# Topic 10 Flashcards

1
Q
A
2
Q

What are the different types of error?

A

Types of error
* Random error due to chance
- Related to Precision
* Systematic error (NOT due to chance)
- Related to Accuracy and Bias

3
Q

Define accuracy

A
• Accuracy is a qualitative term referring to whether there is agreement between a measurement made on an object and its true value.
4
Q

Define bias

A
• Bias is a quantitative term describing the difference between the average of
measurements made on the same object
and its true value.
• If it’s not accurate… there’s a bias

systematic = bias

5
Q

Define selection bias

A

Selection bias
* Related with procedures used to select units for a study
* Study group differs from the source population

6
Q

Information bias (AKA ________ bias)
- Related with information that is recorded for a study
- Error in the way something is ________, in particular the _______, _______, or other variables of ________ (e.g. disease status - calling an animal diseased when they are not disease = misclassification –> wreck havoc).

A

Information bias (AKA Misclassification bias)
- Related with information that is recorded for a study
- Error in the way something is measured, in particular the exposures, outcomes, or other variables of interest (e.g. disease status - calling an animal diseased when they are not disease = misclassification –> wreck havoc).

7
Q

Define confounding bias

A
• Confounding “bias”
• Related with other factors other than the exposure of interest
• Distorted effect of exposure on outcome because of a third factor
• Next lecture
• Confounding and Interactions

8
Q

Sampling is where what type of bias can occur?

A

Selection bias

9
Q

As you record disease, exposure, or information on study group, this is where what type of bias comes in?

A

Information buas

10
Q

Even if subjects are correclty classified, other facotds wil distort the effect of an exposure. This would be ?

A

Risk factors

11
Q

What are the consequences of bias?

• Specific consequences depend on the _____ of bias and study _______
• It’s often possible to ‘guess’-timate the direction of the potential bias
1. Descriptive studies
• No _____ factors, so the only bias/problem is towards the ______. Any bias for way you sampled or way test results were measured will only show up as a __________ change.
So what you observe may not be the real prevalence in the _______.
• Higher or Lower estimate of disease frequency
2. Explanatory studies
• ________ and Explanatory variables (_____ factors)
• Higher or Lower estimate of disease frequency; whether you believe your risk factor is a ____ factor or _______ factor
• Effect estimate “______” or “_____ from” the NULL –> if a bias is towards = going to be towards us not finding a difference, a lack of _______ in your study to detect a difference; if away = identifies a risk factor as a real risk factor when in reality it is not, aka my bias is going to __________ how much of a risk truly exists. Which is worse? _______ from the null. Better to have a study that did not pick up a risk factor instead of saying something is a risk factor when it is not.
• NULL = no statistical difference between E__ and E__
• More difficult to estimate the ________ of the bias! The magnitude is = are we talking about a ____ or _____ bias? Harder to answer.
• Small difference or a large difference?
• _______ analyses (simulations) can help
A
• Specific consequences depend on the types of bias and study design
• It’s often possible to ‘guess’-timate the direction of the potential bias
1. Descriptive studies
• No risk factors, so the only bias/problem towards Outcome only. Any bias for way you sampled or way test results were measured will only show up as a prevalence change.
So what you observe may not be the real prevalence in the population.
• Higher or Lower estimate of disease frequency
2. Explanatory studies
• Outcome and Explanatory variables (risk factors)
• Higher or Lower estimate of disease frequency; whether you believe your risk factor is a risk factor or protective factor
• Effect estimate “towards” or “away from” the NULL –> if a bias is towards = going to be towards us not finding a difference, a lack of power in your study to detect a difference; if away = identifies a risk factor as a real risk factor when in reality it is not, aka my bias is going to exaggerate how much of a risk truly exists. Which is worse? Away from the null. Better to have a study that did not pick up a risk factor instead of saying something is a risk factor when it is not.
• NULL = no statistical difference between E+ and E-
• More difficult to estimate the magnitude of the bias! The magnitude is = are we talking about a small or huge bias? Harder to answer.
• Small difference or a large difference?
• Sensitivity analyses (simulations) can help
12
Q

Surveillance bias
* _____/______-clinical disease is more likely to be detected in animals under frequent medical surveillance and/or enrolled in surveillance programs

A

Surveillance bias
* mild/sub-clinical disease is more likely to be detected in animals under frequent medical surveillance and/or enrolled in surveillance programs

if you are monitoring a group of animals through a surveillance program, then you are more likely to find mild disease v/c you are actually looking vs. looking at population as a whole.

