Presentation on determination of size of sample (n)
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The document discusses determining the appropriate sample size (n) when selecting representative samples. It states that sample size should be chosen optimally to balance flexibility, efficiency, reliability and representativeness. The formula n = [z.sd/E]2 is presented, where n is the sample size, z is the confidence level, sd is the population standard deviation, and E is the desired error or difference between the sample and population means. The document also notes factors that impact sample size choice like variability of data, nature of stratification, and risk of biased estimates.
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Sample and sample size
This document discusses sampling and sample size in statistics. It defines key terms like population, sample, sampling unit, sampling frame, and sampling schemes. It explains that sampling allows researchers to generalize results from a subset of the population. The main advantages of sampling are that it is less costly, takes less time, and can provide more accurate results than studying the entire population. The document also discusses different sampling methods like simple random sampling, systematic random sampling, stratified random sampling, and cluster sampling. It notes that sample size depends on several factors and must result in a truly representative sample with small errors.
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2. There are different approaches to sample size calculation depending on the study design and endpoints, such as comparing proportions, estimating confidence intervals, or analyzing time to event outcomes.
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- Sample size, population size, and response distribution (how answers are split) all impact the required sample size to achieve a given confidence level and interval. Higher confidence or lower intervals require larger samples.
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This document discusses determining the appropriate size of a sample from a population. It explains that a sample should be small enough to be practical but large enough to accurately represent the population within a desired level of precision and confidence level. The key factors in determining sample size are the homogeneity of the population, number of classes or groups in the population, nature of the study, type of sampling method, desired accuracy and confidence level, availability of resources, and other considerations like the nature and size of units, size of the population, and time constraints. The document concludes by mentioning an approach to determining sample size based on precision rate and confidence level.
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Sample size calculation
1. Sample size calculation is an important part of ethical scientific research to avoid underpowered studies.
2. There are different approaches to sample size calculation depending on the study design and endpoints, such as comparing proportions, estimating confidence intervals, or analyzing time to event outcomes.
3. Key steps include defining the research hypothesis, primary and secondary endpoints, how and in whom the endpoints will be measured, and determining what difference is clinically meaningful to detect between study groups.
Concept of Inferential statistics
Inferential statistics use samples to make generalizations about populations. It allows researchers to test theories designed to apply to entire populations even though samples are used. The goal is to determine if sample characteristics differ enough from the null hypothesis, which states there is no difference or relationship, to justify rejecting the null in favor of the research hypothesis. All inferential tests examine the size of differences or relationships in a sample compared to variability and sample size to evaluate how deviant the results are from what would be expected by chance alone.
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Sample size
This document provides an outline for a presentation on determining sample size. It discusses key concepts like what sample size is, why determining an appropriate sample size is important, and factors that affect sample size calculations like available resources, required accuracy, and study design. The presentation aims to help audiences understand how to determine sample sizes and how to apply the concept in research and studies.
Determining the Sample Size
Slovin's formula is used to determine sample size from a given population. The formula is n=N/(1+Ne^2) where n is the sample size, N is the population size, and e is the desired margin of error. For a population of 9,000 people with a 2% margin of error, the sample size would be 1,957 according to the formula. Stratified random sampling is then used to determine sample sizes from subgroups to ensure representation.
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This document discusses sample size calculation and determination. It begins by defining a sample as a subset of a population used to make inferences about the whole population. Several factors affect sample size, including required accuracy, available resources, and desired level of precision. The document outlines different formulas and methods for calculating sample size based on study design and outcome measures. It provides examples of calculating sample size for estimating means, proportions, rates, odds ratios, and risk ratios. Computer software and readymade tables can also be used to determine optimal sample sizes.
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This document discusses sampling and sample size determination. It defines key terms like population, population element, census, and provides reasons for using a sample such as cost, speed, accuracy, and avoiding destruction of test units. It outlines the steps in sampling which include defining the target population, selecting a sampling frame, choosing between probability or non-probability sampling, determining the sampling unit, and addressing sources of error. It then discusses different probability and non-probability sampling methods like simple random sampling, systematic sampling, stratified sampling, cluster sampling, convenience sampling, judgment sampling, quota sampling, and snowball sampling. Factors to consider when determining sample size are discussed such as population variance or heterogeneity, acceptable error or confidence interval, confidence level.
