The document discusses sampling and sampling distributions. It defines a population and sample, and explains that sampling is done to make inferences about populations that would be difficult or expensive to measure entirely. It emphasizes the importance of random sampling to ensure samples are representative. It then discusses key concepts like sampling distributions of statistics like the mean and variance, and how the distributions become more normal as the sample size increases due to the central limit theorem.
Sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population
Sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population
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In classical sampling theory, why is a model always developed on a sample even when the whole data is available? Because all the observations and variables may not be needed for developing a model, because they are not relevant for the development.
This presentation includes topics related to sampling and its distributions, estimates related to large samples and small samples using Z test and T test respectively. Also when to use Finite Population Multiplier is explained in detail.
Lecture 5 Sampling distribution of sample mean.pptxshakirRahman10
Objectives:
Distinguish between the distribution of population and distribution of its sample means
Explain the importance of central limit
theorem
Compute and interpret the standard error of the mean.
Sampling distribution of
sample mean:
A population is a collection or a set of measurements of interest to the researcher. For example a researcher may be interested in studying the income of households in Karachi. The measurement of interest is income of each household in Karachi and the population is a list of all households in Karachi and their incomes.
Any subset of the population is called a sample from the population. A sample of ‘n’ measurements selected from a population is said to be a random sample if every different sample of size ‘n’ from the population is equally likelyto be selected.
For the purpose of estimation of certain characteristics in the population we would like to select a random sample to be a good representative of the population.
The set of measurements in the population may be summarized by a descriptive characteristic, called a parameter. In the above example the average income of households would be the parameter.
The set of measurements in a sample may be summarized by a descriptive statistic, called a statistic . For example to estimate the average household income in Karachi, we take a random sample of the population in Karachi. The sample mean is a statistic and is an estimate of the population mean.
Because no one sample is exactly like the next , the sample mean will vary from sample to sample ,and hence is itself a random variable.
Random variables have distribution ,and since the sample mean is a random variable it must have a distribution.
If the sample mean has a normal distribution ,we can compute probabilities for specific events using the properties of the normal distribution.
Consider the population with population mean = μ
and standard deviation = σ.
Next, we take many samples of size n, calculate the mean for each one of them, and create a distribution of the sample means.
This distribution is called the Sampling Distribution of Means.
Technically, a sampling distribution of a statistic is the distribution of values of the statistic in all possible samples of the same size from the same population.
Standard error of the
mean:
The quantity σ is referred to as the standard deviation .it is a measure of spread in the population .
The quality σ/n is referred to as the standard error of the sample mean .It is a measure of spread in the distribution of mean
A very important result of statistics referring to the sampling distribution of the sample mean is the Central Limit Theorem .
Central Limit Theorem:
Consider a population with finite mean and standard deviation . If random samples of n measurements are repeatedly drawn from the population then, when n is large, the relative frequency histogram for the sample means ( calculated from repeated samples)
concept of sample and sampling, sampling process and problems, types of samples: probability and non probability sampling, determination and sample size, sampling and non sampling errors
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http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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