Statistical Methods- Lecture 12/13/14 Flashcards
What are one-sided hypothesis tests?
In one sided hypothesis tests we are interested in p differing from the null value p0 in one direction
- If there is only value in detecting if population parameter is less than p0, then HA: p < p0
- If there is only value in detecting if population parameter is greater than p0, then HA: p > p0
What are two-sided hypothesis tests?
In two sided hypothesis tests we are interested in whether p is either above or below some null value p0: HA: p ≠ p0
.Two-sided tests are often more appropriate as we often want to detect if the data goes clearly in the opposite direction of a hypothesis direction as well
What are the type of errors that can be made when constructing a hypothesis test?
A Type 1 Error is rejecting the null hypothesis when H0
is true
A Type 2 Error is failing to reject the null hypothesis when HA is true
How do we choose a significance level when trying to reduce errors?
- Normally 0.05 is chosen for the significance level
- If making a Type 1 Error is dangerous or expensive, we should choose a small significance level (e.g. 0.01).
- If a Type 2 Error is more dangerous or much more costly than a Type 1 Error, then we should choose a higher significance level (e.g. 0.10)
How do you choose a sample size if there isn’t a previous study?
p̂=0.05
What is the difference between CI and HT?
CI: calculate using observed sample proportion
SE=( p̂(1-p̂)/n)^1/2
HT: calculate using the null value
SE=(p0(1-p0)/n)^1/2
How do you calculate the standard error of the differences between two sample proportions?
SE(p̂1-p̂2)=( (p̂1(1-p̂1)/n1) - (p̂2(1-p̂2)/n2) )^1/2
When conducting a hypothesis test for a population proportion, what do we check for?
we check if the expected number of successes and failures are at least 10 assuming the null is true
np0>10 and n(1-p0)>10
