Section 7: sampling, random error, statisical inference, selection bias & different sampling methods

Question 1

What is a sample?

Answer 1

• selected subset of a source pop
• should be representative of the source pop

Question 2

What is the purpose of taking a sample?

Answer 2

to study smth that we can’t study in the whole pop coz of practical restrictions (finance, time)

Question 3

Can research be conducted in whole populations?

Answer 3

Yes but,
* almost always conducted in samples
* rare cases research conducted in whole pop but usually pop very small

Question 4

What is sampling?

Answer 4

process of selecting # of individuals from all individuals found in a source pop

Question 5

What is a sampling frame?

Answer 5

list (or database) containing all individuals in pop & is used for sampling

Question 6

What are sampling units?

Answer 6

• Individuals to be potentially selected
• most of time individuals but can also have larger sampling units (e.g. fam, streets, hospitals, schools, etc)

Question 7

What is the source population?

Answer 7

group of all individuals in which we’re interested to assess parameters

Question 8

What can the source population be?

Answer 8

• vague (e.g. total pop of a country or city)
• specific (e.g. smokers of a country, all patients with heart disease, etc)

Question 9

Who is the source pop in descriptive research?

Answer 9

should be restricted to country or region where sample was taken

Question 10

Who is the source pop for analytical research?

Answer 10

can be more general regarding source pop but depends on RQ

Question 11

Who is the source population if a study investigated the prevalence of obesity in Cyprus, by recruiting a random sample of adults?

Question 12

Who is the source population if a study investigated the association between smoking and oesophageal cancer among a sample of 35-65 year olds in Canada?

Question 13

Who is the source pop if a study investigated the association between educational attainment and stroke among a sample of elderly individuals in Sweden?

Question 14

What is a population parameter?

Answer 14

measurement of a quantity (or association) in a population that we’re interested about. e.g.:

• mean age
• prev of obesity
• mean diff in BP between men & women
• OR for association between smoking & cancer

Question 15

What is an estimate?

Answer 15

measurement of a quantity (or association) in a sample that’s supposed to represent true quantity or association in source popualtion (parameter)

Question 16

What is sampling variation?

Answer 16

difference between different sample estimates derived from the same source population

Question 17

What is sampling error?

Answer 17

statistical error that occurs when a sample doesn’t represent entire population.

Question 18

What is sampling error also referred to as and why?

Answer 18

Coz sampling erorr is a result of chance, usually referred to as random error

Question 19

How does sample size influence the mangitude of the random error?

Answer 19

larger sample size minimizes the magnitude of the random error

Question 20

Why does research often rely on samples instead of whole populations?

Answer 20

Because of cost & time constraints

Question 21

What is standard error of the mean (SEM)?

Answer 21

variability of means that might be calculated from repeated sampls from the same population

Question 22

What is the relaitonship between sample size & SEM?

Answer 22

Larger sample sizes decreases the SEM

Question 23

What can the standard error be used for to calculate?

Answer 23

degree of uncertainty around an estimate: the 95% confidence interval

Question 24

What do confidence intervals indicate?

Answer 24

range of values, derived from sample data, that is likely to contain the true population parameter (like the mean or proportion) with a specified level of confidence (often 95%).

Question 25

How are confidence intervals calculated?

Answer 25

using standard error of the mean

Question 26

How is the lower confidence interval calculated?

Answer 26

* sample mean - (z * standard error) * if 95% CIs = sample mean - (1.96 * standard error)

Question 27

How is the upper confidence interval calculated?

Answer 27

* sample mean + (Z * standard error) * if 95% CIs = sample mean + (1.96 * standard error)

Question 28

What does the z-value depend on?

Answer 28

depends on significance level (alpha) that is chosen

Question 29

What significance level (alpha) is most commonly used in biomed research?

Answer 29

Alpha = 0.05 (5% signficance level)

Question 30

What is the z-value for a 5% signficance level?

Answer 30

1.96

Question 31

What is the confidence interval for a significance level of 5%?

Answer 31

For significance level of 5%, get 95% confidence intervals

Question 32

For the association between smoking & BP, if the mean difference is 12.3 (95% CI: 10.8; 13.8), how would the CIs be interpreted?

Answer 32

We're 95% certain that the true pop mean difference lies between 10.8 & 13.8

Question 33

For the association between age & BP, interpret the CIs if: the regression coefficient 3.6 (05% CI: 0.5; 6.7)

Answer 33

95% certain that the true pop regression coefficient lies between 0.5 & 6.7

Question 34

For the association between obesity & hypertension, if the OR is 2.10 (95% CI: 1.80; 2.40), how would this be interpreted?

Answer 34

95% certain that true pop OR lies between 1.80 & 2.40

Question 35

What does the Confidence interval indicate?

Answer 35

level of uncertainty around the sample estimate

Question 36

What does a 95% CI indicate?

Answer 36

a range within whcih we can be 95%s certain that true pop measure lies there.

Question 37

What is the relationship between 95% CI and sample size?

