Brainscape's Knowledge GenomeTM

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


See full index

Statistical Concepts - Epiphany > Comparing two samples > Flashcards

Comparing two samples Flashcards

1
Q

What two options of samples must we consider?

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

What is meant by independent samples?

A

Observation of X is unrelated to observation of Y, no association between samples

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

What is meant by paired samples?

A

Each X is “paired with” a similar Y, before\after measurements

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

What two distinct approaches can our method take?

A
  1. Parametric
  2. Non parametric
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is meant by a parametric method?

A

Assume distributions for X, Y. Test difference in population means by comparing parameters.

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

What is meant by a non-parametric method?

A

No assumed distribution, no parameters to compare

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

What is the null hypothesis for an independent sample t-test?

A

No difference in means -

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

How do we estiamte μx - μy by in the independent sample t-test?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the variance of estimate for independent sample t-tests?

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

How is the following distributed?

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

How does the following simplify under the hull hypothesis H0: μx - μy = 0?

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

When σ2 is unkown in the following what do we estimate it with?

A

Pooled sample variance

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

Define the pooled sample variance.

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

What are two properties of the pooled sample variance?

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

Prove the following property of the pooled sample variance.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Prove the following property of the pooled sample variance.

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

What is the standard error of the following?

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

What is the theorem about the independent sample t statistic?

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

Prove the following theorem.

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

What is the significance test of the hypothesis and confidence interval for the independent sample t-test?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What are three assumptions to do the independent sample t-test?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

How do we check the following three assumptions?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What is independent in the paired sample t-test?

A

X, Y are correlated but each pair is independent.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

What is the Cov[X,Y] in the paired sample t-test?

A

Cov[X,Y] = ρσXσY

25
Q

What does ρ stand for?

A

The correlation between X and Y

26
Q

What do we look at in a paired smaple t-test?

A

The differences between each pair

27
Q

What does Di equal?

A

Di = Xi - Yi

28
Q

What is the 𝔼[Di]?

A
29
Q

What is the Var[Di]?

A
30
Q

What distribution do the Di’s have?

A
31
Q

What do we estiamte μX - μY by in the paired sample t-test?

A
32
Q

Show that the following is an unbiased estimate.

A
33
Q

What is the variance of the estimate in paired sample t-test?

A
34
Q

What is the distribution of the estimate in the paired sample t-test?

A
35
Q

What is the effect of correlation in the paired sample t-test?

A

Which means Var[Ď] < Var[Ẍ - Ȳ] (should all be bars), pairing the data and working with difference improves out precision.

36
Q

What is theorem about the paired-sample t test statistic?

A
37
Q

What is the significance test of the hypothesis and confidence interval for the paired sample t-test?

A
38
Q

When the assumptions hold are nonparametric methods or parametric methods more powerful?

A

Parametric

39
Q

What do we focud on in non parametric tests?

A

Ranking the data

40
Q

What is a general null hypothesis for non parametric independent samples?

A

No group difference.

41
Q

Define the rank sum test.

A
42
Q

What do you do when you have tied observations in the rank-sum test?

A
  • Rank-sum test requires that ranking is unique
  • So you assign the average of the tied ranks
43
Q

What two options do we have for the distribtuin for W?

A
44
Q

What value do the tables of W give?

A

TL

45
Q

What is TL and TU?

A

The upper and lower critical values

46
Q

How do you find TU once you have found a value for TL from the W tables?

A
47
Q

When we have found TL and TU when do we reject H0?

A
48
Q

What is the theorem about the Normal approximation to W?

A
49
Q

Prove the following theorem.

A
50
Q

What is the method for the signed-rank test for paried samples?

A
51
Q

Define the signed-rank test.

A
52
Q

What is another name for the signed-rank test?

A

The Wilcoxon signed-rank test

53
Q

How should di = 0 be dealt with in the signed-rank test?

A

Discard these points and reduce n accoridngly

54
Q

What value of V+ or V- can you get from the table of V values?

A

The smallest value

55
Q

When do we reject H0 in the signed-rank test for paired samples?

A
56
Q

What is the theorem about the Normal approximation to V?

A
57
Q

Prove the following theorem.

A
58
Q
A

Statistical Concepts - Epiphany (4 decks)

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