sampling distribution
Sampling distribution
The sampling distribution is the distribution of the values of a sample statistic computed for each possible sample that could be drawn from the target population under a specified sampling plan. Because many different samples could be drawn from a population of elements, the sample statistics derived from any one sample will likely not equal the population parameters. As a result, the sampling distribution supplies an approximation of the true value’s population parameters. The main properties of the sampling distribution are: 1. Normally distributed for large samples. 2. The mean of the sampling distribution of the mean equals , the population parameter for the mean. 3. The standard error of the mean is the standard deviation of the sampling distribution. 4. Assuming no measurement error, the reliability of an estimate of a population parameter can be assessed in terms of its standard error. 5. The standard error of the mean can be estimated by using the sample standard deviation, s, as an estimator of . 6. z values calculate the area under the sampling distribution. 7. When the sample size is over 10% of the population size, the standard error formulas overestimate the standard deviation of the population parameter. A finite population correction factor is used to adjust the estimates.
Statistic inference
The process of generalizing sample results to population results is referred to as statistical inference. Statistics, such as the sample mean and sample proportion, are used to estimate the corresponding true population values. In practice, a single sample of predetermined size is selected and the sample statistics are computed. Hypothetically, in order to estimate the population parameter from the sample statistic, every possible sample that could have been drawn should be examined. If all possible samples were actually to be drawn, the distribution of the statistic would be the sampling distribution.
The sampling distribution is the distribution of the values of a sample statistic computed for each possible sample that could be drawn from the target population under a specified sampling plan. Because many different samples could be drawn from a population of elements, the sample statistics derived from any one sample will likely not equal the population parameters. As a result, the sampling distribution supplies an approximation of the true value’s population parameters. The main properties of the sampling distribution are: 1. Normally distributed for large samples. 2. The mean of the sampling distribution of the mean equals , the population parameter for the mean. 3. The standard error of the mean is the standard deviation of the sampling distribution. 4. Assuming no measurement error, the reliability of an estimate of a population parameter can be assessed in terms of its standard error. 5. The standard error of the mean can be estimated by using the sample standard deviation, s, as an estimator of . 6. z values calculate the area under the sampling distribution. 7. When the sample size is over 10% of the population size, the standard error formulas overestimate the standard deviation of the population parameter. A finite population correction factor is used to adjust the estimates.
Statistic inference
The process of generalizing sample results to population results is referred to as statistical inference. Statistics, such as the sample mean and sample proportion, are used to estimate the corresponding true population values. In practice, a single sample of predetermined size is selected and the sample statistics are computed. Hypothetically, in order to estimate the population parameter from the sample statistic, every possible sample that could have been drawn should be examined. If all possible samples were actually to be drawn, the distribution of the statistic would be the sampling distribution.
References: Naresh, Malhotra. K (2007). Marketing research an applied orientation. 5th ed. Pearson Education