Answer 37

larger the sample size, the narrower the 95% CI

Question 38

What are 2 possibilities for any given association between 2 factors (variables)?

Answer 38

* association doesn/t exist (2 variables arent linked) * association does exist (2 are linked)

Question 39

What is the Null hypothesis H0?

Answer 39

always states that there is no associaiton between the 2 variables

Question 40

What is the alternative hypothesis (H1)?

Answer 40

always states that there is an association between the 2 variables

Question 41

What significance level is often used?

Answer 41

level of 5% = p-value of <0.05 to conclude statistical significance

Question 42

What is the 95% CI & P-value affected by?

Answer 42

* sample size * magnitude of the association

Question 43

What does it mean if we have an estimate with a p-value of <0.05?

Answer 43

statistically signfiicant so exclude possibility of it being a chance finding

Question 44

If we assume the presence of an association in the population....

Answer 44

* **large sample sizes** will give **smaller** p-values * estimates of **large magnitude** will also give **smaller** p-values

Question 45

What can the 95% CI also be used for?

Answer 45

accepting or rejecting the null hypothesis

Question 46

What is random error?

Answer 46

Error introduced solely by **chance** and is inherent in the sampling process

Question 47

What is systematic error?

Answer 47

(AKA bias) introduced via **man-made** acitons relating to the conduct of a study

Question 48

What does selection bias lead to?

Answer 48

A biased sample which almost always = biased estimates

Question 49

What are the types of sampling methods?

Answer 49

* Probability (random) sampling * systematic sampling * non-probability sampling

Question 50

What is probability (random) sampling?

Answer 50

* sample selected by probabalistic methods * involves random selection allowing to make strong statistical conclusions about whole group

Question 51

What is systematic sampling?

Answer 51

Sample selected according to simple, systematic rule

Question 52

What is non-probability sampling?

Answer 52

* Sample selected by easily employment (convinient) * involves non-random seelection based on conveience or other criteria allow easily data collection

Question 53

What are the types of probability sampling methods?

Answer 53

* simple random sampling * stratified RS * cluster sampling * multi-stage sampling

Question 54

What are the types of systematic sampling?

Answer 54

* simple systematic sampling * proportional quota sampling

Question 55

What is simple random sampling?

Answer 55

all individuals in sampling frame have **same probability** of being selected indepentely of all others

Question 56

When is simple random sampling mostly used?

Answer 56

in quantitative research

Question 57

What does simple random sampling ensure given a large sample size?

Answer 57

chosen individuals are **representative** of source pop * demography (age, sex, ethnicity) * other factors (history, disease status, lifestyle factors)

Question 58

What is the procedure for simple random sampling?

Answer 58

* use tools like random # generators or other techniques that are based entirely on chance * e.g. random sample of 100 cancer patients from registry of 1,000. assign a # to each patient in database & use generator to select 100

Question 59

What are the advantages of simple random sampling?

Answer 59

* ensures **representative sample** from source pop (provided sample is large enough) * **cheaper & less time** consuming than other sampling methods * ideal for **quantitative** studies & **testing hypothesis**

Question 60

What are the disadvantages of simple random sampling?

Answer 60

* if **sampling frame is too large/pop is geographically diverse**, can be impractical to perform (difficulty to access lists of full pop) * **if large sample required**, simple random sampling can be time consuming & costly

Question 61

What is stratified random sampling?

Answer 61

* sample principles as simple random sampling but within **strata (subgroups)** of pop * in terms of key demographic characteristics

Question 62

What is an example of stratified random sampling?

Answer 62

* company has 800 female employees & 200 male employeees * need sample of 100 * sort pop into 2 strata based on gender * want to ensure sample reflects gender balance of company so you choose random sampling on each group, selecting 80 women & 20 men = representative sample of 100

Question 63

What is the procedure of stratified random sampling?

Answer 63

* identify source pop * set up sampling frame * decide on sample size * decide on pre-defined pop strata * based on overall proportions of pop, calculate how many ppl should be sampled from each strata * **randomly** select individuals to fill strata

Question 64

What are the disadvantages of stratified random sampling?

Answer 64

* more time consuming than simple RS * can't be used when researchers can't confidnetly classify eveery member of pop into subgroup * higher complexity can give rise to errors (e.g. stratification not done properly)

Question 64

What are the advantages of stratified random sampling?

Answer 64

* allows to draw more precise conclusion by ensuring every subgroup is propertly represented in sample * enables comparison of pop sub-groups

Question 65

What is cluster sampling?

Answer 65

* Based on hierarchical structure of natural clusters (groups) of individuals wihtin the pop * natural clusters can be hospitals, schools, streets, city distrcits, etc

Question 66

What does cluster sampling involve?

Answer 66

taking a random sample of these natural clusters & seleciting all individuals in selected clusters

Question 67

What is the sampling frame?

Answer 67

list of all clusters

Question 68

What is the procedure for cluster sampling?

Answer 68

1. identify source pop 2. set up sampling frame (comprised of clusters) 3. decide on sample size (# of clusters & individuals) 4. randomly select clusters from sampling frame

Question 69

What are the advantages of cluster sampling?

