5. Analysing Proportions Flashcards
What is a binomial distribution?
The probability distribution for the number of successes
○ In a fixed number of…
○ Independent trial…
○ When the probability of success is the same each trial
Know how to use the binomial distribution to perform a binomial test
- start by forming null and alterative hypothesizes
- decide if one tailed or two tailed
- use binomial formula to work out probability of success
- compare to significance level (usually 5%)
What is sample proportion
An unbiased estimator of the population proportion, p
given symbol p-hat
Know how to calculate a sample proportion
number of successes (x) over number of trials (n)
Know how to calculate a 95% confidence interval for the sample proportion
using the Agresti‐Coull method
- work out p’
p’ = (x+2)/(n+4)
- then use p-prime to make 95% confindence intervals
1.96SE
SE = root[ {(p-hat)(1-p)} /n ]
When do you use a chi-squared test?
- when we have observed values
- and when we get expected values by using a proportional model
how do you calculate the degrees of freedom for a chi-squared test?
Df = number of categories - 1 - number of parameters
Higher degree of freedom → less skewed fit.
When cant you use a chi-squared test?
Any category has an expected frequency <1
More than 20% of their categories have an expected frequency of <5
What is a Poisson distribution?
Describes number of successes in blocks of time or space
■ When successes happen independently of each other
■ And occur with equal probability at every instant in time and point space
Used for count data
Used to test whether events are randomly distributed in time/space
How do you use a chi-squared test to identify if data comes from a Poisson distribution?
Calculate expected data using the Poisson distribution calculator
