Random Sampling Error and Sample Size are Related

Sample size Determination It depends on the following factors Precision Level Importance of Decision to be based Affordability Requirements of Analysis

Sample Size Variance (standard deviation) Magnitude of error Confidence level

Sample Size Formula Where, Z = Confidence level E = Range of error S = Standard deviation

Sample Size Formula - Example Suppose a survey researcher, studying expenditures on lipstick, wishes to have a 95 percent confidence level (Z) and a range of error (E) of less than Rs2.00. The estimate of the standard deviation is Rs29.00.

Sample Size Formula - Example

Sample Size Formula - Example Suppose, in the same example as the one before, the range of error (E) is acceptable at Rs 4.00, sample size is reduced.

Sample Size Formula - Example

Calculating Sample Size 99% Confidence [ ] 1389 = 265 . 37 2 53 74 ú û ù ê ë é ) 29 )( 57 ( n 347 6325 18 4

Standard Error of the Proportion

Confidence Interval for a Proportion

Sample Size for a Proportion

E pq z n = Where: n = Number of items in samples 2 E pq z n = Where: n = Number of items in samples Z2 = The square of the confidence interval in standard error units. p = Estimated proportion of success q = (1-p) or estimated the proportion of failures E2 = The square of the maximum allowance for error between the true proportion and sample proportion or zsp squared.

Calculating Sample Size at the 95% Confidence Level 753 = 001225 . 922 ) 24 )(. 8416 3 ( 035 ( . 4 6 (. 96 1. n q p 2

Errors in Sampling Broadly there are two types of errors. Sampling Errors : These are also known as Un-Systematic Errors. Non- Sampling Error : This is also known as Systematic Errors

Sampling Error The difference between the sample results and the result of a census conducted using identical procedures. These are Statistical fluctuation due to chance variations. They can be controlled by increasing sample size.

Non-Sampling Error It may be due to unrepresentative sample results, or due to study design or imperfections in execution. It can be of two types, Non-Response Error: It occurs when some of the respondents do not respond. It actually reduces the decided sample size. Response Error: These errors are related to the responses of the respondents. It can further be classified as,

Types of Response Error Researcher Errors: Measurement error, Data processing error, Population definition error, sampling Frame error etc. Respondent Error: Inability Error, Unwillingness error. Interviewer Error: Respondent selection error, Questioning error, Recording error.

Error Vs. Sample Size Error Sample Size Sampling Error (chance) Non- Sampling Error (bias) Sample Size