Sampling Error and Bias

Question 1

Why is the sampling distribution important?

Answer 1

We never draw lots of samples. We estimate the population parameter from a single or small number of samples. Our point estimate is drawn from a theoretical sampling distribution. Variation associated with this distribution is influenced by sample size.

Question 2

What is sampling distribution?

Answer 2

A sampling distribution is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population.

Question 3

What is the central limit theorem?

Answer 3

Tells us the sampling distribution will approximate to a normal distribution with sufficient sample size, representative sample, random sampling.

Question 4

What is a confidence interval?

Answer 4

defines a range in which we estimate the true value will fall, accept some error (level of confidence 95%)
2xME

Question 5

What does a 95% confidence level mean?

Answer 5

We accept a 5% likelihood that our confidence interval will not contain the true value.

Question 6

What is margin of error?

Answer 6

Confidence interval is constructed by ME either side of our point estimate (mean). SE x 1.96

Question 7

Standard Error

Answer 7

Measure of how much our estimate differs from the true population value.

Question 8

How would you get a precise estimate, with a narrow confidence interval?

Answer 8

Increase sample size

Question 9

When do we use t-scores?

Answer 9

When dealing with small samples (<40). Instead of z scores and normal distribution.

Question 10

What do we have to do when calculating confidence interval for RR and OR?

Answer 10

We must log transform estimate and then antilog it as they do not follow a normal distribution.

Question 11

Define sampling frame.

Answer 11

Actual list of survey population from which the sample is drawn, after which inclusion and exclusion criteria have been determined.

Question 12

define sampling fraction.

Answer 12

Ratio between sample size and population size.

Question 13

What is systematic error?

Answer 13

Sample not representative of population due to inaccuracy in sampling design or procedures of measurement. Form of bias. Predictable and once identified can be avoided. Will likely not form normal distribution.

Question 14

What is random error?

Answer 14

Not predictable. Caused by natural fluctuations in sampling or measurement process. When plotting random errors as a histogram they should always form a normal distribution.

Question 15

Describe the process of simple random sampling?

Answer 15

Identify survey population, create sampling frame, list eligible units, number them, determine sample size needed, randomly draw units (random number generator).

Question 16

What are the advantages of simple random sampling?

Answer 16

simple, sampling error easily measured, every unit in frame has equal probability of being selected

Question 17

What are limitations of simple random sampling?

Answer 17

create list of all units, get list of units from records (what if they don’t represent the population e.g. telephone directory excludes people without telephone), logistical challenge (time and cost), important minority groups may be missed by chance

Question 18

Describe systematic sampling.

Answer 18

identify survey population, sampling frame, arrange units in a sequence (alphabetically), determine sample size, divide sampling population by sample size, choose random starting point, draw units at reg. intervals.

Question 19

Advantages of systematic sampling.

Answer 19

simple, easy to implement, sampling error easily determined, ensures representivity.

Question 20

Limitations of systematic sampling.

Answer 20

Needs a complete list that is representative of target population, patterns in ordering sequence increases probability of some units being selected.

Question 21

Describe cluster sampling.

Answer 21

1. list potential clusters e.g. all schools in a state 2. list of units in each cluster 3. calculate systematic sampling interval (cumulative population/number desired clusters) e.g. say it is 738 4. choose random start number between 1 and 738 5. select remaining clusters

Question 22

Advantages of cluster sampling.

Answer 22

complete list of units not needed, less travel, within clusters all units have equal probability of being selected

Question 23

Limitations of cluster sampling.

Answer 23

positive covariance within a cluster (bias), increased sampling (standard) error

Question 24

Describe stratified sampling.

Answer 24

Stratify the sampling frame into homogenous sub-populations (strata), sample drawn randomly from each strata.

Question 25

Advantages of stratified sampling.

Answer 25

Info on subgroups, increased precision so can have a smaller sample, economical, can have several strata

Question 26

Limitations of stratified sampling.

Answer 26

more effort in administration to classify every unit to a category, a participant may classify into several sub-groups, harder to measure sampling error, ss at strata level may be low (high random error and loss of precision)

Question 27

What is the sampling fraction?

Answer 27

Use in stratified sampling to ensure probability proportional to size. SS/population x100

Question 28

What is multistage sampling?

Answer 28

Use a combo of methods. e.g. 1)identify primary sampling unit (clusters) 2. select sampling units from a cluster

Question 29

What is optimal sampling method is precision and reduction of sampling error were the priorities?

Answer 29

stratified random sampling with replacement

Question 30

What is optimal sampling method if logistics is a consideration or if study is on an intervention targeted at community level?

Answer 30

cluster

Question 31

What is the objective of an estimation study?

Answer 31

Estimate a population parameter (mean or prevalence) from a sample.

Question 32

What is the objective of a comparative study?

Answer 32

Compare groups to assess whether there s any statistically or clinically significant difference between them (expressed as a hypothesis test).

Question 33

What do sample size calculations presume?

Answer 33

simple random sampling, random error

Question 34

What do we need to know for sample size calculations in surveys?

Answer 34

confidence level (z stat- 1.96), sd (if estimating a mean) or proportion/prevalence (if estimating a single proportion), precision (0.05)

Question 35

What do we need to know to calculate sample size of a comparative study?

Answer 35

threshold for a sig. result (0.05), power (0.8/0.9), base level for one of the groups (estimate from previous studies), minimum effect size (min RR or OR)

Question 36

What is power?

Answer 36

The probability of making a correct decision to reject null hypothesis.

Question 37

How would you boost the power of a comparative study

Answer 37

increase significance threshold, increase effect size, reduce variation, use a one tailed test

Question 38

Describe the properties of the normal distribution?

Answer 38

symmetrical shape, deviations away from centre equally in + or - direction, mean and median directly in centre. for cont. normal distributions the probabilities of all poss. outcomes are represented by the area under the curve.

Question 39

How does a standard Normal distribution differ from normal distribution?

Answer 39

Standard normal is referenced to a standardised scale where mean=0 and variance=1.

Question 40

What is a z-score?

Answer 40

found on a standardised normal distribution. calculated by x-mean/sd. They tell us how many sd's an observation is above or below the mean. This allows comparisons of distributions expressed in different units.

Question 41

The 95% reference range lies within how many sd and what z score?

Answer 41

+ and - 2sd and -1.96 +1.96 z-score.

Question 42

When do you use a students t test?

Answer 42

When sample sizes are small or the sd of the population is not known.

Question 43

How is the t-distribution used and what does its shape look like?

Answer 43

Used in t-test to construct CI for diff between 2 population means, and in linear regression analysis. It is bell shaped but with a stronger peak and longer tails.

Question 44

How does a t-score differ from a z-score?

Answer 44

(x-mean) / (sd/root n) | uses sd of sample, not population