I decide which one to use?
# Outcome behind the test

# Shapiro-Wilk-Test #
shapiro.test(VEC.Residuals) # NO normal distribution

# Chi-Square-Test #
pearson.test(VEC.Residuals, adjust = FALSE) # normal distribution

# Kolmogoroff-Smirnov-Lillefors-Test #
lillie.test(VEC.Residuals) # normal distribution

# Shapiro-Francia-Test #
sf.test(VEC.Residuals) # NO normal distribution 

# Anderson-Darling-Test #
ad.test(VEC.Residuals) # normal distribution

数据：

"AIR PRODUCTS & CHEMICALS INC", "AIR PRODUCTS & CHEMICALS INC", 
"AIR PRODUCTS & CHEMICALS INC", "AIR PRODUCTS & CHEMICALS INC", 
"AIR PRODUCTS & CHEMICALS INC", "HESS CORP", "HESS CORP", "HESS CORP", 
"HESS CORP", "HESS CORP", "HESS CORP", "HESS CORP", "APACHE CORP", 
"APACHE CORP", "APACHE CORP", "APACHE CORP", "APACHE CORP", "APACHE CORP", 
"APACHE CORP", "AVERY DENNISON CORP", "AVERY DENNISON CORP", 
"AVERY DENNISON CORP", "AVERY DENNISON CORP", "AVERY DENNISON CORP", 
"AVERY DENNISON CORP", "AVERY DENNISON CORP", "BALL CORP", "BALL CORP", 
"BALL CORP", "BALL CORP", "BALL CORP", "BALL CORP", "BALL CORP", 
"CHEVRON CORP", "CHEVRON CORP", "CHEVRON CORP", "CHEVRON CORP", 
"CHEVRON CORP", "CHEVRON CORP", "CHEVRON CORP", "ECOLAB INC", 
"ECOLAB INC", "ECOLAB INC", "ECOLAB INC", "ECOLAB INC", "ECOLAB INC", 
"ECOLAB INC", "EXXON MOBIL CORP", "EXXON MOBIL CORP", "EXXON MOBIL CORP", 
"EXXON MOBIL CORP", "EXXON MOBIL CORP", "EXXON MOBIL CORP", "EXXON MOBIL CORP", 
"FMC CORP", "FMC CORP", "FMC CORP", "FMC CORP", "FMC CORP", "FMC CORP", 
"FMC CORP", "HALLIBURTON CO", "HALLIBURTON CO", "HALLIBURTON CO", 
"HALLIBURTON CO", "HALLIBURTON CO", "HALLIBURTON CO", "HALLIBURTON CO", 
"HELMERICH & PAYNE", "HELMERICH & PAYNE", "HELMERICH & PAYNE", 
"HELMERICH & PAYNE", "HELMERICH & PAYNE", "HELMERICH & PAYNE", 
"HELMERICH & PAYNE", "HOLLYFRONTIER CORP", "HOLLYFRONTIER CORP", 
"HOLLYFRONTIER CORP", "HOLLYFRONTIER CORP", "HOLLYFRONTIER CORP", 
"HOLLYFRONTIER CORP", "HOLLYFRONTIER CORP", "INTL FLAVORS & FRAGRANCES", 
"INTL FLAVORS & FRAGRANCES", "INTL FLAVORS & FRAGRANCES", "INTL FLAVORS & FRAGRANCES", 
"INTL FLAVORS & FRAGRANCES", "INTL FLAVORS & FRAGRANCES", "INTL FLAVORS & FRAGRANCES", 
"INTL PAPER CO", "INTL PAPER CO", "INTL PAPER CO", "INTL PAPER CO", 
"INTL PAPER CO", "INTL PAPER CO", "INTL PAPER CO", "MARATHON OIL CORP", 
"MARATHON OIL CORP", "MARATHON OIL CORP", "MARATHON OIL CORP", 
"MARATHON OIL CORP", "MARATHON OIL CORP", "MARATHON OIL CORP", 
