1 / 22

Sumukh Deshpande n Lecturer College of Applied Medical Sciences

BIOSTATISTICS (BST 211). Sumukh Deshpande n Lecturer College of Applied Medical Sciences. Lecture 5. Statistics = Skills for life. Normal Distribution 1. Empirical vs Theoretical Distributions 1. What are the frequencies?. Freq Tables in previous lectures are empirical.

griffith-torres
Download Presentation

Sumukh Deshpande n Lecturer College of Applied Medical Sciences

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. BIOSTATISTICS (BST 211) Sumukh DeshpandenLecturerCollege of Applied Medical Sciences Lecture 5 Statistics = Skills for life.

  2. Normal Distribution 1

  3. Empirical vs Theoretical Distributions 1 What are the frequencies? Freq Tables in previous lectures are empirical. You don’t know unless told! You can NOT work out EMPIRICAL data

  4. Empirical vs Theoretical Distributions 2 What are the frequencies? Now f = 2x +1 You can calculate THEORETICAL DATA

  5. This is a bell shaped curve with different centers and spreads depending on  and  The Normal Distribution:a theoretical function… (pdf) Note constants: =3.14159 e=2.71828

  6. Bell-Shaped

  7. The Normal Distribution f(X) Changingμshifts the distribution left or right. Changing σ increases or decreases the spread. s m X The good news is: I am NOT expecting much maths

  8. 7-3 Why Study Normal Distribution? • Natural phenomena follow Normal distribution. • Growth, size, height, weight, IQ, weather, …. All more or less follow Normal Distribution • If you learn Normal Distribution you might be able to predict behaviour and have better control

  9. 7-3 Characteristics of a Normal Distribution • The normal curve is bell-shaped and has a single peak at the exact center of the distribution. • The arithmetic mean, median, and mode of the distribution are equal and located at the peak. • Half the area under the curve is above the peak, and the other half is below it.

  10. 7-4 Characteristics of a Normal Distribution • The normal probability distribution is symmetrical about its mean. • The normal probability distribution is asymptotic - the curve gets closer and closer to the x-axis but never actually touches it.

  11. The beauty of the Normal Curve: No matter what  and  are, the area between - and + is about 68%; the area between -2 and +2 is about 95%; and the area between -3 and +3 is about 99.7%. Nearly all values fall within 3 standard deviations.

  12. 68% of the data 95% of the data 99.7% of the data 68-95-99.7 Rule

  13. Another beauty of the Normal Curve: If a dataset (x1, x2,…..xn) follows the Normal distribution with mean m and SD s, then the derived data set [(x1 – m)/s, (x2 – m)/s, ... (xn – m)/s] also follows Normal distribution BUT with mean m = 0 and s = 1. N(m , s) N(0 , 1) Normal distribution with mean m = 0 and s = 1 is called STANDARD NORMAL DISTRIBUTION (SND)

  14. STANDARD NORMAL DISTRIBUTION (SND) SND values, also known as z-scores, are tabulated and you are NOT expected to learn them by heart.. You just need to know how to use these tables!

  15. N(0 ,1) Here is a table of z-scores! What do I do with it?

  16. What do you need to do? • Learn how to convert X to Z • Learn how to use SND Tables

  17. Practice problem If birth weights in a population are normally distributed with a mean of 2 kg and a standard deviation of 0.15 kg, • What is the chance of obtaining a birth weight of 2.369 kg or heavier? • What is the chance of obtaining a birth weight of 1.8 kg or lighter?

  18. Answer a / 1 • What is the chance of obtaining a birth weight of 2.369 kg or heavier? Remember! Z-scores refer to the area on the left of z value (≤) In this case, we want 2.369 kg or HEAVIER…. Z ≥ 2.46

  19. Answer a / 2 Remember! Z-scores refer to the are on the left of z value (≤) In this case, we want 2.369 kg or HEAVIER…. Z ≥ 2.46 P(Z ≥ 2.46) = 1 – P(Z ≤ 2.46) = 1 - ???

  20. Z=2.4? Looking up probabilities in a SND table What is the area to the left of Z=2.46 in a standard normal curve? Area is 99.31% Z=2.46

  21. Answer a /3 Remember! Z-scores refer to the are on the left of z value (≤) In this case, we want 2.369 kg or HEAVIER…. Z ≥ 2.369 P(Z ≥ 2.46) = 1 – P(Z ≤ 2.46) = 1 -??? Therefore P(Z ≥ 2.46) = 1 – P(Z ≤ 2.46) = 1 – 0.9931 = 0.0069 = 0.69%

  22. Answer b b. What is the chance of obtaining a birth weight of 1.8 kg or lighter? • P(-Z) = 1 - P(Z) • P(Z ≤ -1.33) = 1 - P(Z≤1.33) =1 – 0.9082 = 9.18 %

More Related