SlideShare a Scribd company logo
SAMPLE SIZE
    DETERMINATION
              BY
         DR ZUBAIR K.O.
       DEPT OF MEDICAL MICROBIOLOGY.NHA
                 MBBS(IL),SR II




1
OUTLINE
    • Our take home…………….
    • What is sample size?
    • What is sample size determination?
    • How large a sample do I need?
    • What are the methods of determining it?
    • What are the factors that affect it?
    • Mind my language
    • How do you determine it?
    • How do you use it?
    • A final word………………..


2
OUR TAKE HOME
    At the end of this presentation, we should be able to;

     Understand the significance of sample size.
     Determine sample size.
     Understand factors that may affect sample size
     Use sample size in our research or study.




3
WHAT IS SAMPLE SIZE?
     This is the sub-population to be studied in order to make an
      inference to a reference population(A broader population to
      which the findings from a study are to be generalized)
     In census, the sample size is equal to the population size.
      However, in research, because of time constraint and budget, a
      representative sample are normally used.
     The larger the sample size the more accurate the findings from a
      study.



4
 Availability of resources sets the upper limit of the sample
      size.
     While the required accuracy sets the lower limit of sample
      size
     Therefore, an optimum sample size is an essential
      component of any research.




5
6
WHAT IS SAMPLE SIZE DETERMINATION
     Sample size determination is the mathematical estimation of
       the number of subjects/units to be included in a study.
     When a representative sample is taken from a population,
       the finding are generalized to the population.
     Optimum sample size determination is required for the
       following reasons:
    4. To allow for appropriate analysis
    5. To provide the desired level of accuracy
    6. To allow validity of significance test.


7
HOW LARGE A SAMPLE DO I NEED?
     If the sample is too small:
    2. Even a well conducted study may fail to answer it research
       question
    3. It may fail to detect important effect or associations
    4. It may associate this effect or association imprecisely




8
CONVERSELY
     If the sample size is too large:
    2. The study will be difficult and costly
    3. Time constraint
    4. Available cases e.g rare disease.
    5. Loss of accuracy.


    Hence, optimum sample size must be determined before
     commencement of a study.



9
MIND MY LANGUAGE
      Random error               Type I(a) error
      Systematic error (bias)    Type II (b) error
      Precision (reliability)    Power (1-b)
      Accuracy (Validity)        Effect size
      Null hypothesis            Design effect
      Alternative hypothesis




10
 Random error: error that occur by chance. Sources are sample
       variability, subject to subject differences & measurement errors.
       It can be reduce by averaging, increase sample size, repeating the
       experiment.
      Systematic error: deviations not due to chance alone. Several
       factors, e.g patient selection criteria may contribute. It can be
       reduce by good study design and conduct of the experiment.
      Precision: the degree to which a variable has the same value
       when measured several times. It is a function of random error.
      Accuracy: the degree to which a variable actually represent the
       true value. It is function of systematic error.



11
12
 Null hypothesis: It state that there is no difference among
       groups or no association between the predictor & the
       outcome variable. This hypothesis need to be tested.

      Alternative hypothesis: It contradict the null hypothesis.
       If the alternative hypothesis cannot be tested directly, it is
       accepted by exclusion if the test of significance rejects the
       null hypothesis. There are two types; one tail(one-sided) or
       two tailed(two-sided)



13
 Type I(a) error: It occurs if an investigator rejects a null
         hypothesis that is actually true in the population. The
         probability of making (a) error is called as level of
         significance & considered as 0.05(5%). It is specified as Za
         in sample size computing. Za is a value from standard
         normal distribution ≡ a. Sample size is inversely
         proportional to type I error.
        Type II(b) error: it occur if the investigator fails to reject a
         null hypothesis that is actually false in the population. It is
         specify in terms of Zb in sample size computing. Zb is a
         value from standard normal distribution ≡b



14
 Power(1-b): This is the probability that the test will correctly
       identify a significant difference, effect or association in the
       sample should one exist in the population. Sample size is directly
       proportional to the power of the study. The larger the sample
       size, the study will have greater power to detect significance
       difference, effect or association.

      Effect size: is a measure of the strength of the relationship between
       two variables in a population. It is the magnitude of the effect
       under the alternative hypothesis. The bigger the size of the effect
       in the population, the easier it will be to find.




15
 Design effect: Geographic clustering is generally used to
       make the study easier & cheaper to perform.
          The effect on the sample size depends on the number of
       clusters & the variance between & within the cluster.
           In practice, this is determined from previous studies and
       is expressed as a constant called ‘design effect’ often
       between 1.0 &2.0. The sample sizes for simple random
       samples are multiplied by the design effect to obtain the
       sample size for the cluster sample.



16
 odds ratio is a measure of effect size, describing the
       strength of association or non-independence between two
       binary data values.

      relative risk (RR) is the risk of an event (or of developing
       a disease) relative to exposure. Relative risk is a ratio of the
       probability of the event occurring in the exposed group
       versus a non-exposed group.




17
POWER ANALYSIS
      When the estimated sample size can not be included in a
       study, post-hoc power analysis should be carried out.
      The probability of correctly rejecting the null hypothesis is
       equal to 1 – b, which is called power. The power of a test
       refers to its ability to detect what it is looking for.
      the power of a test is our probability of finding what we are
       looking for, given its size.
      post-hoc power analysis is done after a study has been
       carried out to help to explain the results if a study which did
       not find any significant effects.


18
AT WHAT STAGE CAN SAMPLE SIZE BE
      ADDRESSED?

     It can be addressed at two stages:
     2. Calculate the optimum sample size required during the
        planning stage, while designing the study, using appropriate
        approach & information on some parameters.
     3. Or through post-hoc power analysis at the stage of
        interpretation of the result.




19
APPROACH FOR ESTIMATING SAMPLE
     SIZE/POWER ANALYSIS
      Approaches for estimating sample size and performing power
        analysis depend primarily on:
     2. The study design &
     3. The main outcome measure of the study


     There are distinct approaches for calculating sample size for
       different study designs & different outcome measures.




20
1. THE STUDY DESIGN
      There are many different approaches for calculating the sample
       size for different study designs. Such as case control design,
       cohort design, cross sectional studies, clinical trials,
       diagnostic test studies etc.
      Within each study design there could be more sub-designs and
       the sample size calculation will vary accordingly.
      Therefore, one must use the correct approach for computing the
       sample size appropriate to the study design & its subtype.