"NEWMONT CORP", "NEWMONT CORP", "NEWMONT CORP", "NEWMONT CORP", 
"NEWMONT CORP", "NEWMONT CORP", "NEWMONT CORP", "NUCOR CORP", 
"NUCOR CORP", "NUCOR CORP", "NUCOR CORP", "NUCOR CORP", "NUCOR CORP", 
"NUCOR CORP", "OCCIDENTAL PETROLEUM CORP", "OCCIDENTAL PETROLEUM CORP", 
"OCCIDENTAL PETROLEUM CORP", "OCCIDENTAL PETROLEUM CORP", "OCCIDENTAL PETROLEUM CORP", 
"OCCIDENTAL PETROLEUM CORP", "OCCIDENTAL PETROLEUM CORP", "ONEOK INC", 
"ONEOK INC", "ONEOK INC", "ONEOK INC", "ONEOK INC", "ONEOK INC", 
"ONEOK INC", "PPG INDUSTRIES INC", "PPG INDUSTRIES INC", "PPG INDUSTRIES INC", 
"PPG INDUSTRIES INC", "PPG INDUSTRIES INC", "PPG INDUSTRIES INC", 
"PPG INDUSTRIES INC", "CONOCOPHILLIPS", "CONOCOPHILLIPS", "CONOCOPHILLIPS", 
"CONOCOPHILLIPS", "CONOCOPHILLIPS", "CONOCOPHILLIPS", "CONOCOPHILLIPS", 
"SCHLUMBERGER LTD", "SCHLUMBERGER LTD", "SCHLUMBERGER LTD", "SCHLUMBERGER LTD", 
"SCHLUMBERGER LTD", "SCHLUMBERGER LTD", "SCHLUMBERGER LTD", "SHERWIN-WILLIAMS CO", 
"SHERWIN-WILLIAMS CO", "SHERWIN-WILLIAMS CO", "SHERWIN-WILLIAMS CO", 
"SHERWIN-WILLIAMS CO", "SHERWIN-WILLIAMS CO", "SHERWIN-WILLIAMS CO", 
"VULCAN MATERIALS CO", "VULCAN MATERIALS CO", "VULCAN MATERIALS CO", 
"VULCAN MATERIALS CO", "VULCAN MATERIALS CO", "VULCAN MATERIALS CO", 
"VULCAN MATERIALS CO", "WILLIAMS COS INC", "WILLIAMS COS INC", 
"WILLIAMS COS INC", "WILLIAMS COS INC", "WILLIAMS COS INC", "WILLIAMS COS INC", 
"WILLIAMS COS INC", "PIONEER NATURAL RESOURCES CO", "PIONEER NATURAL RESOURCES CO", 
"PIONEER NATURAL RESOURCES CO", "PIONEER NATURAL RESOURCES CO", 
"PIONEER NATURAL RESOURCES CO", "PIONEER NATURAL RESOURCES CO", 
"PIONEER NATURAL RESOURCES CO", "FREEPORT-MCMORAN INC", "FREEPORT-MCMORAN INC", 
"FREEPORT-MCMORAN INC", "FREEPORT-MCMORAN INC", "FREEPORT-MCMORAN INC", 
"FREEPORT-MCMORAN INC", "FREEPORT-MCMORAN INC", "DEVON ENERGY CORP", 
"DEVON ENERGY CORP", "DEVON ENERGY CORP", "DEVON ENERGY CORP", 
"DEVON ENERGY CORP", "DEVON ENERGY CORP", "DEVON ENERGY CORP", 
"VALERO ENERGY CORP", "VALERO ENERGY CORP", "VALERO ENERGY CORP", 
"VALERO ENERGY CORP", "VALERO ENERGY CORP", "VALERO ENERGY CORP", 
"VALERO ENERGY CORP", "EOG RESOURCES INC", "EOG RESOURCES INC", 
"EOG RESOURCES INC", "EOG RESOURCES INC", "EOG RESOURCES INC", 
"EOG RESOURCES INC", "EOG RESOURCES INC", "CABOT OIL & GAS CORP", 
"CABOT OIL & GAS CORP", "CABOT OIL & GAS CORP", "CABOT OIL & GAS CORP", 
"CABOT OIL & GAS CORP", "CABOT OIL & GAS CORP", "CABOT OIL & GAS CORP", 
