Sample Size DeterminationConcept

Population vs. sample

Population

Population mean of the change in blood pressure

Random sample

InferenceSample mean of the change in blood pressure

Calculation

Purpose of sample size

• Sample size based on – Financial resources

– Manpower resources

– Level of reliability

– objectives

Why study sample• Cost : much lower cost than a census• Accuracy : Much better control over

data • Timeliness : Timely decision making• Amount of information : Amount of

information• Destructive test : when test involves

destruction of an item

How collected• The data is collected through interviews

, field notes, observations, vedios, personal journals, memos, or other varieties of pictorial or written material, which are then analyzed by a coding procedure to illuminate patterns or concepts that are the building blocks of theory.

Grounded theory• Grounded theory is a process by which a

researcher generates theory that is grounded in the data

• The procedure allows for a systematic analysis of the data and follows a given, repeatable procedure

• The rigor of the grounded theory approaches , offers qualitative researchers a set of clear guidelines from which to build explanatory frameworks that specify relationships among concepts.

Sample size in qualitative research

The key to ground theory is to generate enough in depth data that can

• Illuminate patterns• Concepts• Categories• Properties• And dimensions of the given

phenomenon

IT IS VERY ESSENTIAL TO GET AN APPROPRIATE SAMPLE SIZE THAT WILL GENERATE ENOUGH DATA

So !!!!!!!!!!

What size is the appropriate one• Theoretical saturation is the answer and

it occurs when– No new or relevant data seem to emerge

regarding a category

– The categories are well developed in terms of properties and dimensions

– Relationships among categories are established and validated

THE RESEARCHER WOULD CONTINUE INTERVIEWING CLIENTS UNTIL THE DATA THEY ARE GATHERING FROM THE INTERVIEWS BECOME REPETITIVE-NO NEW DATA EMERGE

So !!!!!!!!!!

Sample size inQuantitative

research

Steps• Identify major study variable• Determine type of estimate• Indicate expected

frequency/measurement of factor of interest

• Desired precision of the estimate• Allowable error / acceptable risk

α..confidence interval• Adjust for estimated design effect [ DE ]• Adjust for expected response rate

Basic concept• The objectives in interval estimation

are to obtain narrow interval with high reliability

• If we look at the components of the confidence interval, we see that the width of the interval is determined by the magnitude of the [reliability coefficient X standard error]

• Total width of the interval is twice this amount

• This quantity is usually called the precision of the estimate or the margin of error.

• For a given standard error, increasing reliability means a larger reliability coefficient

• A larger reliability coefficient for a fixed standard error makes wider interval

• For a fix reliability coefficient, the only way to reduce the width of the interval is to reduce the standard error

• Since the standard error is equal to and since σ is a constant, the only way to obtain a small standard error is to take a large sample

n

Estimating σ2

• A pilot or preliminary sample may be drawn and variance computed from this may be used

• σ2 may be available from previous or similar studies

• If population is normally distributed, one may assume the fact that range is approximately equal to 6 standard deviation and compute σ = R/6but it requires the knowledge of the smallest and largest value

Size depends on ???

• The size of δ, the population SD

• The desired degree of reliability

• The desired degree of precision..the allowable margin of error

• We know

• Which when solved for n gives

nZd

Sample size

Standard deviation

Reliability co-efficientDegree of precision/

margin of error

StandardError

2

22

dZn

• When sampling is without replacement from a small finite population, the finite population correction is required and equation becomes :

• Which when solved for n gives

1

NnN

nZd

222

22

)1(*

ZNd

ZNn

problem• A clinician would like to explore the mean

fasting blood glucose value of diabetic patients at DMCH over the past 10 years. We are interested in determining the number of records the clinician should examine in order to obtain a 95 % confidence interval for µ ( the population mean fasting blood glucose ) if the desired width of the interval is 6 units and a pilot sample yields a variance of 60.

• Also want to find the sample size that should be taken to examine if the total number of records is 10,000.

Three information• The desired width of the confidence

interval i.e. margin of error

• The level of confidence desired

• The magnitude of the population variance

solution• Here we are given;

Z = 1.96 for a 95% confidence intervald = margin of error = 3δ2 = variance of the populationtherefore,

thus the number of records should be examined is 26

61.25360*96.1

2

2

2

22

dZn

solution• Thus the number of records for finite

population

55.25

60*96.1)110000(360*10000*96.1

)1(

222

22

222

22

zNd

Nzn

2

2

dpqZn

Where

p = Sample proportion or percentage of incidence or prevalence, q = 1-p

z = The value of standard normal variate at a given confidence level

d = acceptable margin of error

n = size of the sample

Finite population

pqZNdpqNZn 22

2

)1(

p = Sample proportion or percentage of incidence or prevalence, q = 1-p

z = The value of standard normal variate at a given confidence level

d = acceptable margin of error

n = size of the sample

Note: When N is large in comparison to n (i.e. n/N ≤ .05 ) the finite population correction may be ignored

Problem• A group of researcher feels confident

that a new drug will cure about 70% of the hypertensive patients. What the researcher want to know is how large should the sample size be for the group 95% certain that the sample proportion of cure is within ± 5% of the proportion of all cases that the new drug will cure.

solutionHere we are given population infinite p = sample proportion or percentage

of incidence or prevalence q = 1- p = 1- 0.70 = .30 z = 1.96 for a 95% of confidence

interval d = margin of error = 5% = .05

calculation

8.322

0025.807.

05.30.*70.*96.1

2

2

2

2

dpqZn

The necessary sample size is 323

Problem• A hospital administrator wishes to know what

proportion of discharged patient is unhappy with the care received during hospitalization. He is interested to find out the answers to these questions – how large a sample should be drawn if we let d = 0.05, the confidence coefficient is 0.95 and no other information is available. How large should the sample be if p is approximately by 0.5

solutionHere we are given population infinite p = 50% = 0.50 (we consider the sample

proportion or percentage of incidence or prevalence as 50%)

q = 1- p = 1- 0.50 = .50 z = 1.96 for a 95% of confidence interval d = margin of error = 5% = 0.05

calculation

16.3840025.9604.

05.50.0*50.0*96.1

2

2

2

2

dpqzn

The required sample size is 384