The Statistical Estimation Flashcards
What is a Point Estimate?
Single value estimated for a variable of interest
What does a Point Estimate provide?
Useful information about population parameters but no information about precision of estimate
What are examples of Point Estimate?
Mean and Proportion
What is an Interval Estimate?
A range of values constructed around a point estimate with a certain level of acceptable error
What does a Interval Estimate provide?
Understand the precision of an estimate
What does a Wider interval estimate mean?
Less precision
What does a Narrower estimate mean?
More precision
What is an example of Interval Estimate?
Confidence Interval
What is a Confidence Interval?
Contain the population parameter respective of a specified percentage of the time
What does a Confidence Interval provide?
A level of certainty about the point estimate being able to represent the true value of a population parameter
What does a Confidence Interval represent?
The reliability of a point estimate to represent the true value of a population parameter
What is the equation for Confidence Interval CI?
Point Estimate +/- (Critical Value)(SE)
What is the Z Critical Value for a = 0.05?
1.96
What is the Z Critical Value for a = 0.01
2.58
Does changing the point estimate change the width of the interval?
NO
What is SE?
Standard of Error of the estimate
What does SE represent?
Represents the sampling error associated with the particular estimate
What are the types of SE?
Mean and Proportion
What changes when calculating CI?
SE specifically the type aka Mean or Proportion
SE Mean Formula
SD/ (square root of n)
SE Proportion Formula
(Square Root of (p (1-p)/ n))
OR
Square Root of (pq) / n
What is p in the SE Proportion?
P = proportion
1 - p = q
What is a Probabilistic Approach?
Probability of the interval containing the population estimate in repeated samples
What is a True Approach?
States that the true variable (mean or proportion) can be as low as the calculated low bound and as high as the calculated upper bound with a certain level of confidence
Ex. At least 95 out of 100 times with the mean falling between X and Y
Probabilistic
Ex. With 95% confidence the true mean can be as low as X and as high as Y
True
What causes for a WIDER CI Width?
- Increase % Confidence
- Decrease Alpha
- Increase Standard Error
- Decrease Sample Size
What causes for a NARROWER CI Width?
- Decrease % Confidence
- Increase Alpha
- Decrease Standard Error
- Increase Sample Size
Wider CI Intervals means what?
Less Precise Estimate
Narrower CI Intervals means what?
More Precise Estimate
If the Confidence Interval does NOT contain the NULL Value =
REJECT the null hypothesis
If the Confidence Interval DOES contain the NULL Value =
We FAIL to reject the null hypothesis
What is the null value for a test of DIFFERENCE?
= 0
0 = NOT different from each other
What is the null value for a test of ratios (2 quantities
=1