Answer 69

can **reduce cost & time** of data collection esp when pop is **spread over large area**

Question 70

What are the disadvantages of cluster sampling?

Answer 70

* considerable differences between clusters can cause errors * difficult to gaurantee that sampled clusters rlly are representative of whole pop

Question 71

When can the representativeness be compromised in cluster sampling?

Answer 71

Representativeness can be comprised if: * too few clusters selected * clusters too specific * clusters contain too few individuals

Question 72

What is multi-stage sampling?

Answer 72

* Uses hierarchical structure of natural clusters (groups) of individuals within the pop * similar to cluster sampling

Question 72

What are the advantages of multi-stage sampling?

Answer 72

* can improve sampling representativeness (compared to simple RS) - esp if pop is geographically divers or sample is too small * cheaper & less time consuming (dep on # of stages tho)

Question 73

What are the disadvantages of multistage sampling?

Answer 73

representativeness of sample compromised if: * Too few clusters are selected and/or * Clusters are too specific and/or * Clusters contain too few individuals

Question 74

What is (simple) systematic sampling?

Answer 74

* sampl selected according to simple, **systematic** rule but **not** randomly

Question 75

what are examples of simple systematic sampling?

Answer 75

Selecting ppl from sampling frame: * whose name starts with certain letter * who were born in selected month * selecting every 2nd/5th/10 person from sampling frame

Question 76

What is the procedure of (simple) systematic sampling?

Answer 76

* identify source pop * set up smpling frame * deicde on sample size * systematically select individuals from sampling frame * example of systematic rule: recruit every 3rd individual

Question 77

What are the advantages of (simple) systematic sampling?

Answer 77

* acceptable, more conveniet, alternative approach if random sampling isn't possible * faster & possibly cheaper

Question 78

What are the disadvantages of (simple) systematic sampling?

Answer 78

**representativeness** of sample can be **compromised** if system of choice selects indviiduals in **non-random** way

Question 79

What is the procedure of proportioanl quota sampling?

Answer 79

* identify soruce pop * set up sampling frame * decide on sample size * decide on pre-defined pop strata * select individuals to fill strata non-randomly (i.e. using systematic sampling)

Question 80

What are the advantages of proportional quota sampling?

Answer 80

* acceptable, more convenient, alternative approach if stratified random sampling isn't possible * Compared to simple systematic sampling, could ensure original pop structure as it uses predefined population strata

Question 81

What are the disadvantages of proportional quota sampling?

Answer 81

* representativeness of sample may be compromised as individuals are selected in a non-random fashion

Question 82

What is convinience sampling?

Answer 82

* most frequent example of non-probability sampling * Individuals are selected in non-random fashion, solely based on convenience (i.e. they are easy to access)

Question 83

What's an example of convenience sampling?

Answer 83

* Researching anxiety of university students, so after a class of an elective course, you ask your fellow students to complete a survey on the topic. * This is a convenient way to gather data, but as you only surveyed students at the same year and elective course as you, the sample is not representative of all the students of your class nor the university.

Question 84

What is the procedure of convenience sampling?

Answer 84

* identify source pop * set up samploing frame * decide on sample size * conveniently select individuals

Question 85

What are the advantages of convenience sampling?

Answer 85

* cheap * fast * convenient

Question 86

What are the disadvantages of convenience sampling?

Answer 86

representativeness of sample definitely **compromised** coz individuals are selected in a **non-random fashion**

Question 87

What are the types of non-random sampling methods?

Answer 87

* Convenience sampling * Purposive sampling * Voluntary response sampling * Snowball sample

Question 88

What is purposive sampling?

Answer 88

select individuals with the characteristics the researcher wants in the study

Question 89

What is voluntary response sampling?

Answer 89

ppl volunterr themselves for the study

Question 90

What is snowball sample?

Answer 90

participants recruit other participants

Question 91

What does the choice of sampling method in order to minimize selection bias depend on?

Answer 91

* aim of study * natur of source pop * sample size * pracitcal issues (financial resources, time, etc)

Question 92

Which sampling method to choose in order to minimize selection bias when there are **no financial & time constraints?**

Answer 92

* always advised to use **probability (random) sampling** tehcnicues to minimize selection bias * **stratified RS** is ideal method if **sample is small**

Question 93

What can we assume when non-random sampling techniques have been used?

Answer 93

* representativeness of sampl is always questionable * assume that **selection bias** is operating at some extent

Question 94

What should always be avoided whatever the study design?

Answer 94

Convenience sampling!

Question 95

What do we do with confounding?

Answer 95

We adjust for it (e.g., stratify, regress)

Question 96

What do we do for effect mdoification?

Answer 96

report it, can't adjust it

Question 97

What is stratification?

Answer 97

Dividing (stratifying) your study population into subgroups (strata) based on levels of a confounder & then analyzing exposure–outcome relationship within each stratum. E.g. * Stratum 1: non-smokers * Stratum 2: smokers You then estimate coffee–heart disease association separately within each group.