Absolute risk
The probability of something happening
Relative risk
Relative risk = Absolute risk of event A / Absolute risk of event B
Relative risk > 1
This means that the risk of having (event) for (variable 1) is (relative risk) as likely as the risk of having (event) for (variable 2).
Relative risk = 1
This means that the risk of having (event) for (variable 1) is the same as the risk of having (event) for (variable 2).
Relative risk < 1
This means that the risk of having (event) for (variable 2) is (relative risk) as likely as the risk of having (event) for (variable 1).
Features of normal distribution
The graph of (x axis variable) is not distributed evenly (bell shaped) and symmetrical about the mean.
- There are more (x axis variable) concentrated around the (left/right) tail and the (left/right) tail of the distribution is longer, whereas in a normal distribution, these (x axis variable) would be at the centre.
- The graph is right-skewed and the mean > median. In a normal distribution, the mean and median would be equal.
Question - Give reasons for why it is unlikely that (x axis variable) would be normally distributed
We would not expect (x axis variable) to be symmetrically distributed as a normal distribution because
- (reason), hence the large number of (small/large) (x axis variable).
- (reason), hence the data being (right/left) skewed and not symmetrical.
Probability calculations
- Menu/Stat/Dist/NORM/Ncd
(Make sure setting is variable)
σ - Standard deviation
μ - Mean
E 99 - Uppermost value
E -99 - Lowermost value
Inverse normal calculations
To find x
(Calculator can only be used to find the value of x)
- Menu/Stat/Dist/NORM/InvN
(Make sure setting is variable)
Tail - Right/Left (Depending on which side of the mean the x value you are trying to find is on)
Area - Probability in decimal form of area under graph you are trying to find
σ - Standard deviation
μ - Mean
Inverse normal calculations
To find μ
- Draw picture
- Use the probability to look up the Z value
(Note - Z will be negative if the area under graph you are trying to find is to the left of the mean) - Use the Z value to calculate the value of x with
Z = x - μ / σ
- Write answer as a sentence in context
- Check that the answer makes sense
Inverse normal calculations
To find σ
- Draw picture
- Use the probability to look up the Z value
(Note - Z will be negative if the area under graph you are trying to find is to the left of the mean) - Use the Z value to calculate the value of σ with
Z = x - μ / σ
- Write answer as a sentence in context
- Check that the answer makes sense
Describing graphs of distributions
- The lowest and highest values
(indicates where on the x-axis the distribution is located) - The range - (highest - lowest value)
(indicates the width of the distribution) - The mode(s)
(indicates the highest point(s) of the distribution) - The shape - (normal, triangular, rectangular, irregular or bimodal)
- Symmetry - (symmetrical or assymetrical)
Equally likely outcomes
Probability = number of favourable outcomes/total possible outcomes
Long run relative frequency
Probability = number of times an event occurs/total number of trials
Expected number of outcomes
Expected number of outcomes = P(event) x number of trials
Combining probabilities
- If one event and another occurs, multiply the probabilities
- If one event or another occurs, add the probabilities
Probability trees
- Decide the events in order
- Write the probabilities on each v branch and check they add to 1
- List the outcomes and their probabilities at the end of each branch by multiplying along each branch
- Check that these probabilities at the end all add to 1
If asked - If it was (a) in variable 2, what is the probability that it is also (a) in variable 1 on the same day?
- Add the probabilities from end of the tree of outcomes that have (a) for variable 2
- Find probability from end of the tree that accomplishes the desired value (a) for both variable 1 and variable 2. Take this and divide it by the answer for 1.
