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What is S.D. is 1.96 the confidence limit is - and explain in detail?
Ans. is 'c' i.e., 95% For 1.96 SD 2 SD, confidence limit is 95%. Area under standard normal distribution curve o It can be understand by the 68-95-99.7 rule - i) The area between one standard detion on either side of the mean ( +- 1 a) will include 68 percent of the values. ii) The area between two standard detions on either side of the mean will cover 95% of values. iii) The area between three standard detion will include 99.7% of values. o These limits on either side of the mean is called "confidence limits". o For example, if we are considering the 95 percent confidence limits (Area under 2 SD), that means that 95% of the values in the distribution will be included between the limits (2 SD --> x +- 2 a). Therefore, the probability of a reading falling outside confidence limit (95%) is only 5%, i.e. 1 in 20 (P = 0.05). o So, For 1 SD, confidence limit 68% For 2 SD, confidence limit 95% For 3 SD, confidence limit --> 99.7% Note: Generally we consider that for 2SD, confidence limit is 95%. However, actual (exact) values are slightly different-o Actual parameters in a Normal (Gaussian) distribution. o Mean +- 1 SD ( la) limits include 68.27% values o Mean +- 2SD ( 26) limits include 95.45% values o Mean +- 1.96SD ( 1.966) limits include 95% values o Mean +- 3SD ( 3a) limits include 99.73% values o Mean +- 2.58SD ( +- 2.58 a) limits include 99% values Also know: o Values that differ from the mean by more than 2SD are rare, being only 4.55%. o Values higher or lower than the Mean +- 3SD ( 36) are very rare, being only 0.27%. o 6 SD (3 on either side of mean) cover almost the entire range of a variable character (SD divides the range into 6 equal sub-range) o Minimum sample size required for establishment of normal range for any health parameter: 300 healthy subjects. o Confidence limits of normal curve can never be 100%. therefore the limbs of curve never touch base line.