"LINDE PLC", "LINDE PLC", "LINDE PLC", "LINDE PLC", "LINDE PLC", 
"LINDE PLC", "LINDE PLC", "EASTMAN CHEMICAL CO", "EASTMAN CHEMICAL CO", 
"EASTMAN CHEMICAL CO", "EASTMAN CHEMICAL CO", "EASTMAN CHEMICAL CO", 
"EASTMAN CHEMICAL CO", "EASTMAN CHEMICAL CO", "MARTIN MARIETTA MATERIALS", 
"MARTIN MARIETTA MATERIALS", "MARTIN MARIETTA MATERIALS", "MARTIN MARIETTA MATERIALS", 
"MARTIN MARIETTA MATERIALS", "MARTIN MARIETTA MATERIALS", "MARTIN MARIETTA MATERIALS", 
"ALBEMARLE CORP", "ALBEMARLE CORP", "ALBEMARLE CORP", "ALBEMARLE CORP", 
"ALBEMARLE CORP", "ALBEMARLE CORP", "ALBEMARLE CORP", "NATIONAL OILWELL VARCO INC", 
"NATIONAL OILWELL VARCO INC", "NATIONAL OILWELL VARCO INC", "NATIONAL OILWELL VARCO INC", 
"NATIONAL OILWELL VARCO INC", "NATIONAL OILWELL VARCO INC", "NATIONAL OILWELL VARCO INC", 
"PACKAGING CORP OF AMERICA", "PACKAGING CORP OF AMERICA", "PACKAGING CORP OF AMERICA", 
"PACKAGING CORP OF AMERICA", "PACKAGING CORP OF AMERICA", "PACKAGING CORP OF AMERICA", 
"PACKAGING CORP OF AMERICA", "MOSAIC CO", "MOSAIC CO", "MOSAIC CO", 
"MOSAIC CO", "MOSAIC CO", "MOSAIC CO", "MOSAIC CO", "CELANESE CORP", 
"CELANESE CORP", "CELANESE CORP", "CELANESE CORP", "CELANESE CORP", 
"CELANESE CORP", "CELANESE CORP", "CF INDUSTRIES HOLDINGS INC", 
"CF INDUSTRIES HOLDINGS INC", "CF INDUSTRIES HOLDINGS INC", "CF INDUSTRIES HOLDINGS INC", 
"CF INDUSTRIES HOLDINGS INC", "CF INDUSTRIES HOLDINGS INC", "CF INDUSTRIES HOLDINGS INC", 
"LYONDELLBASELL INDUSTRIES NV", "LYONDELLBASELL INDUSTRIES NV", 
"LYONDELLBASELL INDUSTRIES NV", "LYONDELLBASELL INDUSTRIES NV", 
"LYONDELLBASELL INDUSTRIES NV", "LYONDELLBASELL INDUSTRIES NV", 
"LYONDELLBASELL INDUSTRIES NV"), Year = c(2011, 2012, 2013, 2014, 
2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 
2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 
2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 
2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 
2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 
2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 
2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 
2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 
2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 
2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 
2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 
2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 
2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 