21
2.PRIMARY OUTCOME MEASURE
     1⁰ outcome measure is usually reflected in the 1⁰ research
       question of the study & also depend on the study design.
      For estimating the risk in control study, it will be the odds
       ratio, while for cohort study it will be the relative ratio.
      For case control study, it could be the difference in
       means/proportions of exposure in case & controls,
       crude/adjusted odds ratio etc.
      Hence, while calculating sample size, one of these
       1⁰outcome measures has to be specified b/c there are
       distinct approach for calculating the sample size

22
statistical inference from the study
      results

  In addition, there are also different procedure for calculating
     sample size for two approaches of drawing statistical inference
     from the study result i.e
  2. Estimation (Confidence interval approach)
  3. Hypothesis testing(Test of significance approach)
  A researcher needs to select the appropriate procedure for
     computing the sample size & accordingly use the approach of
     drawing a statistical inference subsequently.

   NB: Test of significance: Chi-squared, T-test, Z-test, F-test, P-
23  value
ADDITIONAL PARAMETERS
     Depending upon the approach chosen for calculating the sample
       size, one also needs to specify some additional parameters such
       as;
      Hypothesis
      Precision
      Type I error
      Type II error
      Power
      Effect size
      Design effect


24
PROCEDURE FOR CALCULATING
        SAMPLE SIZE.

     There are four procedures that could be used for calculating sample
        size:
     2. Use of formulae
     3. Ready made table
     4. Nomograms
     5. Computer software




25
USE OF FORMULAE FOR SAMPLE SIZE
     CALCULATION & POWER ANALYSIS
        There are many formulae for calculating sample size &
          power in different situations for different study designs.
        The appropriate sample size for population-based study is
          determined largely by 3 factors
       3. The estimated prevalence of the variable of interest.
       4. The desired level of confidence.
       5. The acceptable margin of error.




26
 To calculate the minimum sample size required for accuracy, in
        estimating proportions, the following decisions must be taken:
     2. Decide on a reasonable estimate of key proportions (p) to be
        measured in the study
     3. Decide on the degree of accuracy (d) that is desired in the study.
        ~1%-5% or 0.01 and 0.05
     4. Decide on the confidence level(Z) you want to use. Usually
        95%≡1.96.
     5. Determine the size (N) of the population that the sample is
        supposed to represent.
     6. Decide on the minimum differences you expect to find statistical
        significance.



27
 For population >10,000.
                       n=Z2pq/d2

     n= desired sample size(when the population>10,000)
      Z=standard normal deviate; usually set at 1.96(or a~2), which correspond to
       95% confidence level.
      p=proportion in the target population estimated to have a particular
       characteristics. If there is no reasonable estimate, use 50%(i.e 0.5)
     q=1-p(proportion in the target population not having the particular
       characteristics)
      d= degree of accuracy required, usually set at 0.05 level( occasionally at 2.0)




28
 E.g if the proportion of a target population with certain
       characteristics is 0.50, Z statistics is 1.96 & we desire
       accuracy at 0.05 level, then the sample size is

     n=(1.962)(0.5)(0.5)/0.052
     n=384.




29
If study population is < 10,000

     nf=n/1+(n)/(N)

     nf= desired sample size, when study population <10,000
     n= desired sample size, when the study population > 10,000
     N= estimate of the population size



     Example, if n were found to be 400 and if the population size were estimated at 1000,
       then nf will be calculated as follows

                                       nf= 400/1+400/1000
                                           nf= 400/1.4
                                              nf=286

30
SAMPLE SIZE FORMULA FOR COMPARISON OF GROUPS

     If we wish to test difference(d) between two sub-samples regarding a
        proportion & can assume an equal number of cases(n1=n2=n’) in two sub-
        samples, the formula for n’ is

                    n’=2z2pq/d2

     E.g suppose we want to compare an experimental group against a control group
       with regards to women using contraception. If we expect p to be 40 & wish
       to conclude that an observed difference of 0.10 or more is significant at the
       0.05 level, the sample size will be:
                n’= 2(1.96)2(0.4)(0.6)/0.12
                  =184
     Thus, 184 experimental subject & another 184 control subjects are required.

31
USE OF READYMADE TABLE FOR SAMPLE
     SIZE CALCULATION
      How large a sample of patients should be followed up if an
       investigator wishes to estimate the incidence rate of a disease to
       within 10% of it’s true value with 95% confidence?
      The table show that for e=0.10 & confidence level of 95%, a
       sample size of 385 would be needed.
      This table can be used to calculate the sample size making the
       desired changes in the relative precision & confidence level .e.g
       if the level of confidence is reduce to 90%, then the sample size
       would be 271.
      Such table that give ready made sample sizes are available for
       different designs & situation

32
33
USE OF NOMOGRAM FOR SAMPLE SIZE
     CALCULATION

      For use of nomogram to calculate the sample size, one
       needs to specify the study(group 1) & the control
       group(group 2). It could be arbitrary or based on study
       design; the nomogram will work either way.
      The researcher should then decide the effect size that is
       clinically important to detect. This should be expressed
       in terms of % change in the response rate compared with
       that of the control group.


34
 E.g if 40% of patients treated with standard therapy are
       cured and one wants to know whether a new drug can cure
       50%, one is looking for a 25% increase in cure rate .
       (50%-40%/40% = 25% )




35
36
USE OF COMPUTER SOFTWARE FOR SAMPLE
     SIZE CALCULATION & POWER ANALYSIS
     The following software can be used for calculating sample size
       & power;
      Epi-info
      nQuerry
      Power & precision
      Sample
      STATA
      SPSS




37
Epi-info for sample size determination
      In STATCALC:
      1 Select SAMPLE SIZE & POWER.
      2 Select POPULATION SURVEY.
      3 Enter the size of population (e.g. 15 000).
      4 Enter the expected frequency (an estimate of the true
       prevalence, e.g.80% ± your minimum standard).
      5 Enter the worst acceptable result (e.g. 75%) i.e the margin
       of error is 5%



38
How to use sample size formulae
     Steps:
     1st Formulate a research question
     2nd Select appropriate study design, primary outcome measure,
        statistical significance.
     3rd use the appropriate formula to calculate the sample size.