13
Q
• Referral bias (AKA _______ ____ bias, Berkson’s fallacy)
• Differential referral patterns are a source of bias in hospital-based case-control studies. Explain this.
A
• Referral bias (AKA Admission risk bias, Berkson’s fallacy)
• Differential referral patterns are a source of bias in hospital-based case-control studies

Case control studies coming from referral hospitals. Is this a good source for our controls (hospital). Want controls to represent population, so if only choosing from hospital is that introducing a bias.

14
Q

Non-response bias
* Non-response or _______ to participate in a study
* When we are losing >___-___% of the responses, this is what we worry about

A

Non-response bias
* Non-response or refusal to participate in a study
* When we are losing >20-30% of the responses, this is what we worry about

15
Q

Missing data bias
* >__-___% (like non-response bias)

A
• Missing data bias
• > 20-30% (like non-response bias)
16
Q

Loss to follow-up and Follow-up bias
* Similar to _____-________ bias, but occurs in the ________-___ period of longitudinal studies

A

Loss to follow-up and Follow-up bias
* Similar to non-response bias, but occurs in the follow-up period of longitudinal studies

if animal dies or is no longer apart of study.
you are losing information each time and is there a selection process going on that we are unaware of

17
Q

Selective entry or survival bias
* Traits are _______ selected when choosing a group of subject
* e.g. ‘Healthy worker’ effect in occupational-heath studies
* Treatments that prolong _______ will increase prevalence of disease

A

Selective entry or survival bias
* Traits are naturally selected when choosing a group of subject
* e.g. ‘Healthy worker’ effect in occupational-heath studies
* Treatments that prolong lifespan will increase prevalence of disease

18
Q

How do you reduce selection bias?

1. ________ sampling
* This allows us to assess the probability of ______. This is the tool, but what is really important is having the right sample ____.
* Sample _____ dictates probabilities of differences between Target and Study population. Random sampling just ensures you have ______ sampling.
2. Maximize response rate
* Or ensure _____ response by E+|E-and D+|D-
3. Minimize ________ rates
* Or ensure equal _______ by E+|E- and D+|D-
E.g. have animals for time, minimize losing animals (so follow up). Maximize = provide incentive to get 100% response so you minimize selection bias.
* Cannot correct selection bias using analytical techniques.
A
1. Random sampling
* Random sampling allows us to assess the probability of bias. This is the tool, but what is really important is having the right sample size.
* Sample size dictates probabilities of differences between Target and Study population. Random sampling just ensures you have proportional sampling.
2. Maximize response rate
* Or ensure equal response by E+|E- and D+|D-
3. Minimize withdrawal rates
* Or ensure equal withdrawal by E+|E- and D+|D-
E.g. have animals for time, minimize losing animals (so follow up). Maximize = provide incentive to get 100% response so you minimize selection bias.
* Cannot correct selection bias using analytical techniques.
19
Q

Reducing selection bias
* Observational studies – consider ‘forces’ at play with selecting individuals; how are you selecting in this study design?
1. Case-control
* Use ______ cases (new case that will be apart of case definition), and get controls from ______ source population as the cases. (do not want controls to misrepresent where your cases came from)
2. Cohort
* B/c following animals through time, want to keep those animals in the study. Persistent _________-___ (equal E+|E-) with creative strategies for maintaining ____ participation.

• Controlled trials – “Randomize and blind…everything should be fine”
1. Randomize allocation to intervention/comparison groups. Keeps groups fair.
2. Blind to intervention allocation (E+|E-)
• If recruiters selectively enroll patients into study based on the next likely treatment. (e.g. wait to push patient until treatment where they know they wont get placebo)
• Minimize withdrawals
• Maximize retention (follow-up)
A

Reducing selection bias
* Observational studies – consider ‘forces’ at play with selecting individuals; how are you selecting in this study design?
1. Case-control
* Use incident cases (new case that will be apart of case definition), and get controls from same source population as the cases. (do not want controls to misrepresent where your cases came from)
2. Cohort
* B/c following animals through time, want to keep those animals in the study. Persistent follow-up (equal E+|E-) with creative strategies for maintaining full participation.

