Sample size Definition, to understand a sample size let us consider a simple example. A survey is done on a group of 50 children as to know the particular type of game they like. This size of 50 children is taken as a sample and hence is called the sample size. So, we can define Sample size for a given population as the number of observations used while calculating the estimates for that population. It is the number of sample units which are to be included in a particular sample like in the above example ‘50 children’ is the sample size. A statistically significant sample size is that which uses a valid sample size, like when we consider how many people we need to survey to get a significant result. A valid methodology is to be used to get a significant sample size, this methodology includes three main elements, how many people make a group whose behavior is to be represented, the desired error margin and the preferred confidence level.
To determine a survey sample size:
• first we need to consider a planned analysis for the results
• then we need to check the variability in population or Population variability
• we need to then consider the confidence levels, it means whether the true value of the estimate in the target population falls within the confidence interval. Confidence is inversely proportional to the accuracy of the estimate; level of confidence and
• we need to consider the sampling error or the margin error which indicates the level of precision of the desirable estimate
• Finally estimate the response rate, that is when we study a sample we expect a response, this estimation of response rate gives the proportion of the study
After understanding how to determine a survey sample size the next thing which comes to the mind is How to calculate sample size. For Calculating Sample Size we need to first determine the confidence interval which is the number of percentage points above or below the proportion that the true proportion should lie within. Then this confidence level is to be converted into a Z-score using a Z-score table. Next step would be to predict the proportion of the study. Now, we can compute the sample size required by using the formula, Sample Size Formula = Z2[P(1-P)]/I2. [Z=Z-score, P=Proportion, I=confidence interval in percent]
For example, given the Z-score is 3.24 (Z), the proportion (P) is 0.58 and the confidence interval (I) is 4.2% (0.042), the required sample size can be calculated as follows,
Sample Size = Z2[P(1-P)]/I2
= (3.24)2[0.58(1-0.58)]/(0.042)2
= [(3.24)2(0.58)(0.42)]/(0.042)2 = 1450
The sample size required is 1450
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