NORMAL CURVE in biostatistics and application
- 2. • DATA can be distributed (spread out) in different ways It can be spread out more on the left Or more on the right Or it can be all jumbled up
- 3. • But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a "Normal Distribution" like this: It is often called a "Bell Curve" because it looks like a bell.
- 4. Many things closely follow a Normal Distribution: • Heights of people • Size of things produced by machines • Errors in measurements • Blood pressure • Marks on a test
- 5. We say the data is "normally distributed": The Normal Distribution has: mean= median= mode symmetry about the center Asymptoptic 50% of values less than the mean and 50% greater than the mean
- 6. STANDARD DEVIATIONS • The Standard Deviation is a measure of how spread out numbers are (read that page for details on how to calculate it). • When we calculate the standard deviation we find that generally: 68% of values are within 1 standard deviation of the mean 95% of values are within 2 standard deviations of the mean 99.7% of values are within 3 standard deviations of the mean
- 7. • It is good to know the standard deviation, because we can say that any value is: • likely to be within 1 standard deviation (68 out of 100 should be) • very likely to be within 2 standard deviations (95 out of 100 should be) • almost certainly within 3 standard deviations (997 out of 1000 should be)
- 8. STANDARD SCORES • The number of standard deviations from the mean is also called the "Standard Score", "sigma" or "z-score“ • So to convert a value to a Standard Score ("z-score"): first subtract the mean, then divide by the Standard Deviation • The z-score formula that we have been using is: z is the "z-score" (Standard Score) x is the value to be standardized μ ('mu") is the mean σ ("sigma") is the standard deviation
- 9. And doing this is called "Standardizing": We can take any Normal Distribution and convert it to The Standard Normal Distribution.
- 10. Why Standardize ... ? • It can help us make decisions about our data. • It also makes life easier because we only need one table (the Standard Normal Distribution Table), rather than doing calculations individually for each value of mean and standard deviation.
- 11. DIVERGENCE IN NORMALITY • In the normal curve model ,the mean ,median and mode all coincide and there is perfect balance between the right and left values of the curve • A perfect symmetrical curve rarely exists in our actual dealing – slight deviated or distorted bell shaped curve is also accepted as a normal distribution.
- 12. • In case where the score of individual in the group seriously deviate from the average ,the curve representing these distribution also deviate from the shape of a normal curve. This deviation or divergence from normality tends to vary in 2 ways Skewness kurtosis
- 13. SKEWNESS • A distribution is said to be skewed when the mean and median fall at different points in the distribution and the balance ie the point of center of gravity is shifted to one side or the other (to the left or right) negative skewness positive skewness
- 16. KURTOSIS • Kurtosis refers to the divergence in the height of the curve , specially in the peakedness • They are of 3 types 1. Platy kurtic-flatter peak at the center than normal curve 2. Lepto kurtic—more peaked at the center than normal curve 3. Meso kurtic-almost resembles a normal curve
- 18. Test of normality Analytical method Graphical distribution Kolmogorov smirnov test Shapiro-wilk test Anderson darling test Histogram Q-q plot Kolmogorov smirnov test If sample size is more than 50 Shapiro-wilk test If sample size is less than 50
- 19. Analytical method • Null gypothesis – these data are normally distributed- • P Value is less than 0.05 not normally distributed • More than 0.05-normally distributed • Disadvatnage- Calculated p value is infulenced by sample small sample-p value is larger than 0.00.5 Distribution of the popultn deviates very slightly from normal distribution
- 20. Graphical distribution • Histogram • Q-q plot • Stem and leaf plot