• Controlled trials – “Randomize and blind…everything should be fine”
1. Randomize allocation to intervention/comparison groups. Keeps groups fair.
2. Blind to intervention allocation (E+|E-)
• If recruiters selectively enroll patients into study based on the next likely treatment. (e.g. wait to push patient until treatment where they know they wont get placebo)
• Minimize withdrawals
• Maximize retention (follow-up)
20
Q

Recall bias
* Problem when interviewing owners; How well do they recall info? Cases are better at recalling (remembering) past exposure compared with non-cases.

A
21
Q

Interview bias
* Interviewers are privy to the hypothesis under investigation. The way question is asked and answered may be different if they know what the study is about. Kind of inevitable unless you can blind your interviewer.

A
22
Q

Pre-verification bias
* Subjects may have _______ motives for overestimating exposure (e.g. ________)

A

Pre-verification bias
* Subjects may have ulterior motives for overestimating exposure (e.g. compensation)

23
Q

Obsequiousness bias (‘______ _____’ effect)
* AKA ‘_______ __________ bias’
* Refers to animal ________
* Subjects systematically alter responses towards ________ desirable answers
* Hans was trained horse who could perform arithmetic tasks
* He was getting non-verbal clues from his trainer to determine when to stop stomping his hoof in response to a question

A

Obsequiousness bias (‘Clever Hans’ effect)
* AKA ‘Social desirability bias’
* Refers to animal welfare
* Subjects systematically alter responses towards perceived desirable answers
* Hans was trained horse who could perform arithmetic tasks
* He was getting non-verbal clues from his trainer to determine when to stop stomping his
hoof in response to a question

24
Q

Consequences of information bias (misclassification)
1. Non-differential
* Systematic errors in one group (e.g. E) are _________ of the other group (e.g. D)
* So in a Case-control study, you would have Equal amounts of systematic error in ____, regardless of the __ status.
* In a cohort study, the bias in your _____ is regardless of ____ status. Equal amounts of systematic error in ___, regardless of the ___ status.
* Non-differential misclassification = error is always going towards the _____
2. Differential
* Systematic error occurs to a greater extent in one group than the other (If the bias in one is dependent on another, you call it a differential).
* Unequal amount of systematic error in __, depending on the __ status
* Unequal amount of systematic error in D, depending on the __ status
* Differential misclassification = err in any direction (can see either towards or away from NULL; making it very difficult to figure out information bias)
* Unless you have an idea of how much error is present and where…

A

Consequences of information bias (misclassification)
1. Non-differential
* Systematic errors in one group (e.g. E) are independent of the other group (e.g. D)
* So in a Case-control study, you would have Equal amounts of systematic error in E, regardless of the D status.
* In a cohort study, the bias in your disease is regardless of exposure status. Equal amounts of systematic error in D, regardless of the E status.
* Non-differential misclassification = error is always going towards the NULL
2. Differential
* Systematic error occurs to a greater extent in one group than the other (If the bias in one is dependent on another, you call it a differential).
* Unequal amount of systematic error in E, depending on the D status
* Unequal amount of systematic error in D, depending on the E status
* Differential misclassification = err in any direction (can see either towards or away from NULL; making it very difficult to figure out information bias)
* Unless you have an idea of how much error is present and where…

You can misclassify the exposure and the disease. We are worried about the consequences of this mixing up is, whether it is away or towards the null.

1. –> an independent amt of mixing in the exposure and in your disease. When those two are independent, it means that it is balanced error across the board for either your exposure or your disease, but it does not depend on one another.
25
Q

Consequences of information bias (misclassification)
1. Non-differential
* Systematic errors in one group (e.g. E) are independent of the other group (e.g. D)
* So in a Case-control study, you would have Equal amounts of systematic error in E, regardless of the D status.
* In a cohort study, the bias in your disease is regardless of exposure status. Equal amounts of systematic error in D, regardless of the E status.
* Non-differential misclassification = error is always going towards the NULL
2. Differential
* Systematic error occurs to a greater extent in one group than the other (If the bias in one is dependent on another, you call it a differential).
* Unequal amount of systematic error in E, depending on the D status
* Unequal amount of systematic error in D, depending on the E status
* Differential misclassification = err in any direction (can see either towards or away from NULL; making it very difficult to figure out information bias)
* Unless you have an idea of how much error is present and where…

A

You can misclassify the exposure and the disease. We are worried about the consequences of this mixing up is, whether it is away or towards the null.

