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2021 AP STATISTICS > DECK 13: INFERENCE PART B (2 test/ Power/Conditions/Chi-Square/Regression) > Flashcards

DECK 13: INFERENCE PART B (2 test/ Power/Conditions/Chi-Square/Regression) Flashcards

1
Q

What is the “you think it worked but it didn’t” error?

A

Type 1

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2
Q

What is the missed opportunity error? (the “I didn’t notice” error)

A

Type 2

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3
Q

IF you are testing to see if a marketing program increases sales, describe a type 1 and type 2 error.

A

Type 1: you think it increased sales but it didn’g

Type 2: It actually increased sales but you didn’t notice

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4
Q

If you are testing to see if a math program works in your town (that will cost 4 million to implement) describe a type 1 and type 2 error.

A

Type 1: you think it worked, but it didn’t so you spend 4 million on a program that isn’t good.
Type 2: It worked, but you didn’t notice, so you miss the opportunity to adopt a good math program.

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5
Q

If there is a screening test for mathphobia, describe a type 1 and a type 2 error

A

Type 1: You think the person has mathphobia, but they don’t

Type 2: They have mathphobia, but you didn’t notice

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6
Q

Can you decrease alpha while increasing power (even though they move together?)..

A

Yes.. increase samle size. They move together with constant sample size.

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7
Q

How are power and alpha related?

A

they go up and down together

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8
Q

How else can you explain power?

A

The likelihood you correctly reject a false null.. The likelihood you correctly detect what you were trying to detect

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9
Q

If you are doing a 2 tailed test with alpha=.05.. What confidence interval goes with that?

A

95% confidence interval (there is .025 in each tail)

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10
Q

If you are doing a one tailed test with alpha=.05.. What confidence interval goes with that?

A

90% confidence interval tests a one tailed test. There is 5% in the tail.

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11
Q

How can you increase power?

A

Increase alpha or increase sample size..

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12
Q

Can you draw the alpha/beta/power diagram?

A

BE ABLE TO SKETCH THE ALPHA BETA POWER DIAGRAM from the original pregnancy worksheet. Know where everything is. This helps you understand how alpha, beta and power interact.

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13
Q

What is beta?

A

It is probability that you’ll make a Type II error.. P(Type II error)

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14
Q

how are beta and power related

A

as one increases, the other decreases, and vice versa. They have to because they BOTH ADD TO ONE!!! Power + Beta = 1

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15
Q

What is the null for a 2 prop Z?

A

p1=p2 OR… p1-p2=0, there is no diff

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16
Q

What is the null for a 2 sample mean T?

A

mu1=mu2 OR mu1-mu2=0 there is no diff

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17
Q

What is the null for a paired T test?

A

xbar diff=0 (the average diff is zero)

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18
Q

What is the null for a chi squared GOF test?

A

The distribution fits [the expected distribution]

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19
Q

What is the null for a chi squared test for homogeneity?

A

The [samples of —] are similarly distributed.

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20
Q

WHat is the null for a chi squared test for independence”

A

The [two variables in context] are independent.

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21
Q

When you are doing PAIRED or MATCHED or BLOCKED tests.. What are you finding?

A

The average difference.. You are doing 1 sample procedures on a NEW THIRD LIST OF DIFFERENCES

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22
Q

What is difference between 2 Samp T test and a PAIRED T Test

A

In a two sample T test you are comparing TWO SAMPLE AVERAGES to eachother. In a PAIRED T test you are looking just at JUST ONE average of the THIRD LIST… They are paired.. So you find each individual BEFORE-AFTER and take the average of all of those differences. You do ONE SAMPLE T TEST on it because you really have one mean. You just the average or the difference list.

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23
Q

How do you find df in 2 samples?

A

USE CALCULATOR.(or smaller sample-1). you have to run an interval or a test on your TI and read the output (unless you want to use the equation.)

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24
Q

when is data “paired”

A

when you have 2 measurements of the same variable on the same subject (or matched subjects)

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25
Q

How can you decrease alpha and beta at the same time?

A

increase sample size. this will also increase power.

26
Q

What is alpha?

A

It is the rejection threshold. You reject p-values below it.. It is how willing you are to make a Type 1 error? alpa=P(Type I error)

27
Q

How do you make confidence interval for slope?

A

STAT +/- CRIT SE of slope

28
Q

what is df for goodness of fit?

A

cells - 1

29
Q

How do you find Expected Count?

A

for GOF: Exp %(total)..

For indep and homog: ROW*COL/TOTAL

30
Q

What are the three chi-squared models?

A

goodness of fit, test for homogeneity, test for independence

31
Q

What is diff between homogeneity and test for independence?

A

homogeneity is more than one sample and asking about one variable, independence is just one sample with two variables.

32
Q

With regression computer output, how is the t-ratio and the p-value calculated?

A

T ratio is just SLOPE/ST ERROR and the p value is just TCDF(T ratio, 9999, n-2)

33
Q

When do you know it is GOF test?

A

When you have ONE ROW or ONE COLUMN… then it gives you a ratio , like 1:2:5 or it gives you expected percents.

34
Q

what is df for chi squared homogeneity or independence?

