12. SAMPLING, RANDOM ERRORS AND CONFIDENCE INTERVALS Flashcards
1
Q
- What is Statistical Inference?
A
- it is when we look at a specific aspect of a sample
group - we then use these results to make assumptions about
the total population - it is when the sample estimate is used to draw
conclusions about the population - from which the sample was taken
2
Q
- What is a sample?
A
- it is a selected subset of a source population
- the sample should ideally be representative of the
source population
3
Q
- Provide a brief definition of the Source Population?
A
- this is the group of all the individuals that we are
interested in - we use this group to assess certain parameters
- it is the group that we want to make a statistical
inference about
4
Q
- What is the purpose of taking a sample?
A
- it allows us to study a parameter that we cannot study
in the whole population - this is because there are practical restrictions to
studying the whole population - EG: time, money, resources
5
Q
- How is scientific research almost always conducted?
A
- through the use of samples
- research may be conducted in whole populations as
well - these populations are usually very small
6
Q
- What is the process involved when it comes to Sampling?
A
- there is a number of individuals that are selected
- these individuals all come from the same source
population - a sampling frame is necessary to do this
7
Q
- What is a sampling frame?
A
- it is a list or a database
- it contains all the individuals in a population
- it is used for sampling
- sometimes this method cannot be used
8
Q
- What are the Sampling Units?
A
- they are the individuals that have the potential to be
selected - these are individual people most of the time
- there can also be larger sampling units
9
Q
- List 4 examples of larger sampling units.
A
- families
- streets
- hospitals
- schools
10
Q
- What kind of populations can the Source Population be?
A
- it can be the general population
- EG: total population of a city or country
- it can also be specific sub-populations
- EG: all smokers in a country
11
Q
- What is Descriptive Research?
A
- it is a research field in which we investigate the
prevalence and incident rate of a condition in a
population - there is a high focus on frequencies
- EG: prevalence of Covid in Cyprus
12
Q
- What is of high importance when it comes to sampling in Descriptive Research?
A
- the sample has to accurately represent the specific
source population
13
Q
- What is Analytical Research?
A
- this is when we investigate the association between
exposure and outcome - EG: the association between obesity and diabetes
14
Q
- What can be said about the source population obtained during Analytical Research?
A
- the source population can be more general
- this depends on the research question of interest
15
Q
- What can be sad about the source population in situations where we are investigating a biological effect on some disease?
A
- the source population we are identifying can be more
general - this population is not necessarily restricted to a specific
region or country - EG:
- the effect of smoking on cancer
16
Q
- What can be sad about the source population in situations where we are investigating a social or cultural effect on some disease?
A
- we have to be more careful with the source population
- we have to restrict it to a specific country or region
from where the sample was derived - EG:
- the effect of social class on the risk of heart disease
17
Q
- How do we determine the proportion of a characteristic in a population?
A
- we measure it in a sample
- we are measuring the estimate
- this estimate carries an inherent error
- this is known as a sampling error
18
Q
- What does Statistical Inference involve?
A
- it involves the use of statistics
- these determine the degree of uncertainty in the
estimate of interest
19
Q
- Provide a definition for the term “estimate”.
A
- is the proportion of the parameter in a sample
- it is the measurement of a quantity (association) in a
sample - it aims to represent the true quantity in the source
population
20
Q
- What is a Parameter?
A
- it is the measurement of a quantity (association) in a
population - we are interested in this quantity
21
Q
- Provide 4 examples of Parameters.
A
- Mean Age
- Prevalence of Obesity
- Mean difference in blood pressure between men and
women - Odds Ratio for the association between smoking and
cancer
22
Q
- What does the sample estimate attempt to quanitfy?
A
- it attempts to quantify the corresponding population
parameter - we want to see how close the sample estimate will be
to the population parameter
23
Q
- What is the Sampling Error?
A
- it is the difference in magnitude
- between the sample estimates and the actual
population parameter
THIS IS CAUSED BY:
- measuring a quantity (association) in a sample
rather than in the source population
24
Q
- What is Sampling Variation?
A
- this happens when we take numerous different
samples - we measure the same aspect from the same source
population - it is the differences (variation) between the sample
estimates
25
Q
- Why can we refer to Sampling Errors as “Random” or “Statistical” Errors?
A
- this is because the sampling errors are a result of
chance
26
Q
- What does the Sample Size play an important role in?
A
- it plays an important role in the magnitude of the
random error
NB:
- a smaller sample size leads to a larger sampling error
- the two are inversely proportional
- the sample variation will also increase
- the two are inversely proportional
27
Q
- Name all the measurements in which the Sample Size is inversely proportional to both the Sampling Error and the Sample Variation.
A
- Incidence
- Risk Ratio
- Rate Ratio
- Mean Difference
- Correlation Coefficient
- Regression Coefficient
NB:
- all of the above as termed “Estimates”
when they are calculated in a Sample
28
Q
- What is the Standard Error (SE)?
A
- this describes the uncertainty of how well the sample
estimate represents the population represents the
population parameter
29
Q
- What does the Standard Error estimate?
A
- it estimates the standard deviation of the sampling
distribution - EG:
- the average error that can occur whenever we take a
sample of a certain size (n)
30
Q
- For what quantities does the sStandard Error exist?
A
- it exists for all statistical quantities
31
Q
- From which value can the Standard Error be estimated from?
A
- it can be estimated from a single sample
32
Q
- How do we calculate the Standard Error with regards to the mean?
A
S= sample standard deviation
n = sample size
NB:
- you do not have to know this formula
33
Q
- What is the relationship between the Sample Size and the Standard Error?
A
- they are inversely proportional
- an increase in the sample size leads to a decrease in
the standard error - a decrease in the sample size leads to an increase in
the standard error
34
Q
- What can we use the Standard Error to calculate?
A
- it allows us to calculate the degree of uncertainty
around an estimate - this is known as the 95% Confidence Interval
35
Q
- What does the Confidence Interval indicate?
A
- it indicates a range (interval)
- we are confident that the true population parameter
lies within this range - we do still have some uncertainties
36
Q
- How do we calculate the 95% Confidence Level?
(95% Cl)
A
- we work out the Lower Confidence Interval
- we work out the Upper Confidence Interval
LOWER CONFIDENCE INTERVAL:
- Sample Estimate MINUS 1.96 x Standard Error Value
UPPER CONFIDENCE INTERVAL:
- Sample Estimate PLUS 1.96 x Standard Error Value
37
Q
- How do we write the Interpretation for the 95% Confidence Interval?
A
- we are 95% Confident that the Population Parameter is
contained within the Interval Sample Estimate - This interval if found from the Lower Confidence
Interval to the Upper Confidence Interval
38
Q
- What happens when we increase the Sample Size?
A
- we decrease the Confidence Interval
- the estimate becomes more precise