39
Finally
      Sample size determination is one of the most essential
       component of every research/study.
      The larger the sample size, the higher the degree accuracy,
       but this is limit by the availability of resources.
      It can be determined using formulae, readymade table,
       nomogram or computer software.




40
STILL CONFUSED………………………..




        Smart people don’t do it alone…………………




                                 Call a statistician
                                 •Sample selection
41                               •Sample size determination
                                 •Analysis of data
42
References
      Research methodology, 2004, M.O. Araoye; sample size
       determination, page 117
      Research methodology, 2004,Zodpey SP ijvl.com
      Wikipedia, sample size determination




43

More Related Content

What's hot

Confidence interval
Confidence intervalConfidence interval
Confidence interval
Dr Renju Ravi
 
Sample size determination
Sample size determinationSample size determination
Sample size determination
Augustine Gatimu
 
Sample and sample size
Sample and sample sizeSample and sample size
Sample and sample size
Dr. Roshni Maurya
 
Sample size calculations
Sample size calculationsSample size calculations
Null hypothesis
Null hypothesisNull hypothesis
Null hypothesis
Regent University
 
Chi square test
Chi square testChi square test
Chi square test
Patel Parth
 
Sample size calculation
Sample  size calculationSample  size calculation
Sample size calculation
Swati Singh
 
Test of significance
Test of significanceTest of significance
Test of significance
Dr. Imran Zaheer
 
Parametric tests
Parametric testsParametric tests
Parametric tests
heena45
 
Odds ratio
Odds ratioOdds ratio
Odds ratio
Madhur Bora
 
Research Methodology - Study Designs
Research Methodology - Study DesignsResearch Methodology - Study Designs
Research Methodology - Study Designs
Azmi Mohd Tamil
 
Sampling techniques
Sampling techniques  Sampling techniques
Sampling techniques
Dr. Ankita Chaturvedi
 
Parametric tests
Parametric testsParametric tests
Parametric tests
Ananya Sree Katta
 
Type of data
Type of dataType of data
Type of data
Amit Sharma
 
META ANALYSIS
META ANALYSISMETA ANALYSIS
META ANALYSIS
MAHESWARI JAIKUMAR
 
01 parametric and non parametric statistics
01 parametric and non parametric statistics01 parametric and non parametric statistics
01 parametric and non parametric statistics
Vasant Kothari
 
Bias and confounding
Bias and confoundingBias and confounding
Bias and confounding
Ikram Ullah
 
Sampling techniques
Sampling techniquesSampling techniques
Sampling techniques
Bharat Paul
 
How to determine sample size
How to determine sample size How to determine sample size
How to determine sample size
saifur rahman
 
Sampling techniques and types
Sampling techniques and typesSampling techniques and types
Sampling techniques and types
NITISH SADOTRA
 

What's hot (20)

Confidence interval
Confidence intervalConfidence interval
Confidence interval
 
Sample size determination
Sample size determinationSample size determination
Sample size determination
 
Sample and sample size
Sample and sample sizeSample and sample size
Sample and sample size
 
Sample size calculations
Sample size calculationsSample size calculations
Sample size calculations
 
Null hypothesis
Null hypothesisNull hypothesis
Null hypothesis
 
Chi square test
Chi square testChi square test
Chi square test
 
Sample size calculation
Sample  size calculationSample  size calculation
Sample size calculation
 
Test of significance
Test of significanceTest of significance
Test of significance
 
Parametric tests
Parametric testsParametric tests
Parametric tests
 
Odds ratio
Odds ratioOdds ratio
Odds ratio
 
Research Methodology - Study Designs
Research Methodology - Study DesignsResearch Methodology - Study Designs
Research Methodology - Study Designs
 
Sampling techniques
Sampling techniques  Sampling techniques
Sampling techniques
 
Parametric tests
Parametric testsParametric tests
Parametric tests
 
Type of data
Type of dataType of data
Type of data
 
META ANALYSIS
META ANALYSISMETA ANALYSIS
META ANALYSIS
 
01 parametric and non parametric statistics
01 parametric and non parametric statistics01 parametric and non parametric statistics
01 parametric and non parametric statistics
 
Bias and confounding
Bias and confoundingBias and confounding
Bias and confounding
 
Sampling techniques
Sampling techniquesSampling techniques
Sampling techniques
 
How to determine sample size
How to determine sample size How to determine sample size
How to determine sample size
 
Sampling techniques and types
Sampling techniques and typesSampling techniques and types
Sampling techniques and types
 

Viewers also liked

Determining the Sample Size
Determining the Sample SizeDetermining the Sample Size
Determining the Sample Size
University of Rizal System-Morong
 
Sample size calculation
Sample size calculationSample size calculation
Sample size calculation
Pandurangi Raghavendra
 
Sample size calculation - a brief overview
Sample size calculation - a brief overviewSample size calculation - a brief overview
Sample size calculation - a brief overview
Azmi Mohd Tamil
 
determination of sample size
determination of sample sizedetermination of sample size
determination of sample size
Jijo Varghese
 
Sampling design
Sampling designSampling design
Sampling design
Jayaprakash CR
 
Sampling Methods in Qualitative and Quantitative Research
Sampling Methods in Qualitative and Quantitative ResearchSampling Methods in Qualitative and Quantitative Research
Sampling Methods in Qualitative and Quantitative Research
Sam Ladner
 
Sample determinants and size
Sample determinants and sizeSample determinants and size
Sample determinants and size
Tarek Tawfik Amin
 
Sample size determination
Sample size determinationSample size determination
Sample size determination
Gopal Kumar
 
Sample size
Sample sizeSample size
Sample size
Len Fontanilla
 
Research problem
Research problemResearch problem
Research problem
Balaji P
 
Selection of a Research Problem
Selection of a Research ProblemSelection of a Research Problem
Selection of a Research Problem
Dr.Shazia Zamir
 
Methods of termination of pregnancy
Methods of termination of pregnancyMethods of termination of pregnancy
Methods of termination of pregnancy
Ankit Kumar
 