A

(rows-1)(columns - 1) (remove a column and row.. Count boxes)

35
Q

What is a Chi squared model?

A

A sampling distritubion. If you took a bunch of samples and calculated a bunch of Chi-square statistics, the pile of chi squareds would look like that.

36
Q

What is the mean and mode of a chi squared model? What is the 5% cutoff chi-squared?

A

The mean is the degrees of freedom and the mode is df-2. The cutoff is at 1.5df+3.

37
Q

If you have multiple groups and ask them one question, what Chi-squared test is it?

A

Test for homogeneity.

38
Q

If you have one group and ask them two questions, what type of chi squared test is it?

A

Test for independence.

39
Q

If you have one group and ask them one question, what type of chi-squared test is it?

A

Goodness of fit test.

40
Q

If you take two bits of information from each subject there are two possible tests you could do. If the data is quantitative, you can do___ and if it is categorical, you can do a ______

A

regression t test, chi-squared test for independence.

41
Q

If you take two bits of information from each subject there are two possible tests you could do. If the a chi squared test would be for _____ data and a regression t-test would be for ______ data

A

categorical, quantitative.

42
Q

For both a chi squared test for independence and a regression t test you are looking for an association, how do the null hypotheses differ?

A

The chi squared will be in words.. Ho: the variables are not associated. The regression t test will be with symbols (and words). Ho: Beta = 0 (the slope is zero) . Saying “beta=0” is the same as saying “there is no association”

43
Q

What is the null model (the sampling distribution) in a chi squared test?

A

a pile of chi-squared statistics calculated from a bunch of samples

44
Q

What is the null model (the sampling distribution) in a regression t test for slope?

A

A pile of slopes taken from a bunch of samples

45
Q

What is the null model (the sampling distribution) in a 2 sample mean t-test?

A

a pile of differences of TWO MEANS samples, taken from a bunch of PAIRS of samples. Take two samples, calculate two means, subtract to get a difference, PUT THE DIFFERENCE IN THE PILE.

46
Q

What is the null model (the sampling distribution) in a 2-proporiton Z test?

A

a pile of differences of TWO PROPORTIONS, taken from a bunch of PAIRS of samples. Take two samples, calculate proportions, subtract to get a difference, PUT THE DIFFERENCE IN THE PILE.

47
Q

WHat is the null model (the sampling distribution) in a paired T-Test?

A

A pile of average differences. Remember that in a paired test, you are getting an individual differenc from each pair of data, then finding the average of differences.

48
Q

What is the null model(the sampling distribution) in a 1-sample mean T test?

A

A pile of means from a bunch of samples.

49
Q

What is the null model (the sampling distribution) in a 1-proportion Z test?

A

A pile of proportions (%) from a bunch of samples.

50
Q

How is a paired T test different from a 2 sample mean T test?

A

A paired test talks about an AVERAGE OF DIFFERENCES from one list, whereas a 2 sample mean t-test talks about a DIFFERENCE OF AVERAGES between two samples.

51
Q

What is the general formula for ALL CONFIDENCE INTERVALS?

A

STAT +/- CRIT SE

52
Q

sample size calcs FOR PROP AND MEANS

A

n= (z^2 * p * q )/ (ME ^2) and n = ( t*s / ME) ^ 2 (start with Z then do T)

53
Q

CONDITIONS: What are the three conditions that you have to check with pretty much every inference procedure (every test and every interval)

A
  1. Randomly chosen sample (or assigned treatment). Circle the word random or explain why you think it is.
  2. Sample size is less than 10% of the population. Show that 10n is less than N. Example, for 50 students, write 10(50)=500 is less than all students.
  3. Nearly normal (or large enough sample)- this differs based on the type of data and test.
54
Q

What is a way to think about the three conditions?

A
  1. Sample is random
  2. Sample is small enough (<10%)
  3. Sample is large enough (np&nq>10 for props, n>30 for means or the histogram is normalish)
    EXTRAS: chi squared exp at least 5 in each cell, regression- random resid
55
Q

What do you have to look for with two sample procedures:

A
  1. You have to check the conditions for each sample AND

2. The samples have to be independent from eachother

56
Q

What is the “nearly normal” condition for means? (aka large enough sample)

A

If n>30, good to go. If n<30, then you have to make sure the histogram of the sample looks normalish.

57
Q

What is the “nearly normal” condition for proportions? (aka large enough sample)

A

np>10 and nq>10. actually Show this calculation

58
Q

What is the “nearly normal” condition for regression? (aka large enough sample)

A

Make sure the histogram of the residuals is normalish.

59
Q

What is the “ large enough sample” condition for Chi Square?

A

Make sure that there are at least 5 in each expected cell.

60
Q

What is the other conditions for regression inference?

A

Random residuals (equal random scatter, no pattern).

61
Q

DEGREES OF FREEEDOM: one sample t, two sample T, regression, chi square gof, chi square hom/indep

A 
one sample t: n-1
two sample t: calc or smaller n-1
regression: n-2
Chi square GOF: cells-1
CHi square hom/indep: ROW-1 x COL-1

2021 AP STATISTICS (15 decks)

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