Statistical Estimation Exam 1 Flashcards
Point estimation
- single value estimated for a variable of interest
- useful information about population parameters, but no information about precision of estimate
- Examples: mean, proportion
Interval estimation
- range of values constructed around a point estimate with a certain level of acceptable error
- Helps us understand the precision of an estimate
- Example: confidence interval
formula for confidence interval
CI = Point Estimate ± (Critical Value)(SE)
SE
- Standard error of the estimate
- Represents sampling error associated with the particular estimate
- Mean and proportion have their own SE formula
What happens when a confidence interval increases?
- wider = less precise
- increase standard error
- decrease sample size
What happens when a confidence interval decreases?
- narrower = more precise
- decrease standard error
- increase sample size
Probabilistic Approach
Probability of the interval containing the population parameter in the event that the study was done repeatedly
True Approach
The true variable can be as low or high as the interval with x% confidence
Confidence intervals
- provide information about the precision of estimates
- contain population parameter respective of a specified percentage of the time
- represent reliability of a point estimate to represent true value of population parameter
importance of confidence interval when testing null hypothesis
- If the interval does not contain the null value, we reject the null hypothesis at the α level.
- If the interval contains the null value, we fail to reject the null hypothesis at the α level.
value of null: mean
For tests of difference, the null value is usually 0 because the difference between two means would be zero if they were not different from each other.
value of null: proportion
For ratios of two quantities, the value representing the null is 1 because this reflects the condition where the numerator and denominator in a ratio are equal.