Molar pregnancy
Molar pregnancyMolar pregnancy
Molar pregnancy
radionadia
 
MTP
MTPMTP
Medical termination of pregnancy
Medical termination of pregnancyMedical termination of pregnancy
Medical termination of pregnancy
Piyush Ranjan Sahoo
 
Medical Termination of Pregnancy Act
Medical Termination of Pregnancy ActMedical Termination of Pregnancy Act
Medical Termination of Pregnancy Act
prajs9
 
Medical termination of pregnancy (mtp) act
Medical termination of pregnancy (mtp) actMedical termination of pregnancy (mtp) act
Medical termination of pregnancy (mtp) act
Chandan Sharma
 
Discriminant analysis
Discriminant analysisDiscriminant analysis
Discriminant analysis
Sandeep Soni Kanpur
 
SAMPLING
SAMPLINGSAMPLING
SAMPLING
Malvika Bansal
 
Significance of research
Significance of researchSignificance of research
Significance of research
Azizur Rahman
 

Viewers also liked (20)

Determining the Sample Size
Determining the Sample SizeDetermining the Sample Size
Determining the Sample Size
 
Sample size calculation
Sample size calculationSample size calculation
Sample size calculation
 
Sample size calculation - a brief overview
Sample size calculation - a brief overviewSample size calculation - a brief overview
Sample size calculation - a brief overview
 
determination of sample size
determination of sample sizedetermination of sample size
determination of sample size
 
Sampling design
Sampling designSampling design
Sampling design
 
Sampling Methods in Qualitative and Quantitative Research
Sampling Methods in Qualitative and Quantitative ResearchSampling Methods in Qualitative and Quantitative Research
Sampling Methods in Qualitative and Quantitative Research
 
Sample determinants and size
Sample determinants and sizeSample determinants and size
Sample determinants and size
 
Sample size determination
Sample size determinationSample size determination
Sample size determination
 
Sample size
Sample sizeSample size
Sample size
 
Research problem
Research problemResearch problem
Research problem
 
Selection of a Research Problem
Selection of a Research ProblemSelection of a Research Problem
Selection of a Research Problem
 
Methods of termination of pregnancy
Methods of termination of pregnancyMethods of termination of pregnancy
Methods of termination of pregnancy
 
Molar pregnancy
Molar pregnancyMolar pregnancy
Molar pregnancy
 
MTP
MTPMTP
MTP
 
Medical termination of pregnancy
Medical termination of pregnancyMedical termination of pregnancy
Medical termination of pregnancy
 
Medical Termination of Pregnancy Act
Medical Termination of Pregnancy ActMedical Termination of Pregnancy Act
Medical Termination of Pregnancy Act
 
Medical termination of pregnancy (mtp) act
Medical termination of pregnancy (mtp) actMedical termination of pregnancy (mtp) act
Medical termination of pregnancy (mtp) act
 
Discriminant analysis
Discriminant analysisDiscriminant analysis
Discriminant analysis
 
SAMPLING
SAMPLINGSAMPLING
SAMPLING
 
Significance of research
Significance of researchSignificance of research
Significance of research
 

Similar to Sample size

Sample Size Determination.23.11.2021.pdf
Sample Size Determination.23.11.2021.pdfSample Size Determination.23.11.2021.pdf
Sample Size Determination.23.11.2021.pdf
statsanjal
 
Sample size estimation
Sample size estimationSample size estimation
Sample size estimation
HanaaBayomy
 
Sample Size Estimation and Statistical Test Selection
Sample Size Estimation  and Statistical Test SelectionSample Size Estimation  and Statistical Test Selection
Sample Size Estimation and Statistical Test Selection
Vaggelis Vergoulas
 
Sample size &amp; meta analysis
Sample size &amp; meta analysisSample size &amp; meta analysis
Sample size &amp; meta analysis
drsrb
 
Sample size determination.pptx
Sample size determination.pptxSample size determination.pptx
Sample size determination.pptx
MohammedAbdela7
 
Sample-size-comprehensive.pptx
Sample-size-comprehensive.pptxSample-size-comprehensive.pptx
Sample-size-comprehensive.pptx
ssuser4eb7dd
 
Advanced Biostatistics and Data Analysis abdul ghafoor sajjad
Advanced Biostatistics and Data Analysis abdul ghafoor sajjadAdvanced Biostatistics and Data Analysis abdul ghafoor sajjad
Advanced Biostatistics and Data Analysis abdul ghafoor sajjad
HeadDPT
 
SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptx
SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptxSAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptx
SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptx
ssuserd509321
 
Sample and effect size
Sample and effect sizeSample and effect size
Sample and effect size
Sarithrakamalesan
 
Biostatistics_Unit_II_ResearchMethodologyBiostatistics.pptx
Biostatistics_Unit_II_ResearchMethodologyBiostatistics.pptxBiostatistics_Unit_II_ResearchMethodologyBiostatistics.pptx
Biostatistics_Unit_II_ResearchMethodologyBiostatistics.pptx
Prachi Pandey
 
Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...
Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...
Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...
RAHUL PAL
 
Sample size determination
Sample size determinationSample size determination
Sample size determination
Sathish Rajamani
 
Sampling Variability And The Precision Of A Sample by Dr Sindhu Almas copy.pptx
Sampling Variability And The Precision Of A Sample by Dr Sindhu Almas copy.pptxSampling Variability And The Precision Of A Sample by Dr Sindhu Almas copy.pptx
Sampling Variability And The Precision Of A Sample by Dr Sindhu Almas copy.pptx
DrSindhuAlmas
 
Research Hypothesis
Research HypothesisResearch Hypothesis
Research Hypothesis
Ravinder Singh
 
Chapter 3 part3-Toward Statistical Inference
Chapter 3 part3-Toward Statistical InferenceChapter 3 part3-Toward Statistical Inference
Chapter 3 part3-Toward Statistical Inference
nszakir
 
bias and error-final 1.pptx
bias and error-final 1.pptxbias and error-final 1.pptx
bias and error-final 1.pptx
laxmibhattalamichhan
 
Running head PROJECT PHASE 4-INFECTIOUS DISEASES1PROJECT PHASE.docx
Running head PROJECT PHASE 4-INFECTIOUS DISEASES1PROJECT PHASE.docxRunning head PROJECT PHASE 4-INFECTIOUS DISEASES1PROJECT PHASE.docx
Running head PROJECT PHASE 4-INFECTIOUS DISEASES1PROJECT PHASE.docx
toltonkendal
 