2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 
2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 
2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 
2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 
2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 
2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 
2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 
2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 
2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 
2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 
2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2011, 2012, 
2013, 2014, 2015, 2016, 2017, 2011, 2012, 2013, 2014, 2015, 2016, 
2017, 2011, 2012, 2013, 2014, 2015, 2016, 2017), ggroup = c(1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1010, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510
), StockPrice.WINS = c(85.19, 84.02, 111.78, 144.23, 130.11, 
143.82, 164.08, 56.8, 52.96, 83, 73.82, 48.48, 62.29, 47.47, 
90.58, 78.5, 85.94, 62.67, 44.47, 63.47, 42.22, 28.68, 34.92, 
50.19, 51.88, 62.66, 70.22, 114.86, 17.86, 22.38, 25.83, 34.09, 
36.37, 37.54, 37.85, 106.4, 108.14, 124.91, 112.18, 89.96, 117.7, 
125.19, 57.81, 71.9, 104.27, 104.52, 114.38, 117.22, 134.18, 
84.76, 86.55, 101.2, 92.45, 77.95, 90.26, 83.64, 43.02, 58.52, 
75.46, 57.03, 39.13, 56.56, 94.66, 34.51, 34.69, 50.75, 39.33, 
34.04, 54.09, 48.87, 58.36, 56.01, 84.08, 67.42, 53.55, 77.4, 
64.64, 23.4, 46.55, 49.69, 37.48, 39.89, 32.76, 51.22, 52.42, 
66.54, 85.98, 101.36, 119.64, 117.83, 152.61, 29.6, 39.84, 49.03, 
53.58, 37.7, 53.06, 57.94, 29.27, 30.66, 35.3, 28.29, 12.59, 
17.31, 16.93, 60.01, 46.44, 23.03, 18.9, 17.99, 34.07, 37.52, 
39.57, 43.16, 53.38, 49.05, 40.3, 59.52, 63.58, 93.7, 76.61, 
95.1, 80.61, 67.61, 71.23, 73.66, 43.35, 42.75, 62.18, 49.79, 
24.66, 57.41, 53.45, 41.75, 67.68, 94.83, 115.58, 98.82, 94.76, 
116.82, 72.87, 57.99, 70.65, 69.06, 46.69, 50.14, 54.89, 68.31, 
69.3, 90.11, 85.41, 69.75, 83.95, 67.39, 29.76, 51.27, 61.17, 
87.68, 86.53, 89.58, 136.68, 39.35, 52.05, 59.42, 65.73, 94.97, 
125.15, 128.37, 33.02, 32.74, 38.57, 44.94, 25.7, 31.14, 30.49, 
89.48, 106.59, 180.63, 148.85, 125.38, 180.07, 172.85, 36.79, 
34.2, 37.74, 23.36, 6.77, 13.19, 18.96, 62, 52.04, 61.87, 61.21, 
32, 45.67, 41.4, 21.05, 34.12, 50.4, 49.5, 70.71, 68.32, 91.91, 
49.26, 60.4, 83.92, 92.07, 70.79, 101.1, 107.91, 32.14, 39.79, 
51.4, 43.86, 40.88, 50.54, 61.59, 106.9, 109.45, 130.03, 129.56, 
