Module 3

Question 1

How does the binomial distribution work?

Answer 1

In a population, and a fixed proportion of individuals are assigned to 1/2 groups: successes or failures.

Question 2

Define “Binomial distribution” (2 things that it provides)

Answer 2

Provides the probability distribution for the number of successes in a fixed number of independent trials aka the proportion of successes.
-Has a Bernoulli trial (not many)

BD = X successes in n trials.
*look at formula (no need to mem)

Question 3

What are the assumptions of the binomial distribution?

Answer 3

1. The number of trials is fixed
2. Separate trials are independent
   3 The probability of success is the same in every trial.

Question 4

How does n affect the binomial distribution?

Answer 4

N is large = narrow distribution

N is small = broad distribution

Question 5

What are the assumptions for a Goodness-of-fit test?

Answer 5

1. Individuals in a data set are random samples from a population
2. Individuals are chosen independently from one another.
3. No category has expected frequency of <1.
4. No more than 20% have a frequency of <5.

Question 6

What is the purpose of the Poisson distribution?

Answer 6

Tests whether successes occur randomly in time or space. Describes the number of successes over time or space.
-Has many Bernoulli trials

Question 7

What is a goodness-of-fit test used for? (ex. Chi-squared)

Answer 7

To compare observed and expected variables to see if they’re significantly different from one another.

Question 8

What is a goodness-of-fit test used for? (ex. Chi-squared)

Answer 8

To compare observed and expected variables to see if they’re significantly different from one another.

Question 9

Define “extrinsic data”

Answer 9

When expected info is derived from info other than the data you are analysing

Question 10

Define “Intrinsic data”

Answer 10

When expected info is derived from the data you are analysing

Question 11

What variables does the GOF test use?

Answer 11

1 categorical variable

Question 12

How do you calculate the degrees of freedom for a GOF test?

Answer 12

df= k-p-1

Question 13

How do you calculate the degrees of freedom for an extrinsic data test?

Answer 13

df= k-p-1

• k = # of categories
• p = # of parameters estimated (columns-1)

Question 14

What are the alternative distributions to Poisson?

Answer 14

1. Clumped - successes occur closer together than expected by chance. Variance > mean.
2. Dispersed - successes occur more evenly spread out than expected by chance. Mean > Variance.

Question 15

What is a Bernoulli trial ??

Answer 15

A trial with only 2 possible outcomes.

Question 16

What is a contingency test used for?

Answer 16

Used to test the dependence of a (categorical) variable to another.

Question 17

How do you calculate the degrees of freedom of an intrinsic data test?

Answer 17

df=rc-[(r-1)+(c-1)]-1
r = row
c=column

Question 18

What type of test uses intrinsic data to generate expected values?

Answer 18

Contingency

Question 19

What type of test uses intrinsic data to generate expected values?

Answer 19

Contingency

Question 20

What are the conditions that need to be met for a Poisson distribution to occur?

Answer 20

1. The probability of two or more occurrences in a single sample subdivision is negligibly small.
2. The probability of one occurrence in a sample subdivision is proportional to the size of the subdivision (in time or space). Ex. 3 times area = 3 times probability.
3. The outcome in one subdivision of the sample unit is independent of the outcome in all other Bernoulli.
4. The probability of an occurrence is identical for all sample subdivisions.

Question 21

What is the purpose of a G-test?

Answer 21

Testing the null hypothesis (of no association) between two or more categorical variables.

Question 22

What are the assumptions of a G-test?

Answer 22

1. Random samples
2. No more than 20% of cells have a frequency of <5
3. No cell has a frequency of <1.

Question 23

What are the degrees of freedom for a G-test?

Answer 23

(r-1)(c-1) ***not sure if this is correct