Hypothesis Testing. Inferential Statistics pt. 2
Hypothesis Testing. Inferential Statistics pt. 2Hypothesis Testing. Inferential Statistics pt. 2
Hypothesis Testing. Inferential Statistics pt. 2
John Labrador
 
Research techniques; samling and ethics elt
Research techniques; samling and ethics eltResearch techniques; samling and ethics elt
Research techniques; samling and ethics elt
Abdo90nussair
 
Sample size calculation
Sample size calculationSample size calculation
Sample size calculation
Santam Chakraborty
 

Similar to Sample size (20)

Sample Size Determination.23.11.2021.pdf
Sample Size Determination.23.11.2021.pdfSample Size Determination.23.11.2021.pdf
Sample Size Determination.23.11.2021.pdf
 
Sample size estimation
Sample size estimationSample size estimation
Sample size estimation
 
Sample Size Estimation and Statistical Test Selection
Sample Size Estimation  and Statistical Test SelectionSample Size Estimation  and Statistical Test Selection
Sample Size Estimation and Statistical Test Selection
 
Sample size &amp; meta analysis
Sample size &amp; meta analysisSample size &amp; meta analysis
Sample size &amp; meta analysis
 
Sample size determination.pptx
Sample size determination.pptxSample size determination.pptx
Sample size determination.pptx
 
Sample-size-comprehensive.pptx
Sample-size-comprehensive.pptxSample-size-comprehensive.pptx
Sample-size-comprehensive.pptx
 
Advanced Biostatistics and Data Analysis abdul ghafoor sajjad
Advanced Biostatistics and Data Analysis abdul ghafoor sajjadAdvanced Biostatistics and Data Analysis abdul ghafoor sajjad
Advanced Biostatistics and Data Analysis abdul ghafoor sajjad
 
SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptx
SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptxSAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptx
SAMPLE SIZE CALCULATION IN DIFFERENT STUDY DESIGNS AT.pptx
 
Sample and effect size
Sample and effect sizeSample and effect size
Sample and effect size
 
Biostatistics_Unit_II_ResearchMethodologyBiostatistics.pptx
Biostatistics_Unit_II_ResearchMethodologyBiostatistics.pptxBiostatistics_Unit_II_ResearchMethodologyBiostatistics.pptx
Biostatistics_Unit_II_ResearchMethodologyBiostatistics.pptx
 
Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...
Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...
Biostatistics_Unit_II_Research Methodology & Biostatistics_M. Pharm (Pharmace...
 
Sample size determination
Sample size determinationSample size determination
Sample size determination
 
Sampling Variability And The Precision Of A Sample by Dr Sindhu Almas copy.pptx
Sampling Variability And The Precision Of A Sample by Dr Sindhu Almas copy.pptxSampling Variability And The Precision Of A Sample by Dr Sindhu Almas copy.pptx
Sampling Variability And The Precision Of A Sample by Dr Sindhu Almas copy.pptx
 
Research Hypothesis
Research HypothesisResearch Hypothesis
Research Hypothesis
 
Chapter 3 part3-Toward Statistical Inference
Chapter 3 part3-Toward Statistical InferenceChapter 3 part3-Toward Statistical Inference
Chapter 3 part3-Toward Statistical Inference
 
bias and error-final 1.pptx
bias and error-final 1.pptxbias and error-final 1.pptx
bias and error-final 1.pptx
 
Running head PROJECT PHASE 4-INFECTIOUS DISEASES1PROJECT PHASE.docx
Running head PROJECT PHASE 4-INFECTIOUS DISEASES1PROJECT PHASE.docxRunning head PROJECT PHASE 4-INFECTIOUS DISEASES1PROJECT PHASE.docx
Running head PROJECT PHASE 4-INFECTIOUS DISEASES1PROJECT PHASE.docx
 
Hypothesis Testing. Inferential Statistics pt. 2
Hypothesis Testing. Inferential Statistics pt. 2Hypothesis Testing. Inferential Statistics pt. 2
Hypothesis Testing. Inferential Statistics pt. 2
 
Research techniques; samling and ethics elt
Research techniques; samling and ethics eltResearch techniques; samling and ethics elt
Research techniques; samling and ethics elt
 
Sample size calculation
Sample size calculationSample size calculation
Sample size calculation
 

Recently uploaded

Climate Impact of Software Testing at Nordic Testing Days
Climate Impact of Software Testing at Nordic Testing DaysClimate Impact of Software Testing at Nordic Testing Days
Climate Impact of Software Testing at Nordic Testing Days
Kari Kakkonen
 
Essentials of Automations: The Art of Triggers and Actions in FME
Essentials of Automations: The Art of Triggers and Actions in FMEEssentials of Automations: The Art of Triggers and Actions in FME
Essentials of Automations: The Art of Triggers and Actions in FME
Safe Software
 
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdfUnlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Malak Abu Hammad
 
PCI PIN Basics Webinar from the Controlcase Team
PCI PIN Basics Webinar from the Controlcase TeamPCI PIN Basics Webinar from the Controlcase Team
PCI PIN Basics Webinar from the Controlcase Team
ControlCase
 
Mind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AIMind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AI
Kumud Singh
 
How to use Firebase Data Connect For Flutter
How to use Firebase Data Connect For FlutterHow to use Firebase Data Connect For Flutter
How to use Firebase Data Connect For Flutter
Daiki Mogmet Ito
 
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
SOFTTECHHUB
 
UiPath Test Automation using UiPath Test Suite series, part 6
UiPath Test Automation using UiPath Test Suite series, part 6UiPath Test Automation using UiPath Test Suite series, part 6
UiPath Test Automation using UiPath Test Suite series, part 6
DianaGray10
 
UiPath Test Automation using UiPath Test Suite series, part 5
UiPath Test Automation using UiPath Test Suite series, part 5UiPath Test Automation using UiPath Test Suite series, part 5
UiPath Test Automation using UiPath Test Suite series, part 5
DianaGray10
 
