How to estimate the sample mean and standard deviation from the sample size, median, extremes or quartiles?_Chinese Journal of Evidence-Based Medicine

Authors：

LUO Dehui ¹ , WAN Xiang ² , LIU Jiming ² ,  TONG Tiejun ¹

1. Department of Mathematics, Hong Kong Baptist University, Hong Kong, 999077, P.R.China;
2. Department of Computer Science, Hong Kong Baptist University, Hong Kong, 999077, P.R.China;

Corresponding author：

TONG Tiejun, Email: tongt@hkbu.edu.hk

Keywords：

Meta-analysis; Median; Range; Sample size; Sample mean; Sample standard deviation

DOI：

10.7507/1672-2531.201706060

Video：

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This article introduces the methods about how to use the summary statistics such as the sample median, minimum and maximum to estimate the sample mean and standard deviation for continuous outcomes. For the purpose of illustration, we also apply the existing methods to a real data example.

Citation： LUO Dehui, WAN Xiang, LIU Jiming, TONG Tiejun. How to estimate the sample mean and standard deviation from the sample size, median, extremes or quartiles?. Chinese Journal of Evidence-Based Medicine, 2017, 17(11): 1350-1356. doi: 10.7507/1672-2531.201706060 Copy

1.	文进, 李幼平. Meta 分析中效应尺度指标的选择. 中国循证医学杂志, 2007, 7(8): 606-613.
2.	Hozo SP, Djulbegovic B, Hozo I. Estimating the mean and variance from the median, range, and the size of a sample. BMC Med Res Methodol, 2005, 5: 13.
3.	Wan X, Wang W, Liu J, et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol, 2014, 14: 135.
4.	Luo D, Wan X, Liu J, et al. Optimally estimating the sample mean from the sample size, median, mid-range and/or mid-quartile range. Stat Methods Med Res, 2017, DOI: 10.1177/0962280216669183.
5.	刘海宁, 吴昊, 姚灿, 等. Meta 分析中连续性数据的深度提取方法. 中国循证医学杂志, 2017, 17(1): 117-121.
6.	侯晓雯, 时景璞, 陈欣. 在 Meta 分析中如何利用中位数、极差和样本量估算均数、标准差. 中国循证医学杂志, 2015, 15(4): 484-487.
7.	Rocha VZ, Ras RT, Gagliardi AC, et al. Effects of phytosterols on markers of inflammation: A systematic review and meta-analysis. Atherosclerosis, 2016, 248: 76-83.
8.	Triola MF. Elementary Statistics. Addison Wesley, 11th edition, 2009: 1-896.
9.	Bland M. Estimating mean and standard deviation from the sample size, three quartiles, minimum, and maximum. Int J Stat Med Res, 2014, 4(1): 57-64.
10.	David HA, Nagaraja HN. Order Statistics. Wiley Online Library, 1970: 1-465.
11.	Blom G. Statistical estimates and transformed beta-variables. Doctoral dissertation, Almqvist & Wiksell, 1958: 1-285.
12.	Nnoaham KE, Clarke A. Low serum vitamin D levels and tuberculosis: a systematic review and meta-analysis. Int J Epidemiol, 2008, 37(1): 113-119.
13.	Davies PD, Brown RC, Woodhead JS. Serum concentrations of vitamin D metabolites in untreated tuberculosis. Thorax, 1985, 40(3): 187-190.
14.	Grange JM, Davies PDO, Brown RC, et al. A study of vitamin D levels in Indonesian patients with untreated pulmonary tuberculosis. Tubercle, 1985, 66(3): 187-191.
15.	Davies PD, Church HA, Brown RC, et al. Raised serum calcium in tuberculosis patients in Africa. Eur J Respir Dis, 1987, 71(5): 341-344.
16.	Kotani K, Sahebkar A, Ursoniu S, et al. Lipoprotein(a) levels in patients with abdominal aortic aneurysm: a systematic review and meta-analysis. Angiology, 2017, 68(2): 99-108.