102.4, 117.19, 154.68, 39.06, 68.05, 80.7, 75.86, 67.51, 75.21, 
92.64, 75.41, 94.28, 99.94, 110.32, 136.58, 180.63, 180.63, 51.51, 
62.12, 63.39, 60.13, 56.01, 86.08, 127.89, 67.99, 68.35, 79.53, 
65.53, 33.49, 37.44, 36.02, 25.24, 38.47, 63.28, 78.05, 63.05, 
84.82, 120.55, 50.43, 56.63, 47.27, 45.65, 27.59, 29.33, 25.66, 
44.27, 44.53, 55.31, 59.96, 67.33, 78.74, 107.08, 29, 40.63, 
46.61, 54.51, 40.81, 31.48, 42.54, 32.49, 57.09, 80.28, 79.39, 
86.9, 85.78, 110.32), EPS.WINS = c(5.75, 5.53, 4.74, 4.66, 5.95, 
2.92, 13.4368, 5.01, 5.93, 13.4368, 8.11, -10.68, -14.812, -12.93, 
11.94, 5.14, 5.65, -14.07, -14.812, -3.71, 3.42, 1.78, 1.65, 
2.49, 2.69, 3.01, 3.63, 3.2, 1.34, 1.3, 1.39, 1.7, 1.02, 0.83, 
1.07, 13.4368, 13.42, 11.18, 10.21, 2.46, -0.27, 4.88, 1.95, 
2.41, 3.23, 4.01, 3.38, 4.2, 5.21, 8.43, 9.7, 7.37, 7.6, 3.85, 
1.88, 4.63, 2.58, 3.02, 2.17, 2.31, 3.66, 1.56, 3.99, 3.09, 2.85, 
2.37, 4.13, -0.79, -6.69, -0.53, 4.07, 5.44, 6.93, 3.57, 3.92, 
-0.53, -1.18, 6.46, 8.41, 3.67, 1.43, 3.92, -1.48, 4.57, 3.32, 
3.13, 4.35, 5.12, 5.21, 5.09, 3.74, 3.1, 1.82, 3.15, 1.3, 2.25, 
2.2, 5.19, 4.15, 2.24, 2.49, 4.48, -3.26, -2.53, -6.73, 0.74, 
3.65, -4.94, 1.02, 0.43, -1.18, -0.18, 2.45, 1.59, 1.53, 2.23, 
1.12, 2.49, 4.12, 8.34, 5.68, 7.34, 0.79, -10.23, -0.75, 1.71, 
1.72, 1.75, 1.29, 1.5, 1.17, 1.67, 1.3, 3.58, 3.07, 11.27, 7.6, 
5.18, 3.3, 6.21, 9.04, 6.78, 7.44, 5.55, -3.57, -2.9, -0.7, 3.7, 
4.13, 5.09, 4.2, 1.65, -1.24, -1.08, 1.42, 2.07, 2.49, 3, 3.81, 
4.11, 6.36, -0.55, -0.41, 0.19, 1.56, 1.66, 3.15, 4.54, 0.64, 
1.26, 0.63, 2.83, -0.76, -0.57, 2.63, 7.14, 1.56, -1.16, 6.46, 
-1.83, -3.35, 4.9, 4.82, 3.2, 2.65, -1.22, -11.27, -3.27, 1.26, 
11.28, -0.51, -0.05, 3.93, -14.812, -6.44, 1.71, 3.71, 3.79, 
5.02, 6.9, 8.03, 4.97, 9.2, 4.15, 1.07, 4.07, 5.37, -8.29, -1.98, 
4.49, 3.7, 6.12, 2.39, 3.09, -5.35, 2.4, 3.89, 5.53, 5.67, 5.94, 
5.79, 5.39, 5.25, 4.31, 4.98, 3, 7.56, 5.02, 5.71, 5.8, 9.56, 
1.8, 1.84, 2.63, 2.73, 4.32, 6.69, 11.34, 4.82, 3.49, 4.93, 1.69, 
3.01, 5.73, 0.49, 4.73, 5.86, 5.46, 5.85, -1.99, -6.41, -0.63, 
1.59, 1.7, 4.52, 3.99, 4.47, 4.81, 7.15, 5.64, 4.54, 4.44, 2.75, 
2.79, 0.85, -0.31, 3.89, 3.82, 6.93, 4.03, 2.02, 6.21, 6.11, 
4.44, 5.79, 4.97, 5.43, 2.97, -1.19, 1.53, 3.75, 4.94, 6.77, 
8.01, 9.61, 9.13, 12.23), BookValuePS.WINS = c(27.21, 30.67, 
33.58, 34.63, 33.73, 32.72, 46.27, 54.46, 61.75, 75.99, 77.68, 
