Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Chpt 12 - 20 > chapter 12 > Flashcards

chapter 12 Flashcards

1
Q

When testing 3 or more population proportions, what is the null hypothesis

A

Ho - all proportions are equal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

When testing 3 or more population proportions what is the alternative hypothesis

A

Ha - not all population proportions are equal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

what does k represent

A

3 or more population proportions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

what is the degrees of freedom for testing 3 or more population proportions

A

k - 1 = df
ie.
3 pops

3 - 1 = 2 degrees of freedom

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

what distribution do we use when testing 3 or more population proportions

A

chi-squared

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

what does Pi stand for

A

is the proportion of the population I, 1 <= I <=k

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

if the chi-square test computations indicate Ho can be rejected, we have what

A

statistical evidence to conclude that not all k population proportions are equal

further analysis can be done to conclude which pop proportion or proportions are significantly different from others

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What do you need in order to see if 3 or more pop proporitons are equal

A
  1. observed frequencies
  2. expected frequencies
  3. Chi-squared test statistic for the test of equal pop proportions
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What does each pop sample provide

A

categorical data

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

How are the expected frequencies determined with what assumption

A

that Ho is true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is the chi-squared test statistic used for

A

to determine whether there is a significant difference between the observed and the expected frequencies

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

How do you calculate the expected frequencies

A

by using the total column and calculating “likely” total for all populations / the total number of all populations
- then apply this % to each of the populations to determine the expected frequencies

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is the degrees of freedom for a chi-square test statistic

A

k-1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

what does the expected frequency need to be at least

A

5 or more for each cell

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

How do you calculate the test stat for tes of equal pop proportions?

A
  1. find the differences between observed and expected frequencies
  2. sqaure the difference
  3. divided the squared difference by expected frequency
  4. add the last column up gives you your chi-square total
  5. go to the chi-square distribution chart and with the correct degrees of frequency, find what the p-value will be between then compare to the level of significance
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

where is the chi-square test for equal population proportions will always be (what kind of tail test)

A

an upper tail test with rejection of Ho occurring when the test statistic is in the upper tail of the chi-square distribution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

when using the critical value approach, what numbers are you comparing?

A

the value in the squared difference divided by expected frequency and the where the level of significance is with the correct degrees of freedom on teh chi-square distribution table

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

If p-value is less than the level of significance then what

A

reject HO

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

if chi-squared value for the squared differences is more than the chi-squared value for the level of significance than what

A

reject Ho

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What is the multiple comparison procedure used for

A
  • used when the chi-squared test concludes that the pop proportions of 3 pop are not all equal
  • this will help identify the differences in the pop proportions
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Using the Marascuilo Procedures what are the steps

A
  1. compute the absolute value of the pairwise difference between sample proportions for each pair of pops in the study
  2. select a level of significance and compute the corresponding critical value for each pairwise comparison using the formula
  3. determine if there are significant differences
22
Q

What is the CV formula for the Marascuilo pairwise comparison procedure

A

see formula

23
Q

What is the test of independence

A

using sample data to test for the independence of two categorical variables

24
Q

How does the test of independence work

A
  • we take a sample and record the observations for two categorical variables
  • we summarize the data by counting the number of responses for each combination of category for variable 1 and a category for variable 2
  • the null hyp for this test is that the two categorical variables are independent
25
Q

What is this an example of

Ho: beer preference is independent of gender

Ha: beer preference is not independent of gender

A

Test of independence

26
Q

Goodness of fit test - Definition

A

A chi-square test

  • used to test that a population probability distribution has a specific historical or theoretical probability distribution.
  • This test is for both a multinomial probability distribution and a normal probability distribution.
27
Q

Marascuilo procedure

A

A multiple comparison procedure that can be used to test for a significant difference between pairs of population proportions. This test can be helpful in identifying differences between pairs of population proportions whenever the hypothesis of equal population proportions has been rejected

28
Q

Multinomial probability distribution

A

A probability distribution where each outcome be-longs to one of three or more categories.
- extends the binomial probability from two to three or more outcomes per trial

29
Q

Test of independence

A

A chi-square test that can be used to test for the independence between two categorical variables. If the hypothesis of independence is rejected, it can be concluded that the categorical variables are associated or dependent

30
Q

What is the Chi-square test used for

A
  1. test of equality (P1=p2=p3)
  2. Test for independence
  3. Goodness of fit test (1. is there a change in pop proportion or 2. test if it has a normal prob distribution)
31
Q

When you do a test of equality, If you reject HO and conclude that not all pops are equal, what can you do

A
  1. use Marascuilo procedure to determine where the differences among the proportions exists
32
Q

what are the steps when you are conducting a goodness of fit test to see whether a sample appears to come from a normal probability distribution?