1. –> an independent amt of mixing in the exposure and in your disease. When those two are independent, it means that it is balanced error across the board for either your exposure or your disease, but it does not depend on one another.

non-differential is best, differential is worst

26
Q

There are a few ways to reduce information bias:
1. E and D status should be assessed ________
* Assess one _______ knowing the other (blinded; person who is writing the disease status has no idea what the ________ is or vice versa)
2. Use ________ and ______ methods for determining D and E (rock solid case definition reduces uncertainty)
* e.g. _______ case definitions for cases
* Use ______ available test (within budget) +/- _________ test
* Measure ______ exposures rather than _______ exposure
3. Use _______ and ______ sources of information
* e.g. complete exposure histories
4. Use objective measures when available
* Questions should elicit ‘_____-evaluative’ responses
5. For interviews/questionnaires
* Minimize ______ between diagnosis and questioning
* Use validated survey instrument, if possible
* Pilot study to test question clarity and detail level
* Standardized interview protocols with clear guidelines
* Well-trained qualified interviewers vs. mail/phone
* State/demonstrate clear confidentiality of information

A

There are a few ways to reduce information bias:
1. E and D status should be assessed independently
* Assess one without knowing the other (blinded; person who is writing the disease status has no idea what the exposure is or vice versa)
2. Use rigorous and valid methods for determining D and E (rock solid case definition reduces uncertainty)
* e.g. explicit case definitions for cases
* Use best available test (within budget) +/- confirmatory test
* Measure specific exposures rather than general exposure
3. Use complete and detailed sources of information
* e.g. complete exposure histories
4. Use objective measures when available
* Questions should elicit ‘non-evaluative’ responses
5. For interviews/questionnaires
* Minimize time between diagnosis and questioning
* Use validated survey instrument, if possible
* Pilot study to test question clarity and detail level
* Standardized interview protocols with clear guidelines
* Well-trained qualified interviewers vs. mail/phone
* State/demonstrate clear confidentiality of information

27
Q

How to correct information bias using analytical techniques?
* If you have a large cohort study, take a Sub-sample and add more verification and double check classification of E and D; Get a second colleague to come in and verify those. Tweaks –> apply post-hoc, etc. Depends on models applied.
* Simple methods have limitations
* Advanced methods are very complicated
* Caution: very sensitive to changes in estimates!
* Much better to prevent information bias than to correct for it after

Doing all of this to change the way you report risk. Don’t do a post-hoc correction. It is messy. Prevent misclassification from happening in the first place.

A
28
Q
• Reducing information bias
• Observational studies
1. Case-control
• Explicit case definitions for cases
• Determining E status should be independent from D status
• Interview should be as soon as possible after becoming a case
2. Cohort
• Determining D status should be independent from E status
• Valid method and objective measures for determining D status
• Controlled trials – “Randomize and blind…everything should be fine”
• Blind to intervention allocation (E+|E-)
• Prevents D status from being influenced by E status
• Valid method and objective measures for determining outcome (D status)
A
29
Q

First six slides

A
30
Q
• Consequences of information bias (misclassification)
• Non-differential
• Systematic errors in one group (e.g. E) are independent of the other group (e.g. D)
• Equal amounts of systematic error in E, regardless of the D status
• Case-control study
• Equal amounts of systematic error in D, regardless of the E status
• Cohort study
• Non-differential misclassification = err towards the NULL
A

RELISTEN

31
Q

Going away from null means?

A

Test is saying there is a real risk factor when there really isn’t one.

32
Q

Differential
* Systematic error occurs to a greater extent in one group than the other
Unequal amount of systematic error in E, depending on the D status, can lead in any direction

A

relisten

33
Q

How do we reduce information bias/misclassification?

A
1. Assess exposure and disease status independently. This has to do with interviewers or researchers. Blinding is key here. This is a preventative measure.
2. Use rigorous and valid methods for determining disease and exposure. Have a good case definition so you will not misclassify your cases and controls. Also use best diagnostic test and if possible confirm that they are truly diseased (not just based on one test that is not very specific or sensitive).
3. Detailed sources of information. Write down as much as possible so you are able to properly classify them on al the information you have on hand.
4. Use objective measures. Questions should elicit non-evaluative responses aka clear-cut responses.
5. For interviews/questionnaires:
* Minimize time between diagnosis and questioning
* Use validated survey instrument, if possible
• Pilot study to test question clarity and detail level
* Standardized interview protocols with clear guidelines
* Well-trained qualified interviewers vs. mail/phone
* State/demonstrate clear confidentiality of information
34
Q

Is it possible to correct for potential information bias?

