dr. moataza mahmoud abdel wahab lecturer of biostatistics high institute of public health university...
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Dr. Moataza Mahmoud Abdel WahabLecturer of Biostatistics
High Institute of Public HealthUniversity of Alexandria
moatazamahmoud@yahoo.com
Important statistical termsImportant statistical terms
Population:Population: a set which includes all a set which includes all measurements of interest measurements of interest to the researcherto the researcher(The collection of (The collection of all all responses, measurements, responses, measurements, or or counts that are of interest)counts that are of interest)
Sample:Sample:A subset of the populationA subset of the population
Why samplingWhy sampling??
Get information about large populationsGet information about large populations
Less costs
Less field time
More accuracy i.e. Can Do A Better Job of Can Do A Better Job of
Data CollectionData Collection
When it’s impossible to study the whole
population
Target Population:Target Population: The population to be studied/ to which the The population to be studied/ to which the
investigator wants to generalize his resultsinvestigator wants to generalize his resultsSampling Unit:Sampling Unit: smallest unit from which sample can be selectedsmallest unit from which sample can be selectedSampling frameSampling frame List of all the sampling units from which sample is List of all the sampling units from which sample is
drawndrawnSampling schemeSampling schemeMethod of selecting sampling units from sampling Method of selecting sampling units from sampling
frameframe
Types of samplingTypes of sampling
Non-probability samples
Probability samples
Non probability samplesNon probability samples
Convenience samples (ease of access)Convenience samples (ease of access)
sample is selected from elements of a population that are easily accessible
Snowball sampling (friend of friend….etc.)Snowball sampling (friend of friend….etc.) Purposive sampling (judgemental)Purposive sampling (judgemental)
You chose who you think should be in the study
Quota sampleQuota sample
Non probability samplesNon probability samples
Probability of being chosen is unknownCheaper- but unable to generalisepotential for bias
Probability samplesProbability samples
Random sampling Each subject has a known probability of
being selected Allows application of statistical sampling
theory to results to: Generalise Test hypotheses
ConclusionsConclusions
Probability samples are the best
Ensure Representativeness Precision
Methods used in probability Methods used in probability samplessamples
Simple random samplingSimple random sampling Systematic samplingSystematic sampling Stratified samplingStratified sampling Multi-stage sampling Multi-stage sampling Cluster samplingCluster sampling
Simple random sampling
Table of random numbersTable of random numbers
6 8 4 2 5 7 9 5 4 1 2 5 6 3 2 1 4 06 8 4 2 5 7 9 5 4 1 2 5 6 3 2 1 4 0
5 8 2 0 3 2 1 5 4 7 8 5 9 6 2 0 2 4 5 8 2 0 3 2 1 5 4 7 8 5 9 6 2 0 2 4
3 6 2 3 3 3 2 5 4 7 8 9 1 2 0 3 2 53 6 2 3 3 3 2 5 4 7 8 9 1 2 0 3 2 5
9 8 5 2 6 3 0 1 7 4 2 4 5 0 3 6 8 69 8 5 2 6 3 0 1 7 4 2 4 5 0 3 6 8 6
Sampling fractionSampling fraction
Ratio between sample size and population Ratio between sample size and population sizesize
Systematic sampling
Systematic sampling
Cluster samplingCluster sampling
Cluster: a group of sampling units close to each other i.e. crowding together in the same area or neighborhood
Cluster samplingCluster sampling
Section 4
Section 5
Section 3
Section 2Section 1
Stratified samplingStratified sampling Multi-stage sampling Multi-stage sampling
Systematic error (or bias) Inaccurate response (information bias)
Selection bias
Sampling error (random error)
Errors in sample
Type 1 errorType 1 error
The probability of finding a difference with The probability of finding a difference with our sample compared to population, and our sample compared to population, and there really isn’t one….there really isn’t one….
Known as the Known as the αα (or “type 1 error”) (or “type 1 error”)
Usually set at 5% (or 0.05)Usually set at 5% (or 0.05)
Type 2 errorType 2 error
The probability of not finding a difference The probability of not finding a difference that actually exists between our sample that actually exists between our sample compared to the population…compared to the population…
Known as the β (or “type 2 error”)Known as the β (or “type 2 error”)
Power is (1- β) and is usually 80%Power is (1- β) and is usually 80%
Sample size
Quantitative Qualitative
2D
2σ2Zn
2
22
21
D
)xFσ(σn
2
2
D
π)π(1Zn
2D
F )P-(1 P 2n
Problem 1Problem 1
A study is to be performed to determine a A study is to be performed to determine a certain parameter in a community. From a certain parameter in a community. From a previous study a sd of 46 was obtained.previous study a sd of 46 was obtained.
If a sample error of up to 4 is to be If a sample error of up to 4 is to be accepted. How many subjects should be accepted. How many subjects should be included in this study at 99% level of included in this study at 99% level of confidence? confidence?
AnswerAnswer
881~3.88024
246 x 22.58n
2D
2σ2Zn
Problem 2Problem 2 A study is to be done to determine effect A study is to be done to determine effect
of 2 drugs (A and B) on blood glucose of 2 drugs (A and B) on blood glucose level. From previous studies using those level. From previous studies using those drugs, Sd of BGL of 8 and 12 g/dl were drugs, Sd of BGL of 8 and 12 g/dl were obtained respectively.obtained respectively.
A significant level of 95% and a power of A significant level of 95% and a power of 90% is required to detect a mean 90% is required to detect a mean difference between the two groups of 3 difference between the two groups of 3 g/dl. How many subjects should be include g/dl. How many subjects should be include in each group? in each group?
AnswerAnswer
groupeachin
243~6.2423
)x10.512(8n
2
22
2
22
21
D
)xFσ(σn
Problem 3Problem 3It was desired to estimate proportion of It was desired to estimate proportion of
anaemic children in a certain preparatory anaemic children in a certain preparatory school. In a similar study at another school school. In a similar study at another school a proportion of 30 % was detected.a proportion of 30 % was detected.
Compute the minimal sample size required Compute the minimal sample size required at a confidence limit of 95% and accepting at a confidence limit of 95% and accepting a difference of up to 4% of the true a difference of up to 4% of the true population. population.
AnswerAnswer
505~21.504(0.04)
0.3)0.3(1 x 1.96n
2
2
2
2
D
π)π(1Zn
Problem 4Problem 4In previous studies, percentage of In previous studies, percentage of
hypertensives among Diabetics was 70% hypertensives among Diabetics was 70% and among non diabetics was 40%and among non diabetics was 40% in a in a certain community.certain community.
A researcher wants to perform a A researcher wants to perform a comparative study for hypertension among comparative study for hypertension among diabetics and non-diabetics at a diabetics and non-diabetics at a confidence limit 95% and power 80%, confidence limit 95% and power 80%, What is the minimal sample to be taken What is the minimal sample to be taken from each group with 4% accepted from each group with 4% accepted difference of true value?difference of true value?
AnswerAnswer
2.24130.04
x7.80.55) -(1 0.55 x 2n
2
2D
F )P-(1 P 2n
PrecisionCost
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