Standard Errors and Confidence Intervals Flashcards
Will you ever know the population (u) mean’s true value depending on sample size?
No but a large sample size is more representative and gives a more precise estimate of the population mean
Why does a large sample size lead to a more precise estimate of population (u) mean?
Because the distribution of samples mean becomes more concentrated about the population mean (u) as the sample size increases
What does standard error of the mean (SEM) or Standard Error measure?
How precisely the sample mean estimates the population mean
How to calculate standard error from a single sample
Why use Standard Error (SE) as well as standard deviation?
- SE is the standard deviation of a HYPOTHETICAL DISTRIBUTION THAT IS NEVER OBSERVED VALUES
- Standard deviation is a DESCRIPTIVE TOOL well as Standard Error is a INFERENTIAL TOOL which measures the precision of estimates of population parameters
- SE is used for standard deviation of the distribution of sample means and to change nomenclature now may cause greater confusion
How should you use standard error?
‘Mean (±2E)’- this is to accurately assert that the population mean lies within 95% confidence intervals (m±2E)
What is an alternative name for confidence intervals?
Interval estimates
What is m in m(±2SE) in confidence intervals?
It is the point estimate which is a single number estimate. This does have advantages as a parameter estimate but DOESN’T FULLY acknowledge the uncertainty in the estimate.
When does the differences between alternative outcomes become apparent
Through the use of confidence intervals
When does standard error decrease
When the sample size increases as the denominator (n) gets larger
Does standard deviation get smaller or larger or neither as sample size increases
Neither therefore SD is a better estimate of population standard deviation as n increases
What does the sqaure root do in the SE formula
It reduces the SE decrease with an increase in sample
How do you half the Standard Error?
The sample size must quadruple
Does the definition of the confidence intervals only work if the sample mean is normally distributed
Yes the definition of the confidence intervals only works if the sample mean is normally distributed
What is the Central Limit Theorem (CLT)
If the samples AREN’T NORMALLY DISTRIBUTED but the SAMPLE MEANS have a distribution that is often very close to a normal distribution
When does the population mean skewness arise
From a variable that has substantial variation.
Large departures from the mean with this variable can only occur through values larger than the mean so an ASYMMETRIC DISTRIBUTION is inevitable
What happens to the curve in a large sample when sample means deviate from the population mean by small amounts
The shape of the distribution is not rendered asymmetric as the sample means must be positive
For 95% CI (Confidence Intervals) what are the equation
m–1.96xs/√ n, m+1.96xs/√ n
What happens to the width when the sample size (n) increases ?
The width decreases
What happens when there is a higher confidence level?
The width increases
What is the P-value
A probability
With a P-value of <0.05 does it provide evidence against the null hypothesis or does it support the null hypothesis
It provides evidence against the null hypothesis and the test is significant
