# Calculating Sample Size

Types of Samples

Subjective or Convenience Sample

- Has some possibility of bias

- Cannot usually say it is representative

- Selection made by ease of collection

Simple Random Sample

- No subjective bias

- Equal chance of selection; e.g., select the fifth chart seen on every third day - Can usually be backed to say it is representative

Systematic Sample

- Is a random sample

- Equal chance of selection due to methodology; e.g., computer-generated list of random numbers, or every fifth name on a generated list

- Can usually be backed to say it is representative

Stratified Sample

- Breakdown the population into subgroups, then take a random sample from each subset - Can usually be backed to say it is representative

Sample Size Calculation

The Automated Method

If you know your population size and desired confidence level you may use this Web-based calculator to automatically calculate sample size.

The Manual Calculation Method

To perform sample size calculation manually, you need the following values: Population Value: Size of the population from which the sample will be selected. (Number of users or number of encounters) Expected Frequency of the Factor under Study always err toward 50%

Worst Acceptable Frequency

If 50% is the true rate in the population, what is the result farthest from the rate that you would accept in your sample? If your confidence interval were 4%, then your worst acceptable frequency would be 54% or 46%.

2. Formula: Sample Size = n / [1 + (n/population)]

In which n = Z * Z [P (1-P)/(D*D)]

P = True proportion of factor in the population, or the expected frequency value D = Maximum difference between the sample mean and the population mean, Or Expected Frequency Value minus (-) Worst Acceptable Value Z = Area under normal curve corresponding to the desired confidence level Confidence Level/ Value for Z

90% / 1.645

95% / 1.960

99% / 2.575

99.9% / 3.29

B. Population Survey Characteristics

1. The sample to be taken must be a simple random or otherwise representative sample. A systematic sample, such as every fifth person on a list, is acceptable if the sample is representative. Choosing every other person from a list of couples would not give a representative sample, since it might select only males or only females. 2. The question being asked must have a "yes/no" or other two-choice answer, leading to a proportion of the population (the "yes's") as the final result.

Examples of Sample Size Calculation

Trait or Factor Prevalence

Suppose that you wish to investigate whether or not the true prevalence of HIV antibody in a population is 10%. You plan to take a random or systematic sample of the population to estimate the prevalence. You would like 95% confidence that the true proportion in the entire population will fall within the confidence level calculated from your sample. Let's say that the population size is 5000, the estimate of the prevalence of 10%, and either 6% or 14% as the "worst acceptable" value, which is the end point of your confidence level. (Please note: the high and low values are calculated by adding and subtracting your confidence level, in this case "4", to your estimate of the prevalence.) Population Value = 5000

Expected Frequency of the Factor under Study = 10%

Worst Acceptable Frequency = 14% or 6%

P = Expected Frequency Value = 10%

D = (Expected Frequency - Worst Acceptable) = 14%-10%=4%, OR 10%-6%=4% Z = 1.960 with Confidence Level of 95% (See Confidence Level values, page 3-2)

Formula: Sample Size = n / [1 + (n/population)]

In which n = Z * Z [P (1-P)/(D*D)]

First, calculate the value for "n".

N = Z * Z [P (1-P)/(D*D)]

N = 1.960 * 1.960 [0.10(1 - 0.10) / (0.04 * 0.04)

N = 1.960 * 1.960 [0.10(0.90) / (0.0016)

N = 1.960 * 1.960 [.09 / .0016]

N = 1.960 * 1.960 [56.25]

N = 1.960 * 110.25

N = 216.09

Next, Calculate the Sample Size. (S = Sample Size)

S = n / [1 + (n / population)

S =...

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