Pushing the limits of ePRTC: 100ns holdover for 100 days
Pushing the limits of ePRTC: 100ns holdover for 100 daysPushing the limits of ePRTC: 100ns holdover for 100 days
Pushing the limits of ePRTC: 100ns holdover for 100 days
Adtran
 
20 Comprehensive Checklist of Designing and Developing a Website
20 Comprehensive Checklist of Designing and Developing a Website20 Comprehensive Checklist of Designing and Developing a Website
20 Comprehensive Checklist of Designing and Developing a Website
Pixlogix Infotech
 
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Building RAG with self-deployed Milvus vector database and Snowpark Container...Building RAG with self-deployed Milvus vector database and Snowpark Container...
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Zilliz
 
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
Neo4j
 
A tale of scale & speed: How the US Navy is enabling software delivery from l...
A tale of scale & speed: How the US Navy is enabling software delivery from l...A tale of scale & speed: How the US Navy is enabling software delivery from l...
A tale of scale & speed: How the US Navy is enabling software delivery from l...
sonjaschweigert1
 
Data structures and Algorithms in Python.pdf
Data structures and Algorithms in Python.pdfData structures and Algorithms in Python.pdf
Data structures and Algorithms in Python.pdf
TIPNGVN2
 
How to Get CNIC Information System with Paksim Ga.pptx
How to Get CNIC Information System with Paksim Ga.pptxHow to Get CNIC Information System with Paksim Ga.pptx
How to Get CNIC Information System with Paksim Ga.pptx
danishmna97
 
20240607 QFM018 Elixir Reading List May 2024
20240607 QFM018 Elixir Reading List May 202420240607 QFM018 Elixir Reading List May 2024
20240607 QFM018 Elixir Reading List May 2024
Matthew Sinclair
 
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
Zilliz
 
Generative AI Deep Dive: Advancing from Proof of Concept to Production
Generative AI Deep Dive: Advancing from Proof of Concept to ProductionGenerative AI Deep Dive: Advancing from Proof of Concept to Production
Generative AI Deep Dive: Advancing from Proof of Concept to Production
Aggregage
 
20240609 QFM020 Irresponsible AI Reading List May 2024
20240609 QFM020 Irresponsible AI Reading List May 202420240609 QFM020 Irresponsible AI Reading List May 2024
20240609 QFM020 Irresponsible AI Reading List May 2024
Matthew Sinclair
 

Recently uploaded (20)

Climate Impact of Software Testing at Nordic Testing Days
Climate Impact of Software Testing at Nordic Testing DaysClimate Impact of Software Testing at Nordic Testing Days
Climate Impact of Software Testing at Nordic Testing Days
 
Essentials of Automations: The Art of Triggers and Actions in FME
Essentials of Automations: The Art of Triggers and Actions in FMEEssentials of Automations: The Art of Triggers and Actions in FME
Essentials of Automations: The Art of Triggers and Actions in FME
 
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdfUnlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
 
PCI PIN Basics Webinar from the Controlcase Team
PCI PIN Basics Webinar from the Controlcase TeamPCI PIN Basics Webinar from the Controlcase Team
PCI PIN Basics Webinar from the Controlcase Team
 
Mind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AIMind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AI
 
How to use Firebase Data Connect For Flutter
How to use Firebase Data Connect For FlutterHow to use Firebase Data Connect For Flutter
How to use Firebase Data Connect For Flutter
 
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
 
UiPath Test Automation using UiPath Test Suite series, part 6
UiPath Test Automation using UiPath Test Suite series, part 6UiPath Test Automation using UiPath Test Suite series, part 6
UiPath Test Automation using UiPath Test Suite series, part 6
 
UiPath Test Automation using UiPath Test Suite series, part 5
UiPath Test Automation using UiPath Test Suite series, part 5UiPath Test Automation using UiPath Test Suite series, part 5
UiPath Test Automation using UiPath Test Suite series, part 5
 
Pushing the limits of ePRTC: 100ns holdover for 100 days
Pushing the limits of ePRTC: 100ns holdover for 100 daysPushing the limits of ePRTC: 100ns holdover for 100 days
Pushing the limits of ePRTC: 100ns holdover for 100 days
 
20 Comprehensive Checklist of Designing and Developing a Website
20 Comprehensive Checklist of Designing and Developing a Website20 Comprehensive Checklist of Designing and Developing a Website
20 Comprehensive Checklist of Designing and Developing a Website
 
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Building RAG with self-deployed Milvus vector database and Snowpark Container...Building RAG with self-deployed Milvus vector database and Snowpark Container...
Building RAG with self-deployed Milvus vector database and Snowpark Container...
 
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
 
A tale of scale & speed: How the US Navy is enabling software delivery from l...
A tale of scale & speed: How the US Navy is enabling software delivery from l...A tale of scale & speed: How the US Navy is enabling software delivery from l...
A tale of scale & speed: How the US Navy is enabling software delivery from l...
 
Data structures and Algorithms in Python.pdf
Data structures and Algorithms in Python.pdfData structures and Algorithms in Python.pdf
Data structures and Algorithms in Python.pdf
 
How to Get CNIC Information System with Paksim Ga.pptx
How to Get CNIC Information System with Paksim Ga.pptxHow to Get CNIC Information System with Paksim Ga.pptx
How to Get CNIC Information System with Paksim Ga.pptx
 
20240607 QFM018 Elixir Reading List May 2024
20240607 QFM018 Elixir Reading List May 202420240607 QFM018 Elixir Reading List May 2024
20240607 QFM018 Elixir Reading List May 2024
 
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...
 
