Flashcards in Stat - Exam #3 Deck (68)

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1

## How do you make inferences on two DEPENDENT samples (paired samples)?

###
-Need to convert the two population situation to a one population situation;

-Take the difference between teh values of the two individuals in a pair and treat the mean of difference (d-bar) and the stat of choice

2

## What is the null or status quo of dependent samples?

### d-bar = 0

3

## What are dependent samples?

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-When the individuals selected from one sample influence which individuals are in the second sample;

-Also called "matched-pair samples"

4

## What are independent samples?

### When the individuals selected for one sample do NOT influence which individuals are in the second group

5

## What is the best stat for testing a paired sample?

###
-the DIFFERENCE (d_i);

-Subtract the value of one individual of the matched-pair from the value of the other individual in the matched-pair;

-The mean (d-bar) and standard deviation (s_d) are calculated normally

6

## What are the Assumptions for DEPENDENT Samples?

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1. Random sample of matched pairs;

2. Sample average of the difference data is normally distributed;

3. Population standard deviations are NOT known (same for one-sample t-test)

7

## What is the null hypothesis in a paired-sample hypothesis test?

### The mean difference between the paired samples is zero (H_0: u_d=0)

8

## What is the confidence interval for a paired-sample?

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Statistic +/- Critical Value;

-The Point-estimate is the sample average of the difference data (d-bar), the critical value is a t-value, and the standard error of the mean has usual form (S_d/(sqrt n))

9

## When can you makes inference about two population means?

### -When the individuals in the two samples are UNRELATED to each other

10

## How do you make inferences on two INDEPENDENT samples?

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-Calculate the mean of each population and treat the DIFFERENCE in the means as the stat of choice;

-The status quo in this case is (u1-u2=0), meaning the mean of the two populations is the SAME

11

## What is needed to conduct inferential stats on independent samples?

###
Sampling Distribution =

1. Mean and

2. Standard Deviation….

of the difference in the means of the samples

12

## What are the two possible situations for populations when the populations standard deviation is NOT known?

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*Can ALWAYS calc the sample standard deviation;

1. Equal population standard deviations;

or

2. Unequal population standard deviations

13

## What test can be used to determine equality in variances, but is NOT recommended?

### an “F-Test” can be used, but it is not robust to even account for small deviations from normality

14

## What is the best estimate of the population standard deviation when the pop. standard deviations are EQUAL?

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-Pooling together the two sample standard deviations;

-a T-STAT using the pooled standard deviations , exactly follows t-distibution with (n-2) degrees of freedom

15

## What is the best estimate of the population standard deviation when the pop. standard deviations are UNEQUAL?

###
-an exact method of inference does NOT exist because you CANNOT determine degrees of freedom;

-There is NO formula for a t-stat that follows the t-distribution;

-But WELCH’S APPROX and SATTWERWAITE’S APPROX are close;

-Both use the same formula with different degrees of freedom approximations

16

## What is Welch’s Approximation of Degrees of Freedom?

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-Take the SMALLER number of the observations (n1 or n2), then subtract 1 to determine the degrees of freedom for the t-test (t_0);

-A conservative approximation;

-Easy to use by hand

17

## What is Satterwaite’s Approximation of Degrees of Freedom?

###
-A more exact approximation that uses an extensive equation;

-Best used when calculated by machine

18

## How many columns of data can ANOVA be used for?

### -As many columns of data as needed

19

## What are the three possible hypotheses with 3 columns of data for a t-test?

###
1. H0: u1=u2;

2. H0:u1=u3

3. H0:u2=u3

20

## What is the problem with running 3 independent t-tests?

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*Significance Level;

-Becomes additive each time a t-test is run since the t-tests are essentially independent of one another;

alpha = .05+.05+.05 = .15;

*Chance of error increased 3x than preferred

21

## What is a significance level?

### The chance of making an incorrect conclusion

22

## How do you make inferences on 3 columns of data?

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-Use a stat test that compares two VARIANCES to each other, instead of two means to each other;

-Called an F-TEST because an F-stat is calculated, and follows an F-distribution = critical values and P-values

23

## What is ANOVA?

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A statistical method used to test whether the population means of three or more columns of data are equal to each other;

-Uses the F-test to make decisions;

-Requires only ONE hypothesis test so it controls the significance level at the level set no matter how many populations compared

24

## What is One-Way ANOVA?

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An ANOVA method with only one classification variable, called a FACTOR;

-The factor is DISCRETE data that can have as many levels as needed

25

## What is a FACTOR?

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A classification variable used to separate data into several columns;

-EX: Age, gender, species, class, etc;

-LEVELS of a factor are the possible categories

-EX:

Factor = Classification

Levels= Freshman, Sophomore

26

## What is an ANOVA Hypothesis test?

### Conducts ONE hypothesis test to find out whether all three populations are EQUAL to each other;

27

## What is the alternative hypothesis test with ANOVA?

###
-At least ONE population means is DIFFERENT from the others;

-Cannot tell if only one population mean s different or if all are different

28

## What stat test does ANOVA use to test the hypothesis?

### -F-test to find out which is closer to the truth

29

## What is an F-test?

###
A stat test to determine whether two VARIANCES are equal;

-Tests for the equality of two variances

30