A

if you do a subsample of your study and followup and validate they are correclty classified, if not in theory you can back calculate and reclassify. Never really done in real life. For the most part, you can’t really correct it but you can prevent it.
Selection and info can not be correctly analytically.

35
Q

How do you reduce info bias in a case control study? Observational study

A
• Explicit case definitions for cases
• Determining E status should be independent from D status
• Interview should be as soon as possible after becoming a case
36
Q

How do you reduce info bias in a cohort study? Observational study

A
• Determining D status should be independent from E status. Researchers should not know exposure group subjects were in when trying to determine disease status.
• Valid method and objective measures for determining D status.
37
Q

How do you reduce info bias in a blind study? Controlled trial

A

“Randomize and blind…everything should be fine”
* Blind to intervention allocation (E+|E-)
* Prevents D status from being influenced by E status
* Valid method and objective measures for determining outcome (D status)

38
Q

Confounding comes from the latin word?

A

Confundere meaning to mix together

39
Q

Confounding is defined as?

A

“A distortion of the true underlying relationship between an exposure
and an outcome of interest, because of the influence of a third factor”

Relisten

40
Q

Being on one exposure will not necessarily change these things.
Being on grass will not change the age of a cow. May be associated in the sense tht different age groups can be on different grass patches, but the grass isn’t causing the age differences.

A
41
Q

Criteria
* A confounder must be ______ associated with the outcome …in non-exposed animals
* A confounder must be ___________ associated with the exposure
* The _______ and the _________ must be on two separate causal pathways to the outcome
* Cannot be affected by the _______ nor the ________

A

Criteria
* A confounder must be causally associated with the outcome
* …in non-exposed animals
* A confounder must be non-causally associated with the exposure
* The confounder and the exposure must be on two separate causal pathways
to the outcome
* Cannot be affected by the exposure nor the outcome

42
Q

In this study, if you were younger you were less likely to die of tolbutamide and if you were older you were more likely to die of Tolbutamide.

What are the three criteria that need to be met to determine if the results are confounding? Are these criteria met?

A
1. Must be associated with the outcome
…in non-exposed
- Despite randomization, there was still a difference of age by treatment (52% of Tolb patients <55y, while 59% of Plac <55y). This means that there is no =? (relisten)
2. Must be associated with the exposure
- (RR = 0.188/0.042 = 4.5; OR = (16/69)/(5/115) = 5.3) If older, 4.5x more likely to die.
3. Must be on separate causal pathways
- (relisten to this explanation)

Obvs: Tolbutamide does not change age.

43
Q

What is the Mantel-Haenszel equation? What does it do?

A

Combined OR AKA Age-adjusted OR reported on regular basis
combines two odds ratio to say what it is if age is present.

44
Q

How do we utilize the MH equation to determine if our study is confounding or not?

A

Confounding is an issue when
>20-30% change in OR between
Crude OR and M-H OR

If there is more than a 20-30% change, it is changing your estimate.

When it does confound, you should report the adjusted value. If they are almost the same, it does not really matter which value you report.

45
Q
A

When you only have 1 variable, it reports the OR. If you put multiple variables in, it automatically reports the MH.

46
Q

How do you control for confounding at the beginning of your study?

1. _________ (Exclusion)
* Built into the study ______
• Purposefully restrict to a ______ group of individuals
• Loss of ‘_________’ (________ validity)
2. ________
* In __________ trials
• Randomized allocation to E__ and E_ groups
• Produces very ______ groups

If you always randomize, you should roughly have = size groups between exposed and unexposed.

A
1. Restriction (Exclusion)
* Built into the study design
• Purposefully restrict to a specific group of individuals
• Loss of ‘generalizability’ (external validity)
2. Randomization
* In controlled trials
• Randomized allocation to E+ and E- groups
• Produces very similar groups

If you always randomize, you should roughly have = size groups between exposed and unexposed.

47
Q

What is matching?

