EIP - Probability and Significance Tests - Week 7 Flashcards
Define probability.
The probability that an event will happen under given circumstances is the proportion of repetitions of those circumstances in which an event would occur in the long run
Define random variable.
A variable that can take on more than one value with given probabilities
Must you sum probabilities of events if they are mutually exclusive? What about if they are not? What is this called?
They must be summed only if they are mutually exclusive
This is the addition rule
Describe the multiplication rule.
If two probability events are independent, we have to multiply the probabilities
Define conditional probability. How might this be relevant clinically?
The probability of an event that follows another event - e.g. how one treatment might work following another treatment, or what diagnosis might follow a particular combination of symptoms
What is the null hypothesis? Is it assumed to be true or not at the beginning?
It is the hypothesis that there is no significant difference between specified populations with any observed differences being due to sampling/experimental error.
It is assumed to be true until evidence indicates otherwise (i.e. a statistical analysis of data).
What is the purpose of the p-value?
The decision on whether to reject or fail to reject the null hypothesis is based on whether the p-value is on one side or the other of a threshold value
Threshold value is commonly chosen to be 0.05 (5%)
Describe a type I error. Describe how p-values fit into this.
Falsely rejecting the null hypothesis.
At a p-value <0.05, we accept a 1 in 20 chance we will commit a type I error.
Describe a type II error. When can it happen?
Falsely accepting the null hypothesis.
Can happen when the uncertainty (variability) in the data drowns out the real difference between groups.
How can type II errors be decreased? Explain why (2).
By increasing the sample size.
- if there is a real difference, it wil be maintained no matter how big the sample size gets
- the variability of the data will decrease as a proportion of that real difference as the sample gets bigger
Define power of a study.
The ability to detect differences between groups
What is the usual convention for the power of a study? Explain what this value means. Describe what this means for type II errors.
Power should be 0.8 - an 80% chance of detecting the difference we seek.
We accept a 20% chance of a type II error.