17.	Sofi F, Marcucci R, Giusti B, et al. High levels of homocysteine, lipoprotein (a) and plasminogen activator inhibitor-1 are present in patients with abdominal aortic aneurysm. Thromb Haemost, 2005, 94(5): 1094-1098.
18.	Galora S, Saracini C, Palombella AM, et al. Low-density lipoprotein receptor-related protein 5 gene polymorphisms and genetic susceptibility to abdominal aortic aneurysm. J Vasc Surg, 2013, 58(4): 1062-1068.
19.	Franks PJ, Edwards RJ, Greenhalgh RM, et al. Risk factors for abdominal aortic aneurysms in smokers, Eur J Vasc Endovasc Surg, 1996, 11(4): 487-492.
20.	Gagliardi ACM, Maranhao RC, De Sousa HP, et al. Effects of margarines and butter consumption on lipid profiles, inflammation markers and lipid transfer to HDL particles in free-living subjects with the metabolic syndrome. Eur J Clin Nutr, 2010, 64(10): 1141-1149.
21.	Devaraj S, Autret BC, Jialal I. Reduced-calorie orange juice beverage with plant sterols lowers C-reactive protein concentrations and improves the lipid profile in human volunteers. Am J Clin Nutr, 2006, 84(4): 756-761.
22.	Devaraj S, Jialal I, Vega-Lopez S. Plant sterol-fortified orange juice effectively lowers cholesterol levels in mildly hypercholesterolemic healthy individuals. Arterioscler Thromb Vasc Biol, 2004, 24(3): e25-e28.
23.	Hansel B, Nicolle C, Lalanne F, et al. Effect of low-fat, fermented milk enriched with plant sterols on serum lipid profile and oxidative stress in moderate hypercholesterolemia. Am J Clin Nutr, 2007, 86(3): 790-796.
24.	Sialvera TE, Pounis GD, Koutelidakis AE, et al. Phytosterols supplementation decreases plasma small and dense LDL levels in metabolic syndrome patients on a westernized type diet. Nutr Metab Cardiovasc Dis, 2012, 22(10): 843-848.
25.	Athyros VG, Kakafika AI, Papageorgiou AA, et al. Effect of a plant stanol ester-containing spread, placebo spread, or mediterranean diet on estimated cardiovascular risk and lipid, inflammatory and haemostatic factors. Nutr Metab Cardiovasc Dis, 2011, 21(3): 213-221.
26.	Banuls C, Martinez-Triguero ML, Lopez-Ruiz A, et al. Evaluation of cardiovascular risk and oxidative stress parameters in hypercholesterolemic subjects on a standard healthy diet including low-fat milk enriched with plant sterols. J Nutr Biochem, 2010, 21(9): 881-886.
27.	Clifton PM, Mano M, Duchateau GS, et al. Dose-response effects of different plant sterol sources in fat spreads on serum lipids and C-reactive protein and on the kinetic behavior of serum plant sterols. Eur J Clin Nutr, 2008, 62(8): 968-977.
28.	de Jong A, Plat J, Bast A, et al. Effects of plant sterol and stanol ester consumption on lipid metabolism, antioxidant status and markers of oxidative stress, endothelial function and low-grade inflammation in patients on current statin treatment. Eur J Clin Nutr, 2008, 62(2): 263-273.
29.	Hallikainen M, Lyyra-Laitinen T, Laitinen T, et al. Endothelial function in hypercholesterolemic subjects: effects of plant stanol and sterol esters. Atherosclerosis, 2006, 188(2): 425-432.
30.	Cohen J. Statistical power analysis for the behavioral sciences Lawrence Earlbaum Associates. Hillsdale NJ, 1988: 20-26.