A

in a cohort study you can match by exposure. e.g. exposed individual that is a male, you can find a male that was not exposed. See who develops disease.
Problem? Unable to estimate effect of that matched factor (e.g. if you are matching on gender, you will no longer know the effect of gender on disease). But in this case you want to remove gender as a potential bias but you won’t be able to measure anymore (losing a bit of info).

48
Q

Matching does not control confounding in case control studies but it can increase statistical powers. So how would you match?

A

you have a case, this case is a male, then the next case would also be a male as your control.

49
Q

Stratification means we are splitting the confounder into groups.
This can only be done once a ta time.
Most powerful and common way to do it: multivariable techniques. You can throw everything into model and then it is automatically adjustedl.

A
50
Q
A
51
Q

Univariable analyses
* AKA: ‘Univariate’, ‘unconditional
associations’, ‘raw’, ‘crude’, ‘bivariate
logistic regression’, etc.
* No control for confounding

Estimate produced can be prone to the effects of confounding variables.

A
52
Q
• Report M-H OR, not just Crude OR
• No mention? …assume not done
• Multivariable regressions
• AKA: ‘Multivariate’ (not correct term,
but OK), ‘Conditional regression’, etc.
• Must see confounder/factors
included in the same mode
A
53
Q

Difference between confounding and interaction?

A

If a confounding is a third factor that distorts the true underlying effect, that is confoudning. However if third factor is necessary to explain the relationshi, do the outcme depdends on the exposure and the factor, this is called an interaction.

54
Q
A

line parallel = no interaction
nonparallel = interaction

• Synergistic (positive)
• Joint effect is greater than the sum of independent (factor) effects
• Antagonistic (negative)
• Joint effect is less than the sum of independent (factor) effects
55
Q

How do we know if it is confounding or interaction?

A

Test of homogeneity
* Formal statistical test to see if interaction exists
–> Test of homogeneity
* P ≥ 0.05 = homogeneity
* No differences among strata
* P < 0.05 = lack of evidence of homogeneity = heterogeneity
* Differences among strata

56
Q

Consequence?
Need to use strata-specific estimates
* e.g. RR or OR for each stratum

A
57
Q
A

All herds = don[‘t know if they had clox or not, because you are just including everyone.

Look at test of homogeneity to see if 29.3 is different from 1.5
p is less than 0.5, so yes it is different.
Based off this, you know that not having clox is a problem

58
Q

when you hear the words “depends on” that means there is an ?

A

interaction

59
Q

A

Look at OR for young people, then old people
Look at crude ratio –> ?
Look at MH adjustment –> tobutamide effect is when accounting for age
Do we report the crude or the combined?

60
Q

If confounding, you do the adjustment.
If an interaction, you do?

A
61
Q

How do assess confounding and interactions?

A

If test of homo is not significant, therefore there is no differnece between two age groups, go down cascade and ask if it chages the OR? Does it confound our relatonship. Around 20-30% diff between crude or when you account for other factor does it change your underklying OR. If cahnges it by omore than 20-30%, you have to report that is happening, If it is less than 20%, stick with the crude. The

62
Q
A

Does age have to do with obesity? It might be a confounder or an interaction or it may not matter at all.

When you are a puppy, the OR is 1.05
Prevalence in puppies that eat ad lib = 5.4, resitrcited =5.2. Makes sense OR is close to one because there is no real difference.
Adults: prevlance is 54.5, restricted is 33.3%. OR is above 1 so it is a risk and the CI is above 1 so it is significant. So ad lib is a signficaitn risk if you are an adult dog, but not for a puppy.

So the q is is there a real difference? aka is 2.42 different from 1.05. So frist step: is there an interaction? The test of homogenity will tell yo this. The p val is greater than 0.05 so there is no differnece between the 2. (pr>chi2 = 0.2416)

Then calculate difference 1.56-2.32 / 1.56 = 48.7%. Leave change in and report adjusted value. Must report 2.32 b/c if the diff bet crude and adjust is more tahn20% you need to report the adjusted.

63
Q
A

Is there an interaction? meaning is the homogenity test showing that they are similar or different?
if p val < 0.05 = There is a difference between puppy and adult.
0.67 is different from 2.22. Report these two different values and you stop here.

64
Q
A
1. look at tet of homo. p = 0.1604, < 0.05 so no difference
2. is there a diff between 1.56 and 1.63. Looking for 20-30% difference. 1.56-1.63/1.56 = 4.5%. This means you can just use the crude