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