Test of association Flashcards
What is the Poisson Distribution used for? What are its assumptions?
A discrete probability distribution, often used to describe the number of rare events. tells you if events are random
Assumptions: Events are random and independent
Parameter is λ
Mean and variance are equal: μ = σ²= λ
Can make hypothesis about a process and calculate an expected value and work out whether it is close to the true value or not
What does a goodness-of-fit test look for (Chi-squared)?
What are the different notations used?
Evidence that observed data is consistent with some claimed distribution
Looks for associations between categorical predictor variables= Not continuous
Notation:
n total number of trials
k number of possible outcomes for each trial (how many categories there are in total)
O Observed frequencies (counts) [# trials associated with the outcome]
E Expected frequencies (counts) [# trials associated with the outcome]
When do you reject the null hypothesis?
What does that tell you?
If χ^2 > χ^2crit
The larger the test statistic, the bigger the difference and therefore the more significant it will be
Know that there is some association but the test does not tell us which categories within the variables differ
When should a Chi squared test be used?
If the expected number of counts in all categories is 5 or more
If expected number of counts in one or more categories is less than 5, should merge one or more categories to create new categories so that each has an expectation of 5 or more
What does a contingency table show?
Describes frequencies corresponding to paired variables
Tests for any association between two categorical variables- does knowing one variable help predict the other?
How do you calculate expected values?
Using the observed table, take the totals from the row and the column, multiply them together and divide them by the overall total
How do you interpret P-values near 0.05?
Think about what might have happened if one or a few of the sample data were slightly different- could a small change make you change from retaining or rejecting the null hypothesis?
Do not make a strong claim about the results
