Some variations of ranked set sampling

If, for example, the numerical data 3. In another example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2. In these examples, the ranks are assigned to values in ascending order. In some other cases, descending ranks are used. Ranks are related to the indexed list of order statistics, which consists of the original dataset rearranged into ascending order.

Some ranks can have non-integer values for tied data values. Transforms are usually applied so that the data appear to more closely meet the assumptions of a statistical inference procedure that is to be applied, or to improve the interpretability or appearance of graphs.

some variations of ranked set sampling

Nearly always, the function that is used to transform the data is invertible and, generally, is continuous. The transformation is usually applied to a collection of comparable measurements. Guidance for how data should be transformed, or whether a transform should be applied at all, should come from the particular statistical analysis to be performed.

However, the constant factor 2 used here is particular to the normal distribution and is only applicable if the sample mean varies approximately normally. The central limit theorem states that in many situations, the sample mean does vary normally if the sample size is reasonably large. However, if the population is substantially skewed and the sample size is at most moderate, the approximation provided by the central limit theorem can be poor, and the resulting confidence interval will likely have the wrong coverage probability.

Thus, when there is evidence of substantial skew in the data, it is common to transform the data to a symmetric distribution before constructing a confidence interval. If desired, the confidence interval can then be transformed back to the original scale using the inverse of the transformation that was applied to the data. Data can also be transformed to make it easier to visualize them. For example, suppose we have a scatterplot in which the points are the countries of the world, and the data values being plotted are the land area and population of each country.

If the plot is made using untransformed data e. Simply rescaling units e. However, following logarithmic transformations of both area and population, the points will be spread more uniformly in the graph. Population Versus Area Scatterplots : A scatterplot in which the areas of the sovereign states and dependent territories in the world are plotted on the vertical axis against their populations on the horizontal axis.

The upper plot uses raw data. In the lower plot, both the area and population data have been transformed using the logarithm function.A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location.

They are also classed as summary statistics. The mean often called the average is most likely the measure of central tendency that you are most familiar with, but there are others, such as the median and the mode.

some variations of ranked set sampling

The mean, median and mode are all valid measures of central tendency, but under different conditions, some measures of central tendency become more appropriate to use than others. In the following sections, we will look at the mean, mode and median, and learn how to calculate them and under what conditions they are most appropriate to be used. The mean or average is the most popular and well known measure of central tendency.

It can be used with both discrete and continuous data, although its use is most often with continuous data see our Types of Variable guide for data types. The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. You may have noticed that the above formula refers to the sample mean.

So, why have we called it a sample mean? This is because, in statistics, samples and populations have very different meanings and these differences are very important, even if, in the case of the mean, they are calculated in the same way.

The mean is essentially a model of your data set. It is the value that is most common. You will notice, however, that the mean is not often one of the actual values that you have observed in your data set.

However, one of its important properties is that it minimises error in the prediction of any one value in your data set. That is, it is the value that produces the lowest amount of error from all other values in the data set.

An important property of the mean is that it includes every value in your data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero. The mean has one main disadvantage: it is particularly susceptible to the influence of outliers.

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These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. For example, consider the wages of staff at a factory below:.

Two-stage cluster samples with ranked set sampling designs

Staff 1 2 3 4 5 6 7 8 9 10 Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k 95k. The mean is being skewed by the two large salaries. Therefore, in this situation, we would like to have a better measure of central tendency. As we will find out later, taking the median would be a better measure of central tendency in this situation.

Another time when we usually prefer the median over the mean or mode is when our data is skewed i. If we consider the normal distribution - as this is the most frequently assessed in statistics - when the data is perfectly normal, the mean, median and mode are identical.The Ohio State University. As the access to this document is restricted, you may want to search for a different version of it.

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On comparison of some variation of ranked set sampling

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Please note that corrections may take a couple of weeks to filter through the various RePEc services. Economic literature: papersarticlessoftwarechaptersbooks. FRED data. Two-stage cluster samples with ranked set sampling designs. Abstract This paper draws statistical inference for population characteristics using two-stage cluster samples.Kamarulzaman Ibrahim, On comparison of some variation of ranked set sampling. Sains Malaysiana, 40 4. ISSN Many sampling methods have been suggested for estimating the population median.

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In the situation when the sampling units in a study can be easily ranked than quantified, the ranked set sampling methods are found to be more efficient and cost effective as compared to the simple random sampling.

In this paper, the superiority of several ranked set sampling methods over the simple random sampling are illustrated through some simulation study.

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In addition, some new research topics under ranked set sampling are suggested. Repository Staff Only: item control page. On comparison of some variation of ranked set sampling.

ISSN Preview. Abstract Many sampling methods have been suggested for estimating the population median. Login Create Account. On comparison of some variation of ranked set sampling Kamarulzaman Ibrahim, On comparison of some variation of ranked set sampling. PDF kB.

On comparison of some variation of ranked set sampling

Sains Malaysiana. Mr Azam.Scientific Research An Academic Publisher.

some variations of ranked set sampling

Australian Journal of Agricultural Research, 3, The American Statistician, 59, Biometrics, 28, Annals of the Institute of Statistical Mathematics, 20, Biometrical Journal, 38, Journal of Applied Statistical Sciences, 6, Journal of Applied Mathematics and Computation, Electronic Journal of Applied Statistical Analysis, 1, American Journal of Mathematics and Statistics, 5, Statistical Science, 19, Wiley Interdisciplinary Reviews: Computational Statistics, 2, Springer, New York.

