Estimation Flashcards
What is a confidence interval?
A range of values centred on the sample estimate which is likely to include the population parameter with a given probability. Usually 95%
Why are confidence intervals used?
To give a range of plausible values for the effect of an intervention on an outcome
What is a population?
Any collection of individuals (or measurements made) in which we are interested in
What is population distribution?
The frequency distribution of a variable in the population
Give examples of population parameters
Means
Medians
Standard deviations
Proportions
What is a sample?
Any subset of a population, ideally selected to be representative
What are the two types of sampling methods?
Probability and non-probability
What is probability sampling?
Each member of the population has a known probability of being selected
Give examples of probability sampling
Random
Systematic
Stratified
Cluster
Multistage
What is non-probability sampling?
Members are selected from the population in a non-random manner
Give examples of non-probability sampling
Convenience
Self-selecting
Judgement
Quota
What are sample statistics
Summary values calculated in samples
E.G Means and proportions
What is accuracy?
The absence of bias
If samples we repeatedly drawn and the means drawn, the sample mean should be centred about the population mean
What is precision?
Repeatability
If samples we repeatedly drawn and the means calculated, these sample means should show little variation. The answers should be closer together
What is the sampling distribution of a statistic?
The frequency of distribution of that statistic over all possible samples of a given size selected from the population
What is standard error?
The standard deviation of the sampling distribution of a statistic
How do you calculate confidence intervals?
Estimate +/- M x standard error of estimate
What multiplier do you use when calculation 95% confidence intervals? And why?
1.96
Because 95% of a normal distribution lies within 1.96 standard deviations of the mean
What is defined as a large sample?
A sample larger than 30
n >30
How do you calculate the standard error of a sample mean?
SE(x bar) = s / sqr rt n
How do you calculate the 95% confidence interval for a population proportion (pie)?
When n is large
P +/- 1.96 (sqr rt) (P(P-1) / n)
What is the definition of 95% confidence intervals?
In 95% of repeated samples from the population, confidence intervals calculated this way will capture the population parameter
What is classified as a small sample?
Less than 30 people
n<30
What are the two changes made when calculating confidence intervals when using a small sample?
Assume that the variable of interest is normally distributed in the population from which the sample came.
No longer use normal distribution to obtain the multiplier, instead the multiplier comes from the students t distribution ( shape depends on degrees of freedom)
What is the equation for working out the 95% confidence intervals when using a small sample size?
(X bar) +/- (t, (n-1, 0.025) s/ sqr rt n)