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Sample Size For Continuous Data
Consider the following example:
We want to estimate average call length in handling customer inquiries, and we want our estimate to be accurate to within 1 minute. Based on a small random sample of 30 inquiries we know that the variation in call length, as measured by standard deviation, is 5 minutes. We want to have 95% confidence that the estimate will be in the range of specified accuracy – i.e., 1 minute.
Therefore, from the statistical theory we can answer according to the formula
Where n = sample size, u = standard deviation and ∆= degree of precision required. In our example, the required sample size is:
n = [(1.96*5)/1] 2 = 96.04 or 96 samples
Extending the same logic, we can find out the sample size required while dealing with discrete population
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All of the data available is often referred to as a Population (N).
The purpose of sampling is to draw conclusions about the population using the sample (n). This is know as statistical inference.
One of the first questions to ask is ‘Do I need to sample?” The major reason sampling is done is for efficiency reasons-it is often too costly or time consuming to measure all of the data. Sampling provides a good alternative to collect data in an effective and efficient manner. If the circumstances surrounding the data collection plan do not justify sampling, then sampling should not be done. This is often the case in low volume processes.
All items in the population have an equal chance of being chosen in the sample
Example: A customer satisfaction survey team picking the customers to be contacted at random
How to do random sampling
Generate random numbers from
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- Common sources of sampling error (e.g. population specification error, selection error) and non-sampling error in statistical studies.
- The concept of a sampling distribution as the probability distribution of a statistic calculated from different samples of a population.
- Other related terms like degrees of freedom, which refers to the number of values in a data set that can vary freely.
Reseach Methdology Statistic- Module 6.pptx
This document discusses key concepts in statistical inference including parameters, statistics, sampling distributions, sampling errors, non-sampling errors, and degrees of freedom. A parameter describes characteristics of the entire population, while a statistic describes characteristics of a sample from the population. The sampling distribution is the probability distribution of a statistic calculated from different samples. Both sampling errors and non-sampling errors can occur and affect the representativeness of sample data. Degrees of freedom refers to the number of values in a data set that can vary independently.
26738157 sampling-design
The document discusses different sampling techniques used in research. It describes probability sampling methods like simple random sampling, systematic sampling, stratified random sampling, and multistage cluster sampling which ensure that each population element has a known chance of selection. It also covers non-probability sampling which uses arbitrary selection. Key advantages of probability sampling include controlling for bias and representing the population, while non-probability sampling has lower costs. Sample size is based on desired precision, population variability, and confidence level.
Chapter 11
To determine the appropriate sample size for quantitative research, key factors must be considered including:
1) The desired level of precision or acceptable margin of error for results.
2) The required confidence level, typically 95%.
3) An estimate of the population variability based on available data.
Using a basic formula that incorporates these factors, the sample size can be computed to achieve the desired precision at the specified confidence level. Probability sampling methods like simple random and stratified sampling are generally most effective when a sampling frame is available.
Sampling
The document discusses the process of sampling from a population. It explains that sampling is used because it is not always possible to study the entire population. It then outlines the 7 key steps to analyzing sample data from a population: 1) estimating population parameters, 2) estimating population variance, 3) computing standard error, 4) specifying confidence level, 5) finding critical values, 6) computing margin of error, and 7) defining the confidence interval. The document provides formulas for estimating means, variances, standard errors, and computing confidence intervals.
5_lectureslides.pptx
This document provides an overview of Module 5 on sampling distributions. It discusses key concepts like parameters vs statistics, sampling variability, and sampling distributions. It explains that the sampling distribution of a sample mean is a normal distribution with a mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. The central limit theorem states that as the sample size increases, the distribution of sample means will approach a normal distribution regardless of the shape of the population distribution. The module also covers binomial distributions for sample counts and proportions.