67.77, 45.92, 35.08, 75.5, 80.54, 80.7108, 67.54, 6.79, 16.46, 
19.46, 15.53, 12.13, 17.21, 11.53, 10.61, 10.48, 11.88, 3.69, 
3.6, 4.11, 3.73, 4.56, 10.85, 11.25, 61.1, 70, 77.78, 80.7108, 
80.7108, 77.72, 78.67, 23.92, 20.78, 24.49, 24.38, 23.31, 23.59, 
26.31, 31.7, 35.84, 39.36, 40.76, 40.72, 40.12, 44.1, 8.74, 10.75, 
11.24, 11.48, 13.95, 14.62, 19.97, 14.38, 17.02, 15.12, 19.18, 
18.13, 10.93, 9.57, 30.66, 35.9, 41.81, 45.37, 45.45, 42.23, 
38.38, 32.84, 29.49, 29.94, 28, 27.84, 6.58, 30.49, 13.73, 15.4, 
17.99, 18.76, 19.77, 20.42, 21.3, 15.32, 14.45, 18.3, 11.89, 
9.32, 10.65, 15.79, 24.16, 25.9, 27.44, 30.91, 27.4, 20.71, 13.77, 
26.11, 27.77, 20.35, 20.63, 22.18, 20.18, 19.9, 23.58, 24.02, 
23.96, 24.3, 23.14, 24.66, 27.31, 46.32, 49.45, 53.63, 44.76, 
31.81, 28.14, 26.89, 10.69, 10.33, 11.35, 2.83, 1.6, 0.89, 18.58, 
10.33, 13.24, 17.2, 18.73, 18.36, 18.17, 21.7, 47.43, 38.58, 
42.32, 41.95, 32.02, 28.08, 25.07, 23.17, 26.13, 29.83, 29.23, 
28.36, 30.27, 26.54, 4.89, 5.87, 5.86, 3.45, 3.14, 6.82, 13.25, 
29.31, 28.99, 30.23, 31.77, 33.44, 34.33, 37.5, 3.05, 6.98, 7.12, 
11.75, 8.21, 6.19, 11.69, 46.95, 46.27, 48.49, 59.59, 56.16, 
62.67, 66.32, 16.52, 18.49, 20.89, 17.6, 7.23, 4.59, 5.51, 51.39, 
52.67, 50.49, 52.66, 17.11, 11.55, 17.63, 29.17, 32.79, 35.9, 
39.31, 41.3, 43.44, 49.75, 48.08, 24.82, 28.53, 32.6, 23.72, 
25.26, 28.34, 23.29, 28.62, 30.5, 30.16, 19.76, 20.48, 23.92, 
18.16, 20.33, 22.36, 19.22, 15.29, 17.58, 20.82, 13.39, 20.23, 
24.65, 23.48, 26.52, 30.77, 37.31, 30.84, 30.8, 33.29, 76.47, 
60.74, 65.08, 47.4, 17.58, 20.56, 19.41, 17.27, 29.27, 33.77, 
33.13, 41.75, 47.62, 52.18, 48.35, 42.33, 37.07, 37.38, 9.35, 
10.06, 13.6, 15.46, 16.71, 18.82, 23.34, 26.1, 28.16, 31.53, 
28.61, 26.59, 27.35, 27.41, 8.59, 10.93, 17, 18.18, 15.77, 17.86, 
20.94, 13.1, 18.47, 17.24, 16.44, 17.15, 14.38, 15.33, 18.52, 
19.31, 21.89, 15.96, 14.06, 14.4, 22.43)), row.names = c(NA, 
-287L), class = c("tbl_df", "tbl", "data.frame"))```

Answer 1

您正在使用不同的测试，因此没有理由期望它们产生相同的结果。一般来说，用正规的统计检验来检验常态是个坏主意，因为这类测试可能会受到异常值和样本大小的严重影响。如果样本量足够大，即使与正常值相差很小也是“显著的”。此外，许多模型对于偏离常态是非常稳健的。评估常态的一个更好的方法是简单地检查直方图和QQ图。

我强烈推荐这个交叉验证的问答：

Is normality testing 'essentially useless'?

Answer 2

简而言之，这些方法中的每一种都采用了一种稍微不同的方法来测试正常度。就我个人而言，我倾向于使用Shapiro测试，但每个选项对于某些数据子集都是有效的。

主要问题是数据的性质。

此链接很好地概述了这些：https://www.graphpad.com/guides/prism/latest/statistics/stat_choosing_a_normality_test.htm之间的差异。

因为你的数据看上去并不是唯一的价值，皮尔逊检验很可能是你要把握的方向。