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Flashcards in Comparing two samples Deck (58):
1

What two options of samples must we consider?

  1. Independent
  2. Paired

2

What is meant by independent samples?

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

3

What is meant by paired samples?

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

4

What two distinct approaches can our method take?

  1. Parametric
  2. Non parametric 

5

What is meant by a parametric method?

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

6

What is meant by a non-parametric method?

No assumed distribution, no parameters to compare

7

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

No difference in means - 

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8

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

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9

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

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10

How is the following distributed?

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11

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

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12

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

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Pooled sample variance

13

Define the pooled sample variance.

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14

What are two properties of the pooled sample variance?

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15

Prove the following property of the pooled sample variance.

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16

Prove the following property of the pooled sample variance.

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17

What is the standard error of the following?

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18

What is the theorem about the independent sample t statistic?

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19

Prove the following theorem.

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20

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

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21

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

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22

How do we check the following three assumptions?

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23

What is independent in the paired sample t-test?

X, Y are correlated but each pair is independent.

24

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

Cov[X,Y] = ρσXσY

25

What does ρ stand for?

The correlation between X and Y 

26

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

The differences between each pair

27

What does Dequal?

Di = Xi - Yi

28

What is the 𝔼[Di]?

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29

What is the Var[Di]?

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30

What distribution do the Di's have?

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31

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

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32

Show that the following is an unbiased estimate.

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33

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

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34

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

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35

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

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

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36

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

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37

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

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38

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

Parametric 

39

What do we focud on in non parametric tests?

Ranking the data

40

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

No group difference.

41

Define the rank sum test.

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42

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

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

 

43

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

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44

What value do the tables of W give?

TL

45

What is TL and TU?

The upper and lower critical values

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46

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

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47

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

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48

What is the theorem about the Normal approximation to W?

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49

Prove the following theorem.

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50

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

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51

Define the signed-rank test.

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52

What is another name for the signed-rank test?

The Wilcoxon signed-rank test

53

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

Discard these points and reduce n accoridngly 

54

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

The smallest value

55

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

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56

What is the theorem about the Normal approximation to V?

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57

Prove the following theorem.

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58