1. 文进, 李幼平. Meta 分析中效应尺度指标的选择. 中国循证医学杂志, 2007, 7(8): 606-613.
2. Hozo SP, Djulbegovic B, Hozo I. Estimating the mean and variance from the median, range, and the size of a sample. BMC Med Res Methodol, 2005, 5: 13.
3. Wan X, Wang W, Liu J, et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol, 2014, 14: 135.
4. Luo D, Wan X, Liu J, et al. Optimally estimating the sample mean from the sample size, median, mid-range and/or mid-quartile range. Stat Methods Med Res, 2017, DOI: 10.1177/0962280216669183.
5. 刘海宁, 吴昊, 姚灿, 等. Meta 分析中连续性数据的深度提取方法. 中国循证医学杂志, 2017, 17(1): 117-121.
6. 侯晓雯, 时景璞, 陈欣. 在 Meta 分析中如何利用中位数、极差和样本量估算均数、标准差. 中国循证医学杂志, 2015, 15(4): 484-487.
7. Rocha VZ, Ras RT, Gagliardi AC, et al. Effects of phytosterols on markers of inflammation: A systematic review and meta-analysis. Atherosclerosis, 2016, 248: 76-83.
8. Triola MF. Elementary Statistics. Addison Wesley, 11th edition, 2009: 1-896.
9. Bland M. Estimating mean and standard deviation from the sample size, three quartiles, minimum, and maximum. Int J Stat Med Res, 2014, 4(1): 57-64.
10. David HA, Nagaraja HN. Order Statistics. Wiley Online Library, 1970: 1-465.
11. Blom G. Statistical estimates and transformed beta-variables. Doctoral dissertation, Almqvist & Wiksell, 1958: 1-285.
12. Nnoaham KE, Clarke A. Low serum vitamin D levels and tuberculosis: a systematic review and meta-analysis. Int J Epidemiol, 2008, 37(1): 113-119.
13. Davies PD, Brown RC, Woodhead JS. Serum concentrations of vitamin D metabolites in untreated tuberculosis. Thorax, 1985, 40(3): 187-190.
14. Grange JM, Davies PDO, Brown RC, et al. A study of vitamin D levels in Indonesian patients with untreated pulmonary tuberculosis. Tubercle, 1985, 66(3): 187-191.
15. Davies PD, Church HA, Brown RC, et al. Raised serum calcium in tuberculosis patients in Africa. Eur J Respir Dis, 1987, 71(5): 341-344.
16. Kotani K, Sahebkar A, Ursoniu S, et al. Lipoprotein(a) levels in patients with abdominal aortic aneurysm: a systematic review and meta-analysis. Angiology, 2017, 68(2): 99-108.
17. Sofi F, Marcucci R, Giusti B, et al. High levels of homocysteine, lipoprotein (a) and plasminogen activator inhibitor-1 are present in patients with abdominal aortic aneurysm. Thromb Haemost, 2005, 94(5): 1094-1098.
18. Galora S, Saracini C, Palombella AM, et al. Low-density lipoprotein receptor-related protein 5 gene polymorphisms and genetic susceptibility to abdominal aortic aneurysm. J Vasc Surg, 2013, 58(4): 1062-1068.
19. Franks PJ, Edwards RJ, Greenhalgh RM, et al. Risk factors for abdominal aortic aneurysms in smokers, Eur J Vasc Endovasc Surg, 1996, 11(4): 487-492.
20. Gagliardi ACM, Maranhao RC, De Sousa HP, et al. Effects of margarines and butter consumption on lipid profiles, inflammation markers and lipid transfer to HDL particles in free-living subjects with the metabolic syndrome. Eur J Clin Nutr, 2010, 64(10): 1141-1149.
21. Devaraj S, Autret BC, Jialal I. Reduced-calorie orange juice beverage with plant sterols lowers C-reactive protein concentrations and improves the lipid profile in human volunteers. Am J Clin Nutr, 2006, 84(4): 756-761.
22. Devaraj S, Jialal I, Vega-Lopez S. Plant sterol-fortified orange juice effectively lowers cholesterol levels in mildly hypercholesterolemic healthy individuals. Arterioscler Thromb Vasc Biol, 2004, 24(3): e25-e28.
23. Hansel B, Nicolle C, Lalanne F, et al. Effect of low-fat, fermented milk enriched with plant sterols on serum lipid profile and oxidative stress in moderate hypercholesterolemia. Am J Clin Nutr, 2007, 86(3): 790-796.
24. Sialvera TE, Pounis GD, Koutelidakis AE, et al. Phytosterols supplementation decreases plasma small and dense LDL levels in metabolic syndrome patients on a westernized type diet. Nutr Metab Cardiovasc Dis, 2012, 22(10): 843-848.
25. Athyros VG, Kakafika AI, Papageorgiou AA, et al. Effect of a plant stanol ester-containing spread, placebo spread, or mediterranean diet on estimated cardiovascular risk and lipid, inflammatory and haemostatic factors. Nutr Metab Cardiovasc Dis, 2011, 21(3): 213-221.
26. Banuls C, Martinez-Triguero ML, Lopez-Ruiz A, et al. Evaluation of cardiovascular risk and oxidative stress parameters in hypercholesterolemic subjects on a standard healthy diet including low-fat milk enriched with plant sterols. J Nutr Biochem, 2010, 21(9): 881-886.
27. Clifton PM, Mano M, Duchateau GS, et al. Dose-response effects of different plant sterol sources in fat spreads on serum lipids and C-reactive protein and on the kinetic behavior of serum plant sterols. Eur J Clin Nutr, 2008, 62(8): 968-977.
28. de Jong A, Plat J, Bast A, et al. Effects of plant sterol and stanol ester consumption on lipid metabolism, antioxidant status and markers of oxidative stress, endothelial function and low-grade inflammation in patients on current statin treatment. Eur J Clin Nutr, 2008, 62(2): 263-273.
29. Hallikainen M, Lyyra-Laitinen T, Laitinen T, et al. Endothelial function in hypercholesterolemic subjects: effects of plant stanol and sterol esters. Atherosclerosis, 2006, 188(2): 425-432.
30. Cohen J. Statistical power analysis for the behavioral sciences Lawrence Earlbaum Associates. Hillsdale NJ, 1988: 20-26.

Chinese Journal of Evidence-Based Medicine

How to estimate the sample mean and standard deviation from the sample size, median, extremes or quartiles?

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