A
  1. order from smallest to largest
  2. calculate the mean and standard deviation
  3. define intervals n/k (k being the number of sections you want/ intervals) ie 25/5 = 5
  4. find the interval limits - use normal table
    1/k x 100 = ie 1/5 = 0.2 - 20th percentile
  5. look on the z table to find 0.2 x= .84 this is for upper limit and lower is -.84
  6. then find the next one - 40th percentile??why
  7. Find interval limits
    z = -.84 M+ SD/-.84 = 56.72
    z = .84 M+SD/.84 = 85.82
    z = -.25 M + SD/-.25 = 66.75
    z = .25 M+SD/.25 = 75.25
  8. Find the observed frequencies by putting the total number in each category
  9. calculate the test statistic x2 with df - k-p-1
  10. calculate the expected frequency - (n/k for all categories)
33
Q

What are some applications of the chi-squared test?

A
  1. Testing equality of population proportions for 3 or more populations
  2. Testing the independence of two Categorical variables
  3. Testing whether a prob distribution for a population follows a historical or theoretical prob distribution
34
Q

is the Chi-square test restricted to equal sample sizes for each of the k populations?

A

no

35
Q

Why are we using the chi-squared test for pops are equal

A

chi-square test statistic to determine whether there is a significant difference between the observed and expected frequencies.

36
Q

if the differences between the observed and expected frequencies are low, then what can we say

A

If this is the case, the value of the chi-square test statistic will be relatively small and H0 cannot be rejected

37
Q

What type of test is used for testing of equality, proportion and independence

A

The chi-square test presented in this section is always a one-tailed test with the rejection of H0 occurring in the upper tail of the chi-square distribution

38
Q

Each of the k populations in this section had two response outcomes, Yes or No. In effect, each population had a ______distribution with parameter p the population pro-portion of Yes responses. The degrees of freedom here is _________.
An extension of the chi-square procedure in this section applies when each of the k populations has 3 or more possible responses. In this case each population is said to have a __________distribution. the degrees of freedom here is ________________

A

binomial df= k-1

Multinomial df = (r-1) (k-1)
r = # of responses or rows?

39
Q

This chi-square test for test of independence is also a ________ test with rejection of H0 occurring in the _____ tail of a chi-square distribution with _______ degrees of freedom.
x2

A

One tailed test

Upper tail

(r-1)(c-1) df

40
Q

What is a multinomial distribtuion

A

it is an extension of the binomial distribution
- binomial describes pops whos elements are one of two things success or failure

Multinomial distribution describes pops whose elements are one of many things, but a fixed number of things such as years of experience

41
Q

What are the attributes of a multinomial distribution

A
  1. each element of the pop belongs to one, and only one, of k categories
  2. The prob that an element form the pop taken at random will be in category i is some unknown but fixed positive number pi, with pi between o and 1
  3. a random sample from the pop is taken and each element in the sample is classified into one of k categories
42
Q

The test for goodness of fit is always a _____tailed test with the rejection occurring in the ____tail of the chi-square distribution

A

one tailed

Upper tail

43
Q

Goodness of fit for a normal distribution. Because the normal prob distribution is continuous what must we do

A

we must modify the way the categories are defined and how the expected frequencies are computed

44
Q

With a continuous
probability distribution, establish intervals such that
each interval has an expected frequency of ____ or more

A

5 or more

45
Q

What can be used to determine the boundaries in a normal prob distribution

A

standard normal probability tables

46
Q

Chi- sqayre test to determine Normal diatribution steps

A
  1. Defibe intervals (each must have a min of 5 per interval) take total and divide by 5 maybe
  2. Find interval limits using normal table
    If intervals are 25/5 = 5 then 1/5 = .2 or 20th percebtike - look on z table for this number
    (Upper limit) z= 0.25

Then 2/5= .4 find the z number Z= 0.84

  1. Limits
    Z= 0.84. xbar+Sd/-.84=56.72
    Xbar+sd /.84 = 85.28

Z=.25
Xbar+sd / -.25 =66.75
Xbar+sd/.25= 75.25

  1. Find the oberserved frequencies and our them in their categiries

0-56.72 - has 7

  1. 73 - 66.75 has 7
  2. 76-75.25 has 1
  3. 26 - 85.28 has 1
  4. 29 plus has 9
  5. Conpute chi square test
    Expected is 5 all the way theough

Df = k-p-1

47
Q

Marascuillo procedures is used for

A

testing the equality of 3 or more pop proportions

48
Q

In a normal distribution with 30 observations what would the expected number be

A

30/5 = 6
6 indicates intervals
5 is the expected number for each

49
Q

what is the degrees of freedom for the normal distribution

A

k-p-1

p = 2 for mean and sd
k is the total number of observations

50
Q

Using the Marascuillo procedure, when comparing phat 1 - phat 2 to cv12 what is significant

A

FIND ANSWER

Chpt 12 - 20 (10 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions