chapter 12: chi-square tests

Question 1

what are the differences between binomial and multinomial experiments?

Answer 1

both are similar

binomial considers count data classified into two categories

multinomial concerns count data classified into more than two categories

Question 2

what are the assumptions of the multinomial experiment?

Answer 2

1. we perform an experiment in which there are n identical trials with k possible outcomes on each trial
2. probabilities of k outcomes are denoted as p1, p2, p3, …, pk where the sum of all ps is equal to 1.

these probabilities stay the same form trial to trial

3. the trials in an experiment are independent
4. the results of the experiment are observed frequencies (counts) of the number of trials that result in each of the k possible outcomes

the frequencies are denoted as f1, f2, f3, …, fk

f1 is the number of trials resulting in the first possible outcome

f2 is the number of trials resulting in the second possible outcome

etc

Question 3

explain the significance of the chi square statistic

Answer 3

it used to compare the expected frequencies and the actual frequencies

the larger the chi-square statistic, the more likely we are to reject the null hypothesis

if it is beyond the critical value, we reject the null hypothesis

Question 4

when do we reject the null hypothesis using chi-square?

Answer 4

when it is beyond critical value

Question 5

how do you find the critical value for a chi-square statistic

Answer 5

1. you find the degrees of freedom
2. you use a certain level of confidence
3. you see which degree of freedom is corresponding to the level of confidence

Question 6

how do you find the degrees of freedom in a chi square statistic

Answer 6

k - 1

Question 7

how do you find the p-value of the chi square statistic

Answer 7

you find the area under the curve correspond to the right hand tail of the actual value of the chi-square statistic

Question 8

using the p-value, when do you reject the null hypothesis?

Answer 8

when the p value is less than the level of significance

Question 9

how do you test to see in the end if everything Is right and that you can absolutely reject or accept a null hypothesis?

Answer 9

using a confidence interval

Question 10

how do you do a confidence interval with chi square statistic

Answer 10

same as previous formula, but since there are multiple ps to choose from, you gotta do it for specific ones

so you do regarding probabilities

the mean p is the actual frequency recorded earlier, no the expected frequency

Question 11

how big must the sample be for the chi square statistic of a multinomial experience for it to work?

Answer 11

must be big

all the expected cell frequencies (E values) must be larger than 5

the smallest E value must be minimum 1

Question 12

how many groups must there be for the chi square statistic of a multinomial experience for it to work?

Answer 12

must be at least 4

k > 4

Question 13

how do you check if the population from which the sample were selected come from a normally distributed sample?

Answer 13

1. you do the z table thing

you try to find the value of z and you look at the sample mean and sample standard deviation parameters

2. this will each give the expected frequencies
3. you do the chi-square satistic

you look at degrees of freedom

4. if the chi square statistic if bigger than the correspond chi square level of confidence, you reject the null hypothesis

null hypothesis: the population normally distributed

Question 14

how do you find the degrees of freedom when trying to determine if the population from which a Sample was taken is normally distributed?

Answer 14

k - 1 - m

m: number of parameters

Question 15

how can you look at the relationship between two variables using the multinomial experiment?

Answer 15

by classifying the multinomial data on two scales

Question 16

how do you classify the multinomial data on two scales to look at the relationship between two variables using the multinomial experiment?

Answer 16

by setting up a contingency table

Question 17

expected cell frequencies under the independence assumption

Answer 17

counts (frequencies) computed by assuming independence

Question 18

what is the chi square test of independence

Answer 18

you basically want to link up cells and shit and see if they’re independent comparing them to the level of confidence

basically, Ho is this test is independent

Question 19

how do you find the degrees of freedom in the chi square test of independence?

Answer 19

(r -1)(c - 1)