Confidence Intervals
➢ Interpret a confidence level. ➢ Construct and interpret a confidence interval for the mean of a Normal population. ➢ Describe how confidence intervals
Guidelines for Using Confidence Intervals for Public Health
13 jul 2012 However a general description of how to calculate confidence intervals and formulae for calculating confidence intervals in a wide variety of ...
Calculating Approximate Standard Errors and Confidence Intervals
A sample estimate and its estimated standard error can be used to construct confidence intervals; when these estimates are unbiased the statistical properties
Basic Statistics - Probability and Confidence Intervals
interval-training-to-maximize-time-and-fitness/. Page 7. Confidence Levels. ▻ A confidence level is the probability that the interval estimate will include ...
Calculating and Using Confidence Intervals for Model Validation
1 We call the calculated interval [12.0304. 12.0696]
Statistics in Medicine Calculating confidence intervals for some non
21 may 1988 sample of observations. Calculations of confidence intervals for the difference between two population medians or means (a non-parametric ...
t-distribution Confidence Level 60% 70% 80% 85% 90% 95% 98
Confidence Level. 60%. 70%. 80%. 85%. 90%. 95%. 98%. 99%. 99.8% 99.9%. Level of Significance. 2 Tailed. 0.40. 0.30. 0.20. 0.15. 0.10. 0.05. 0.02. 0.01. 0.002.
ci — Confidence intervals for means proportions
https://www.stata.com/manuals/rci.pdf
Interpreting Confidence Intervals
24 dic 2014 This best practice introduces confidence intervals which use observed data to obtain an interval estimate of an unknown population parameter ...
Confidence Intervals for the Median and Other Percentiles
12 dic 2016 The construction of confidence intervals for the median or other percentiles
Confidence Intervals
? Interpret a confidence level. ? Construct and interpret a confidence interval for the mean of a Normal population. ? Describe how confidence intervals
Confidence intervals
Confidence Intervals. I. Interval estimation. The particular value chosen as most likely for a population parameter is called the point estimate.
t-distribution Confidence Level 60% 70% 80% 85% 90% 95% 98
Confidence Level. 60%. 70%. 80%. 85%. 90%. 95%. 98%. 99%. 99.8% 99.9%. Level of Significance. 2 Tailed. 0.40. 0.30. 0.20. 0.15. 0.10. 0.05. 0.02. 0.01.
Basic Statistics - Probability and Confidence Intervals
Probability and Confidence Intervals. Learning Intentions. Today we will understand: ? Interpreting the meaning of a confidence interval.
Asymptotic Confidence Intervals for Indirect Effects in Structural
ASYMPTOTIC CONFIDENCE INTERVALS 291 topic of structural equation models. (For a thorough review of the literature see Bielby and Hauser
Estimation and Confidence Intervals
Estimation and Confidence Intervals. Fall 2001. Professor Paul Glasserman. B6014: Managerial Statistics. 403 Uris Hall. Properties of Point Estimates.
Calculating and Using Confidence Intervals for Model Validation
A confidence interval has an associated confidence level Confidence intervals are of interest in modeling and simulation because they are often used in ...
Confidence Intervals for the Tail Index
regular variation. Keywords: confidence interval; coverage accuracy; Hill estimator; tail index. 1. Introduction. Several estimators
230-2008: ALPHA_CI: A SAS® Macro for Computing Confidence
(summed across items) scores (Crocker & Algina 1986). . ALTERNATIVE METHODS FOR COEFFICIENT ALPHA CONFIDENCE INTERVALS. The sampling distribution of
Confidence Intervals
If we know that each member of the population has
probability p of having a certain characteristic, we can use the CLT theorem to study the distribution of a sample mean.What if we don't know p, all we have is our data
from the sample. We want to make an estimate of p, and give some margin of error. This is essentially what a confidence interval is.For a prescribed level of confidence (less than
100%), we want to determine a range for which we
are THAT confident the true population probability "p" is within the range.Confidence Intervals, cont.
Usually we want a fairly high confidence level:
75%, 95% or 99% are common, but really any
percentage less than 100 is possible. The larger the confidence, the wider the interval.The more sure we are of the confidence interval,
the less precise it is. estimateConfidence intervalMargin of
errorMargin of errorConfidence Interval for Proportion
p is the population proportion (of a certain characteristic)To find a C% confidence interval, we need to
know the z-score of the central C% in a standard-normal distribution. Call this 'z'Our confidence interval is p±z*SE(p)
p is the sample proportionZ values for some CIs
For your reference, these could be useful:
Confidence
%# standard deviations (z)50%0.67449
75%1.15035
90%1.64485
95%1.95996
97%2.17009
99%2.57583
99.9%3.29053To calculate, use
invNorm(CI + (1-CI)/2) e.g. for 75% confidence, invNorm(.75 + (1-.75)/2) =invNorm(.75+ .25/2) =invNorm(.875)Example: Bad Apples
You want to give a 95% confidence interval of how
many apples in a given orchard are bad this year. Of all harvested apples, you randomly test 1000 apples and find 35 of them are bad. p estimate is p=.035, so q=.965The middle 95% is within 1.96 sds
Our confidence interval is .035±1.96*.0058, i.e. between and .0236 and .0464We are 95% confident that in this orchard between
2.36% and 4.64% of apples are bad.^^
Margin of Error
Based on a certain % confidence interval, the
amount we add/subtract from our estimate is the margin of error.In the previous example, the margin of error
was 1.96*.0058=.011368 which is 1.1368%Example: Margin of Error
A poll of 1654 adults asked whether they have
ever bobbed for apples. 76% said "Yes."For 93% confidence, what is the margin of
error?To find the z-score for the central 93%,
remember that 7% is in the tails, 3.5% in the upper tail and 3.5% in the lower tail. So invNorm(.965)=1.812 is our z =.01903, or 1.903%Example: Margin of Error
A poll of 1654 adults asked whether they have
ever bobbed for apples. 76% said "Yes."What is the margin of error for 99% confidence?
Similarly, the z value for central 99% is
invNorm(.995)=2.576ME99%=2.576*.010501=.02705 or 2.705%
As confidence level of the interval
increases, so does the margin of error!Example: Determine Sample Size
for given Confidence & MEIt is estimated that 43% of adults 25-35 sing in
the shower. We want to see if this is true for adults 35 and older. How many do we need to sample to have a margin of error of 5% at a90% confidence level.
So n=16.28652=265.25, so we need 266 people
sampled (round up to the next whole person)Decreasing Margin of Error by
increasing nIf we increase the sample size, the margin of
error goes down, but at a rate of the square root of the change in "n".To halve ME, we need to quadruple (x4) the
sample sizeTo get 1/10th the ME, we need to increase
sample size to be 100 times as largeDetermine CI from Margin of Error
you the confidence level, because you can determine zC, and from that figure out the
confidence level. zThen Confidence level is found:
normalcdf(-zC, zC)
-zCzCExample: Approval Rating
The results of a poll of 656 random citizens give
the mayor's approval rating at 67% with a 4% margin of error. How confident are we that the city-wide approval is between 63% and 71%? normalcdf(-2.1788, 2.1788) = .97065So the poll used a 97.065% confidence level.
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