Generative AI Deep Dive: Advancing from Proof of Concept to Production
Generative AI Deep Dive: Advancing from Proof of Concept to ProductionGenerative AI Deep Dive: Advancing from Proof of Concept to Production
Generative AI Deep Dive: Advancing from Proof of Concept to Production
 
20240609 QFM020 Irresponsible AI Reading List May 2024
20240609 QFM020 Irresponsible AI Reading List May 202420240609 QFM020 Irresponsible AI Reading List May 2024
20240609 QFM020 Irresponsible AI Reading List May 2024
 

Sample size

  • 1. SAMPLE SIZE DETERMINATION BY DR ZUBAIR K.O. DEPT OF MEDICAL MICROBIOLOGY.NHA MBBS(IL),SR II 1
  • 2. OUTLINE • Our take home……………. • What is sample size? • What is sample size determination? • How large a sample do I need? • What are the methods of determining it? • What are the factors that affect it? • Mind my language • How do you determine it? • How do you use it? • A final word……………….. 2
  • 3. OUR TAKE HOME At the end of this presentation, we should be able to;  Understand the significance of sample size.  Determine sample size.  Understand factors that may affect sample size  Use sample size in our research or study. 3
  • 4. WHAT IS SAMPLE SIZE?  This is the sub-population to be studied in order to make an inference to a reference population(A broader population to which the findings from a study are to be generalized)  In census, the sample size is equal to the population size. However, in research, because of time constraint and budget, a representative sample are normally used.  The larger the sample size the more accurate the findings from a study. 4
  • 5.  Availability of resources sets the upper limit of the sample size.  While the required accuracy sets the lower limit of sample size  Therefore, an optimum sample size is an essential component of any research. 5
  • 6. 6
  • 7. WHAT IS SAMPLE SIZE DETERMINATION  Sample size determination is the mathematical estimation of the number of subjects/units to be included in a study.  When a representative sample is taken from a population, the finding are generalized to the population.  Optimum sample size determination is required for the following reasons: 4. To allow for appropriate analysis 5. To provide the desired level of accuracy 6. To allow validity of significance test. 7
  • 8. HOW LARGE A SAMPLE DO I NEED?  If the sample is too small: 2. Even a well conducted study may fail to answer it research question 3. It may fail to detect important effect or associations 4. It may associate this effect or association imprecisely 8
  • 9. CONVERSELY  If the sample size is too large: 2. The study will be difficult and costly 3. Time constraint 4. Available cases e.g rare disease. 5. Loss of accuracy. Hence, optimum sample size must be determined before commencement of a study. 9
  • 10. MIND MY LANGUAGE  Random error  Type I(a) error  Systematic error (bias)  Type II (b) error  Precision (reliability)  Power (1-b)  Accuracy (Validity)  Effect size  Null hypothesis  Design effect  Alternative hypothesis 10
  • 11.  Random error: error that occur by chance. Sources are sample variability, subject to subject differences & measurement errors. It can be reduce by averaging, increase sample size, repeating the experiment.  Systematic error: deviations not due to chance alone. Several factors, e.g patient selection criteria may contribute. It can be reduce by good study design and conduct of the experiment.  Precision: the degree to which a variable has the same value when measured several times. It is a function of random error.  Accuracy: the degree to which a variable actually represent the true value. It is function of systematic error. 11
  • 12. 12
  • 13.  Null hypothesis: It state that there is no difference among groups or no association between the predictor & the outcome variable. This hypothesis need to be tested.  Alternative hypothesis: It contradict the null hypothesis. If the alternative hypothesis cannot be tested directly, it is accepted by exclusion if the test of significance rejects the null hypothesis. There are two types; one tail(one-sided) or two tailed(two-sided) 13
  • 14.  Type I(a) error: It occurs if an investigator rejects a null hypothesis that is actually true in the population. The probability of making (a) error is called as level of significance & considered as 0.05(5%). It is specified as Za in sample size computing. Za is a value from standard normal distribution ≡ a. Sample size is inversely proportional to type I error.  Type II(b) error: it occur if the investigator fails to reject a null hypothesis that is actually false in the population. It is specify in terms of Zb in sample size computing. Zb is a value from standard normal distribution ≡b 14
  • 15.  Power(1-b): This is the probability that the test will correctly identify a significant difference, effect or association in the sample should one exist in the population. Sample size is directly proportional to the power of the study. The larger the sample size, the study will have greater power to detect significance difference, effect or association.  Effect size: is a measure of the strength of the relationship between two variables in a population. It is the magnitude of the effect under the alternative hypothesis. The bigger the size of the effect in the population, the easier it will be to find. 15
  • 16.  Design effect: Geographic clustering is generally used to make the study easier & cheaper to perform. The effect on the sample size depends on the number of clusters & the variance between & within the cluster. In practice, this is determined from previous studies and is expressed as a constant called ‘design effect’ often between 1.0 &2.0. The sample sizes for simple random samples are multiplied by the design effect to obtain the sample size for the cluster sample. 16
  • 17.  odds ratio is a measure of effect size, describing the strength of association or non-independence between two binary data values.  relative risk (RR) is the risk of an event (or of developing a disease) relative to exposure. Relative risk is a ratio of the probability of the event occurring in the exposed group versus a non-exposed group. 17
  • 18. POWER ANALYSIS  When the estimated sample size can not be included in a study, post-hoc power analysis should be carried out.  The probability of correctly rejecting the null hypothesis is equal to 1 – b, which is called power. The power of a test refers to its ability to detect what it is looking for.  the power of a test is our probability of finding what we are looking for, given its size.  post-hoc power analysis is done after a study has been carried out to help to explain the results if a study which did not find any significant effects. 18
  • 19. AT WHAT STAGE CAN SAMPLE SIZE BE ADDRESSED? It can be addressed at two stages: 2. Calculate the optimum sample size required during the planning stage, while designing the study, using appropriate approach & information on some parameters. 3. Or through post-hoc power analysis at the stage of interpretation of the result. 19
  • 20. APPROACH FOR ESTIMATING SAMPLE SIZE/POWER ANALYSIS  Approaches for estimating sample size and performing power analysis depend primarily on: 2. The study design & 3. The main outcome measure of the study There are distinct approaches for calculating sample size for different study designs & different outcome measures. 20
