Abstract
The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a . Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.
Highlights
It is assumed that through some kind of probability sampling, in this case systematic sampling, the observation yi on the ith unit is the correct value for that unit, and that sampling errors may arise solely from the random sampling variation that is present when n units are measured instead of complete population of N units
The true score theory is a good simple model for measurement. It consists of true value and two error components; random error and systematic error
In this project further study is based on The Impact of Measurement Errors on Estimators of Parameters for a finite Population with Linear Trend under Systematic Sampling
Summary
It is assumed that through some kind of probability sampling, in this case systematic sampling, the observation yi on the ith unit is the correct value for that unit, and that sampling errors may arise solely from the random sampling variation that is present when n units are measured instead of complete population of N units. Looking at measurement errors in self-reported BMI Plankey et al examines the consequences of these errors when classifying people according to obesity status [8]. Stommel et al [9] compared self-reported and recorded BMI using US data and found a substantial amount of misclassification of obesity status when using self-reported BMI, in the extreme (overweight or underweight) categories Consequences of this measurement errors were examined when analysing the impact of BMI on a range of health risks. Grellety et al [20] examined the Effect of random error on diagnostic accuracy illustrated with anthropometric diagnosis of malnutrition In this project further study is based on The Impact of Measurement Errors on Estimators of Parameters for a finite Population with Linear Trend under Systematic Sampling. Each sample or a cluster is selected with probability 1 a and observed completely as per the design
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