Module 3 Flashcards
Poisson, Binomial, and Test statistics for discrete distributions
What are the 2 types of discrete probability distributions?
1) Binomial
2) Poisson
What are the statistical tests that can be used for discrete data?
1) G/Chi square Goodness-of-fit Test
2) Contingency analysis
What is the binomial distribution?
Probability for the number of successes in a fixed number of independent trials, where the probability of success is the same in each trial
What are the assumptions of the binomial distribution?
1) Fixed number of trials
2) Probability of success is the same in all trials
3) Outcomes are independent of each other
What are the characteristics of a binomial distribution?
1) Only 2, mutually exclusive outcomes
2) P(failure) = 1 - P(success)
3) Proportion = X/n
4) Determined by p and n
5) mean = np
6) variance = np(1-p)
What is the Poisson distribution?
Describes the probability of an event occurring a certain number of times (# of successes) in blocks of time or space
What does the Poisson distribution assume?
1) Successes happen independently of each other
2) Successes occur with equal probability at every instant in time or point in space
AKA random distribution in time/space
What are the conditions of the Poisson distribution?
1) The probability of 2+ occurrences in a single sample distribution is negligibly small
2) The probability of 1 occurrence in a sample subdivision is proportional to its size
What are the characteristics of a Poisson distribution?
1) defined by the mean
2) mean = variance = rate of success
3) low mean = right skewed
4) high mean = symmetrical
What are the main differences between Binomial and Poisson distribution?
1) Possible outcomes: B = 2, P = infinite
2) Trials: B = fixed, P = infinite
3) Mean and variance: B = mean > variance, P = mean = variance
What is the alternative for Poisson distributions?
Successes are distributed nonrandomly:
1) Clumped together
2) More dispersed
What is the relationship between mean and variance if successes are more clumped together in space/time?
variance > mean
What is the relationship between mean and variance if successes are more dispersed in space/time?
mean > variance
What is the G/Chi squared goodness of fit test?
A test to compare observed frequencies to the probability model (proportional model, binomial distribution, poisssion distribution) as stated by the null hypothesis
What is the proportional model?
A model that assumes the frequency of an event occurring is proportional to the number of opportunities
How do we calculate the degrees of freedom for the Goodness-of-fit tests?
df = (# of categories) - 1 - p
What is the contingency analysis used for?
Determine the association between categorical variables
How do we calculate the degrees of freedom for contingency analysis?
df = (row count - 1)(column count - 1)
What are degrees of freedom?
Determines what null distribution to use for comparison