  • 21. 1. THE STUDY DESIGN  There are many different approaches for calculating the sample size for different study designs. Such as case control design, cohort design, cross sectional studies, clinical trials, diagnostic test studies etc.  Within each study design there could be more sub-designs and the sample size calculation will vary accordingly.  Therefore, one must use the correct approach for computing the sample size appropriate to the study design & its subtype. 21
  • 22. 2.PRIMARY OUTCOME MEASURE 1⁰ outcome measure is usually reflected in the 1⁰ research question of the study & also depend on the study design.  For estimating the risk in control study, it will be the odds ratio, while for cohort study it will be the relative ratio.  For case control study, it could be the difference in means/proportions of exposure in case & controls, crude/adjusted odds ratio etc.  Hence, while calculating sample size, one of these 1⁰outcome measures has to be specified b/c there are distinct approach for calculating the sample size 22
  • 23. statistical inference from the study results In addition, there are also different procedure for calculating sample size for two approaches of drawing statistical inference from the study result i.e 2. Estimation (Confidence interval approach) 3. Hypothesis testing(Test of significance approach) A researcher needs to select the appropriate procedure for computing the sample size & accordingly use the approach of drawing a statistical inference subsequently. NB: Test of significance: Chi-squared, T-test, Z-test, F-test, P- 23 value
  • 24. ADDITIONAL PARAMETERS Depending upon the approach chosen for calculating the sample size, one also needs to specify some additional parameters such as;  Hypothesis  Precision  Type I error  Type II error  Power  Effect size  Design effect 24
  • 25. PROCEDURE FOR CALCULATING SAMPLE SIZE. There are four procedures that could be used for calculating sample size: 2. Use of formulae 3. Ready made table 4. Nomograms 5. Computer software 25
  • 26. USE OF FORMULAE FOR SAMPLE SIZE CALCULATION & POWER ANALYSIS  There are many formulae for calculating sample size & power in different situations for different study designs.  The appropriate sample size for population-based study is determined largely by 3 factors 3. The estimated prevalence of the variable of interest. 4. The desired level of confidence. 5. The acceptable margin of error. 26
  • 27.  To calculate the minimum sample size required for accuracy, in estimating proportions, the following decisions must be taken: 2. Decide on a reasonable estimate of key proportions (p) to be measured in the study 3. Decide on the degree of accuracy (d) that is desired in the study. ~1%-5% or 0.01 and 0.05 4. Decide on the confidence level(Z) you want to use. Usually 95%≡1.96. 5. Determine the size (N) of the population that the sample is supposed to represent. 6. Decide on the minimum differences you expect to find statistical significance. 27
  • 28.  For population >10,000. n=Z2pq/d2 n= desired sample size(when the population>10,000) Z=standard normal deviate; usually set at 1.96(or a~2), which correspond to 95% confidence level. p=proportion in the target population estimated to have a particular characteristics. If there is no reasonable estimate, use 50%(i.e 0.5) q=1-p(proportion in the target population not having the particular characteristics) d= degree of accuracy required, usually set at 0.05 level( occasionally at 2.0) 28
  • 29.  E.g if the proportion of a target population with certain characteristics is 0.50, Z statistics is 1.96 & we desire accuracy at 0.05 level, then the sample size is n=(1.962)(0.5)(0.5)/0.052 n=384. 29
  • 30. If study population is < 10,000 nf=n/1+(n)/(N) nf= desired sample size, when study population <10,000 n= desired sample size, when the study population > 10,000 N= estimate of the population size Example, if n were found to be 400 and if the population size were estimated at 1000, then nf will be calculated as follows nf= 400/1+400/1000 nf= 400/1.4 nf=286 30
  • 31. SAMPLE SIZE FORMULA FOR COMPARISON OF GROUPS If we wish to test difference(d) between two sub-samples regarding a proportion & can assume an equal number of cases(n1=n2=n’) in two sub- samples, the formula for n’ is n’=2z2pq/d2 E.g suppose we want to compare an experimental group against a control group with regards to women using contraception. If we expect p to be 40 & wish to conclude that an observed difference of 0.10 or more is significant at the 0.05 level, the sample size will be: n’= 2(1.96)2(0.4)(0.6)/0.12 =184 Thus, 184 experimental subject & another 184 control subjects are required. 31
  • 32. USE OF READYMADE TABLE FOR SAMPLE SIZE CALCULATION  How large a sample of patients should be followed up if an investigator wishes to estimate the incidence rate of a disease to within 10% of it’s true value with 95% confidence?  The table show that for e=0.10 & confidence level of 95%, a sample size of 385 would be needed.  This table can be used to calculate the sample size making the desired changes in the relative precision & confidence level .e.g if the level of confidence is reduce to 90%, then the sample size would be 271.  Such table that give ready made sample sizes are available for different designs & situation 32
  • 33. 33
  • 34. USE OF NOMOGRAM FOR SAMPLE SIZE CALCULATION  For use of nomogram to calculate the sample size, one needs to specify the study(group 1) & the control group(group 2). It could be arbitrary or based on study design; the nomogram will work either way.  The researcher should then decide the effect size that is clinically important to detect. This should be expressed in terms of % change in the response rate compared with that of the control group. 34
  • 35.  E.g if 40% of patients treated with standard therapy are cured and one wants to know whether a new drug can cure 50%, one is looking for a 25% increase in cure rate . (50%-40%/40% = 25% ) 35
  • 36. 36
  • 37. USE OF COMPUTER SOFTWARE FOR SAMPLE SIZE CALCULATION & POWER ANALYSIS The following software can be used for calculating sample size & power;  Epi-info  nQuerry  Power & precision  Sample  STATA  SPSS 37
  • 38. Epi-info for sample size determination  In STATCALC:  1 Select SAMPLE SIZE & POWER.  2 Select POPULATION SURVEY.  3 Enter the size of population (e.g. 15 000).  4 Enter the expected frequency (an estimate of the true prevalence, e.g.80% ± your minimum standard).  5 Enter the worst acceptable result (e.g. 75%) i.e the margin of error is 5% 38
  • 39. How to use sample size formulae Steps: 1st Formulate a research question 2nd Select appropriate study design, primary outcome measure, statistical significance. 3rd use the appropriate formula to calculate the sample size. 39
  • 40. Finally  Sample size determination is one of the most essential component of every research/study.  The larger the sample size, the higher the degree accuracy, but this is limit by the availability of resources.  It can be determined using formulae, readymade table, nomogram or computer software. 40
  • 41. STILL CONFUSED……………………….. Smart people don’t do it alone………………… Call a statistician •Sample selection 41 •Sample size determination •Analysis of data
  • 42. 42
  • 43. References  Research methodology, 2004, M.O. Araoye; sample size determination, page 117  Research methodology, 2004,Zodpey SP ijvl.com  Wikipedia, sample size determination 43

Editor's Notes

  1. One tailed hypothesis specifies the difference/effect/association in one direction. Two tailed hypothesis specifies the difference/effect/association in either direction