![Standard Deviation
• Most frequently used measure of deviation
• Denoted by Greek letter “sigma” [σ]
• Sample size >30 , denominator= n
• Sample size < 30, denominator= n-1](https://image.slidesharecdn.com/sdandchi-squaretest2-171220170643/85/Standard-Deviation-and-Shi-square-test-2-8-320.jpg)
Standard Deviation and Shi square test (2)
- 1. Biostatistics Standard Deviation Chi-Square Test Dr.Sujit Kumar Kar Assistant Professor of Psychiatry KGMU, Lucknow
- 2. Standard Deviation is a measure of dispersion
- 4. Measures of dispersion Range Mean deviation Standard deviation
- 5. Range • Simplest measure of dispersion • Difference between highest and lowest value in a given sample • Not of much practical importance
- 6. Range India innings (target: 88 runs from 16 overs) Runs B 4s 6s SR K Srikkanth* b Waqar Younis 17 20 2 0 85.0 0 R Lamba run out 10 19 1 0 52.6 3 NS Sidhu c Mansoor Akhtar b Aaqib Javed 2 6 0 0 33.3 3 M Azharuddin c Saleem Malik b Aaqib Javed 21 19 2 0 110. 52 SR Tendulkar c Wasim Akram b Waqar Younis 0 2 0 0 0.00 RJ Shastri b Waqar Younis 1 6 0 0 16.6 6 M Prabhakar lbw b Imran Khan 10 11 1 0 90.9 0 KS More† c Abdul Qadir b Imran Khan 2 6 0 0 33.3 3 V Razdan b Imran Khan 1 4 0 0 25.0 0 SA Ankola not out 7 3 0 1 233. 33 Maninder Singh not out 0 1 0 0 0.00 Extras (b 2, lb 5, w 2) 9 Total (9 wickets; 16 overs) 80 (5.00 runs per over)
- 7. Mean deviation • Average of the deviations from the arithmetic mean • Mean = 11 • Sample – 1, 2, 7, 11, 13, 17, 18, 19 • Total Deviation from mean = 10+9+4+0+2+6+7+8= 45 • Mean deviation = 45/8 =5.625
- 8. Standard Deviation • Most frequently used measure of deviation • Denoted by Greek letter “sigma” [σ] • Sample size >30 , denominator= n • Sample size < 30, denominator= n-1
- 13. Chi-Square test
- 14. • Chi-Square test – an alternative method of testing the significance of difference between two proportions • Can also be used when more than two groups are to be compared
- 18. Team Won Lost Total Win rate Male 40 60 100 40% Female 25 25 50 50% Total 65 85 150 ---------------- Example Steps • Testing the null hypothesis • Applying the χ2 test • Finding the degree of freedom • Referring probability tables
- 19. Null hypothesis • Lets assume - There was no difference between the result of males and females • Then test the hypothesis • Proportion of win = 65/150=0.433 • Proportion of loss = 85/150=0.567 • Expected win in males = 0.433*100= 43.3 • Expected win in females = 0.433*50= 21.15 • Expected loss rate in males=0.567*100=56.7 • Expected loss rate in males=0.567*50=28.35
- 20. Team Won Lost Total Win rate Male 40 (e=43.3) 60 (e=56.7) 100 40% Female 25 (e=21.15) 25 (e=28.35) 50 50% Total 65 85 150 ---------------- Example
- 21. Degree of freedom (d.f) • d.f= (c-1)* (r-1) • c= number of columns • r= number of rows
- 24. Thank You