Journal of Computational and Applied Mathematics,John Wiley and Sons, New York. The paper is not in the journal. Go Back HomePage. Biradar 1C.

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Santosha 2. DOI: Abstract In the situation where the sampling units in a study can be easily ranked than quantified, the ranked set sampling methods are found to be more efficient and cost effective as compared to SRS.

In this paper we propose an estimator of the population mean using paired ranked set sampling RSS method.

some variations of ranked set sampling

The proposed estimator is an unbiased estimator of the population mean when the set size is even. In case of odd set size the estimator is unbiased when the underlying distribution is symmetric. It is shown that the proposed estimator is more efficient than its counterpart SRS method for all distributions considered in this study.

Share and Cite:.The Ranking question asks respondents to compare items to each other by placing them in order of preference. In the Analyze Results section, an average ranking is calculated for each answer choice, allowing you to quickly evaluate the most preferred answer choice.

It's important to make sure that even the lowest ranked options still apply to that respondent. If a respondent doesn't have the option to declare that a ranking item does not apply to them, they will be forced to include that choice in their rankings anyway, which might produce bad data. Under the Options tab, you can further customize the question in the following ways:.

Ranking Question

Learn more: Editing Questions. Before you send out your survey, preview your survey design to see what your survey will look like to respondents. Ranking questions calculate the average ranking for each answer choice so you can determine which answer choice was most preferred overall.

The answer choice with the largest average ranking is the most preferred choice. Weights are applied in reverse. In other words, the respondent's most preferred choice which they rank as 1 has the largest weight, and their least preferred choice which they rank in the last position has a weight of 1. You can't change the default weights. We apply weights in this way to ensure that when the data is presented on a chart, it's clear which answer choice is most preferred.

The chart types available depend on the question type, and the display options you configure. Log In. Get Responses. Analyze Results. Taking Surveys. Ranking Question The Ranking question asks respondents to compare items to each other by placing them in order of preference. Video Overview. Try to limit the number of ranking choices to about 5.

Asking respondents to rank too many items in relation to each other can be overwhelming. An average ranking is calculated for each answer choice, allowing you to quickly evaluate the most preferred answer choice.

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Get answers Sign up Start making better decisions with the world's leading survey platform. Start making better decisions with the world's leading survey platform.

Already have an account?Links are also provided to our articles that discuss that survey glossary terms. The definitions given here are in the context of a survey project. However, many of terms are used in other research fields. For a more detailed discussion, please refer to our Survey Guidebook or consider attending one of our Survey Workshops where we discuss in detail many of these concepts as they apply to designing and executing a successful survey project.

The process of studying some phenomenon. A questionnaire is designed that will generate data to measure various attributes of the phenomenon, the questionnaire will be administered to a target audience, and then the results will be analyzed statistically. Abandonment: Occurs when a survey respondent quits a survey part way through. Abandonment raises the question whether even the submitted data are valid. Accuracy: The extent to which a survey result represents the attribute being measured in the population.

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Acquiescence Bias: One type of response bias where the respondent is predisposed to agree with statements presented to him or her. Actionable data: An objective of a survey program to generate data that provides insights to organizational change initiatives. Proper questionnaire construction and question writing is needed to generate actionable data.

An Unactionable Transaction Survey. Adjective Checklist: A survey question type where the respondent is asked to select among a set of adjectives that describe something. The question type generates categorical data. Administration Biases: Biases introduced into the data set through the survey administration process, resulting in data that do not properly reflect the views of the target population for the research.

These biases include mode bias, selection bias, non-response participation bias, and response bias. Change to Telephone Survey Mode. Administrative Burden: The amount of work required to administer a survey.

This work may include the effort to enter the survey in some survey tool, generating a sample, getting the invitations to the respondent, collecting data from the respondent, and transcribing the data including open-ended comments preparing it for analysis. Administration Mode: The communication medium or media used to invite people to participate in the survey, present questions to them, and collect responses from them. Administration, Survey: The process of managing the survey process for getting responses from the selected group.

It includes selecting the audience to receive the invitations, extending the invitations, collecting responses, and loading the responses into a data set. The administration process will vary according to the administration mode. Ambiguity: Vague, confusing, or unclear question wording that could lead respondents to have multiple interpretations of the question.

Leads to measurement error and loss of validity. Perhaps the most common and destructive form of instrumentation bias. Analytical Burden: The amount of work required to analyze the data generated by a survey or survey question.

Textual responses, for example, have high analytical burden. Interval rating questions generally have a set of anchors that describe ranges or levels of feelings for some dimension of measurement, such as satisfaction, agreement, or likelihood.

Related to but different from confidentiality. Articles: An Honest Survey Invitation? ANOVA AN alysis O f VA riance : A statistical technique that examines the variance structures of responses among different groups to determine if those differences are statistically significant. Such questions include overall satisfaction, likelihood of recommendation, likelihood of repurchase, etc.

These questions may be used as dependent variables in statistical tests. Attribute: The characteristics of the phenomenon under study that are measured through data generated by survey questions.


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