Sample size determination
This document discusses sample size estimation and determination. It defines key terms like population, statistic, parameter, sampling error, and confidence interval. It explains that sample size determination is calculating the number of subjects needed in a study to make inferences about a reference population. An appropriate sample size allows for valid analysis and the desired level of accuracy. The sample should be representative of the population and large enough to minimize errors and bias. Both too large and too small samples have disadvantages. Common methods for calculating sample size are using formulas, ready-made tables, nomograms, and computer software. Formulas are provided for estimating proportions, differences in proportions, means, and differences in means.
Lect 10 Sample Size Estimation.ppt
- The document discusses factors to consider when determining sample size for quantitative studies, including desired level of confidence, margin of error, and how dispersed the population is.
- Sample size is a balance between what is desirable and feasible, and too small a sample may miss important effects or be too imprecise, while too large wastes resources.
- Formulas are provided to calculate the minimum required sample size for estimating a single population proportion based on the expected proportion, desired margin of error, and confidence level. Adjustments may be needed if the population is small.
SAMPLE SIZE DETERMINATION.ppt
The document discusses methods for determining sample sizes in qualitative and quantitative studies. For qualitative studies, the sample size is usually small and taken until theoretical saturation is reached. Judgment sampling is most common. For quantitative studies, sample size is determined based on the level of precision, confidence level, population variability, and external validity. Formulas can be used to calculate sample sizes for proportions, with corrections for finite populations. Software can also assist with determining quantitative sample sizes based on study details.
2_Lecture 2_Confidence_Interval_3.pdf
Census
Everyone in population
Eg. All Cambodian residents
Population
is a set of persons (or objects) having a common observable characteristic.
the entire collection of units about which we would like information
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Statistical inference is the process by which we draw conclusions about a population from data collected on a sample.
In medical research
Population
All patients candidate for treatment
Sample
All patients candidate for treatment who volunteer for your study
Infer results from volunteers (sample) to other candidates for the same treatment (population).
We usually obtain information on an appropriate sample of the community and generalize from it to the entire population.
The way the sample is selected, not its size, determines whether we may draw appropriate inferences about a population.
The primary reason for selecting a sample from a population is to draw inferences about that population.
Statistical inference is the process by which we infer
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Presentation on determination of size of sample (n)
- 1. PRESENTATION ON DETERMINATION OF SIZE OF SAMPLE(n) & CHARACTERISTICS INCLUDED WHILE SELECTING REPRESENTATIVE SAMPLES
- 2. GROUP MEMBERS Nabin jamkatel Rajiv gupta Mohits lama
- 3. Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample Sample sizes may be chosen in several different ways: • once the sample expedience - For example, include those items readily available or convenient to collect. A choice of small sample sizes, though sometimes necessary, can result in wide confidence intervals or risks of errors in statistical hypothesis testing. • using a target variance for an estimate to be derived from the sample eventually obtained • using a target for the power of a statistical test to be applied is collected
- 4. Large sample may waste time, resources and money. To small sample may lead to inaccurate result So we have concluded that size of sample should be optimum(flexibility, efficiency, reliability and representativeness)
- 5. n = [ z. sd / E]² Where n = size of sample z = Value at a specified level of confidence or desired degree of precision Sd = Standard deviation of the population. E = Different between population mean and sample mean. Or desired error in estimation of pop. Mean
- 6. n = [ z. sd / E]² formula was derived from E= z × sd/√n When sample data is collected and the sample mean is calculated, that sample mean is typically different from the population mean µ. This different sample and population mean can be thought of as an error . The margin error E is the maximum difference between the observed sample mean and true value of population mean µ.
- 7. The reasons and objectives of sampling The relationship between accuracy and precision The reliability of estimates with varying sample size The determination of sample size for surveys The variability of data The nature of stratification and its impact on survey cost The risk posed by biased estimates
- 8. Sampling Accuracy It is usually expressed as a relative index in percentage form and indicated the closeness sample based parameter estimator to the true data population value. Sampling Precision It is related to the variability of the sample used . It is measured by C.V.
- 9. Thank you……