Lecture 6 Point and Interval Estimation.pptx

Point and Interval Estimation:
Objectives:
Apply the basics of inferential statistics in terms of point estimation.
Compute point and estimation of population means and confidence interval.
Interpret the results of point and interval estimation.
Estimation:
Estimating the value of parameter from the sample:
An aspect of inferential statistics.
Why to estimate: Population is large enough so we
can only estimate.
Types of estimation:
Point Estimation:
A specified number value (single value) that is an estimate of a population parameter. The point estimate of the population mean µ is the sample mean.
Interval Estimate:
Range of values to estimate about population parameter.
Confidence Interval Estimation:
Range of values to estimate about population parameter.
May contain the parameter or not (Degree of confidence).
Ranges between two values.
Example:
Age (in years) 4 BScN students: 20<µ < 25 or (22.5 +2.5)
FORMULA:
Point estimate (x) + Critical Value x Standard Error.
Confidence Interval is a particular interval of estimate.
Given that sample size is large, the 95% of the sample means taken from same population and same sample size will fall in + 1.96 SD of the population mean.
Three commonly used Confidence Intervals are 90%, 95% (by default) , and 99%.
Why not too small or too large confidence intervals?
Too wide: 99.9% Interval too broad
Too narrow: 80 % More uncertainty to have population mean.
The 99% of the sample means taken from same population and
same sample size will fall in + 2.575 SD of the population mean.
Interpretation:
99% probability that interval will enclose population parameter and 1% chance that it will not have population parameter.
Level of confidence: The level of certainty that the interval will have the true population mean.
Chances of Error: Chances that the interval will not cater the true parameter.
Sum of level of confidence and chances of error =100%

1. Shakir Rahman BScN , MScN , MSc Applied Psychology, PhD Nursing (Candidate) Principal & Assistant Professor Ayub International College of Nursing & AHS Peshawar Visiting Faculty Swabi College of Nursing & Health Sciences Swabi Nowshera College of Nursing & Health Sciences Nowshera

2. By the end of the session, students will be able to: Apply the basics of inferential statistics in terms of point estimation. Compute point and estimation of population means and confidence interval. Interpret the results of point and interval estimation.

3. Descriptive Inferential Statistics Estimation H y p ot h e si s testing Point E s t i mat e Interval E s t i mat e 3

4. A large group of your employees went to restaurant and ordered a dessert. None of you liked it. May be, 45% of them will prefer not eating it and leaving the restaurant and 15% of them will complaint about it to the waiter to get a fresh new dessert. With margin of error of 3% points. You interviewed 400 of employees.

5. How do mentioned estimations or predictions are related to true population parameter? What is margin of error? Is the sample of 400 sufficient to claim anything about population of all employees ordering that dessert?

6. Estimating the value of parameter from the sample . An aspect of inferential statistics. Why to estimate: Population is large enough so we can only estimate. Types of estimation: Point Estimation: A specified number value (single value) that is an estimate of a population parameter. The point estimate of the population mean µ is the sample mean.

7. Interval Estimate: Range of values to estimate about population parameter. Example: What is an estimate of score of nursing students in entry test of Nursing school? (Out of 100 marks) 90 80 c. 80-95 d. 75-85 Point Estimate Interval Estimate

8. The mean height of Pakistani girls at age 20 years is: 5.2 fts 5-5.5 fts 5 fts d. 5.1-5.6 fts Which of the following is an example of point estimate and which is an example of interval estimate.

9. Sample statistics. From random sampling Aims to estimate about population parameter. -  Ѕ ----- Estimates ----- ----- Est i m ates ----- µ  Repeated sampling in experiments will result in more than one sample means, among which any one could be a point estimator to estimate about population parameter or mean.

10. How good is the point estimate?

11. Confidence Interval Estimation. Range of values to estimate about population parameter. May contain the parameter or not (Degree of confidence). Ranges between two values. Example: Age (in years) 4 BScN students: 20<µ < 25 or (22.5 + 2.5)

12. P opul a tion Parameter Upper Confidence Limit Lower Confidence Limit Width of Confidence Interval

13. Population Parameter (22.5 yrs) Upper Confidence Limit (25 yrs) Lower Confidence Limit (20 yrs) Width of Confidence Interval

14. FORMULA: _ Point estimate (x) + Critical Value x Standard Error

15. Confidence Interval is a particular interval of estimate Central Limit Theorem: Given that sample size is large, the 95% of the sample means taken from same population and same sample size will fall in + 1.96 SD of the population mean. _ _ X + 1.96 σ/  n

16. S tandard N ormal C urve 17

17. μ 16 Consider a 95% confidence interval: 1    .95   .05  / 2  .025 Z= 1.96 α  .025 2 α  .025 2 Upper Confidence Limit Point Estimation .475 .475 Z= -1.96 Lower Confidence Limit μ l Z μ u

18. 90 % = 0.05 95 % = 0.025 99 % = 0.005

19. Three commonly used Confidence Intervals are 90%, 95% (by default) , and 99%. Why not too small or too large confidence intervals? Too wide: 99.9%  Interval too broad Too narrow: 80 %  More uncertainty to have population mean.

20. The 99% of the sample means taken from same population and same sample size will fall in + 2.575 SD of the population m ean. _ _ X + 2.575 σ/  n Interpretation: 99% probability that interval will enclose population parameter and 1% chance that it will not have population parameter.

21. Level of confidence (1- ) : The level of certainty that the interval will have the true population mean. Chances of Error : Chances that the interval will not cater the true parameter. Sum of level of confidence and chances of error =100%

22. The more the confidence, the wider will be the confidence interval.

23. FORMULA: _ Point estimate (x) + Critical Value x Standard Error

24. Th e su r v e y o f 3 em e r g e n c y r oo m p a tie n ts found that the average waiting time for treatment was 174.3 minutes. Given that the standard deviation is 46.5 minutes. Find the best point estimate of population parameter (mean). The confidence level is 95%. Reference: Bluman (2012)

25. Point estimate (x) + Critical Value x Standard Error 174.3 + 1.96 x 46.5/ √ 30 174.3 + 1.96 x 46.5/ 5.47 174.3 + 1.96 x 8.5 174.3 + 16.6 157.7, 190.9 (LL , UL) LL: Lower limit UL: Upper limit

26. Sample Size (Increase in sample size will narrow confidence interval). Increase in variability will increase confidence Interval.

27. Bluman (2012). Elementary Statistics: A Step by Step Approach (8 th .). McGraw Hill. Daniel (2014). Biostatistics: Basic Concepts and Methodology for the Health Sciences. New York: John Wiley & Sons.

28. Acknowledgements Dr Tazeen Saeed Ali RM, RM, BScN, MSc ( Epidemiology & Biostatistics), Phd (Medical Sciences), Post Doctorate (Health Policy & Planning) Associate Dean School of Nursing & Midwifery The Aga Khan University Karachi. Kiran Ramzan Ali Lalani BScN, MSc Epidemiology & Biostatistics (Candidate) Registered Nurse (NICU) Aga Khan University Hospital