To simplify the notation the following variables will be used. Pascual's estimator: [5]. Beale's estimator: [6]. Tin's estimator: [7]. Sahoo's estimator: [8]. Sahoo has also proposed a number of additional estimators: [9]. An asymptotically correct estimator is [3].

A jackknife estimate of the ratio is less biased than the naive form. A jackknife estimator of the ratio is. where n is the size of the sample and the r i are estimated with the omission of one pair of variates at a time.

Then the estimator. Other estimators based on the division of the sample into g groups are: [12]. where r i ' is the value of the sample ratio with the i th group omitted. Other methods of estimating a ratio estimator include maximum likelihood and bootstrapping.

where s x 2 and s y 2 are the variances of the x and y variates respectively, m x and m y are the means of the x and y variates respectively and s xy is the covariance of x and y.

Although the approximate variance estimator of the ratio given below is biased, if the sample size is large, the bias in this estimator is negligible. where N is the population size, n is the sample size and m x is the mean of the x variate.

Another estimator of the variance based on the Taylor expansion is. where n is the sample size and N is the population size and s xy is the covariance of x and y. where r i is the ratio with the i th pair of variates omitted and r J is the jackknife estimate of the ratio.

where m x is the mean of the x variate, s x 2 and s y 2 are the sample variances of the x and y variates respectively and s xy is the covariance of x and y.

The skewness and the kurtosis of the ratio depend on the distributions of the x and y variates. Estimates have been made of these parameters for normally distributed x and y variates but for other distributions no expressions have yet been derived.

It has been found that in general ratio variables are skewed to the right, are leptokurtic and their nonnormality is increased when magnitude of the denominator's coefficient of variation is increased. For normally distributed x and y variates the skewness of the ratio is approximately [7].

Because the ratio estimate is generally skewed confidence intervals created with the variance and symmetrical tests such as the t test are incorrect. An alternative method of reducing or eliminating the bias in the ratio estimator is to alter the method of sampling.

The variance of the ratio using these methods differs from the estimates given previously. Note that while many applications such as those discussion in Lohr [13] are intended to be restricted to positive integers only, such as sizes of sample groups, the Midzuno-Sen method works for any sequence of positive numbers, integral or not.

It's not clear what it means that Lahiri's method works since it returns a biased result. The first of these sampling schemes is a double use of a sampling method introduced by Lahiri in Lahiri's scheme as described by Lohr is biased high and, so, is interesting only for historical reasons.

The Midzuno-Sen technique described below is recommended instead. In Midzuno and Sen independently described a sampling scheme that provides an unbiased estimator of the ratio. The first sample is chosen with probability proportional to the size of the x variate.

The remaining n - 1 samples are chosen at random without replacement from the remaining N - 1 members in the population. The probability of selection under this scheme is. where X is the sum of the N x variates and the x i are the n members of the sample. Then the ratio of the sum of the y variates and the sum of the x variates chosen in this fashion is an unbiased estimate of the ratio estimator.

where x i and y i are chosen according to the scheme described above. Särndal, Swensson, and Wretman credit Lahiri, Midzuno and Sen for the insights leading to this method [17] but Lahiri's technique is biased high. Tin [18] described and compared ratio estimators proposed by Beale [19] and Quenouille [20] and proposed a modified approach now referred to as Tin's method.

These ratio estimators are commonly used to calculate pollutant loads from sampling of waterways, particularly where flow is measured more frequently than water quality. For example see Quilbe et al. If a linear relationship between the x and y variates exists and the regression equation passes through the origin then the estimated variance of the regression equation is always less than that of the ratio estimator [ citation needed ].

The precise relationship between the variances depends on the linearity of the relationship between the x and y variates: when the relationship is other than linear the ratio estimate may have a lower variance than that estimated by regression.

Although the ratio estimator may be of use in a number of settings it is of particular use in two cases:. Later Messance ~ and Moheau published very carefully prepared estimates for France based on enumeration of population in certain districts and on the count of births, deaths and marriages as reported for the whole country.

The districts from which the ratio of inhabitants to birth was determined only constituted a sample. In , Laplace wished to estimate the population of France.

No population census had been carried out and Laplace lacked the resources to count every individual. Instead he sampled 30 parishes whose total number of inhabitants was 2,, The parish baptismal registrations were considered to be reliable estimates of the number of live births so he used the total number of births over a three-year period.

The sample estimate was 71, The total number of baptismal registrations for France was also available to him and he assumed that the ratio of live births to population was constant. He then used the ratio from his sample to estimate the population of France.

Karl Pearson said in that the ratio estimates are biased and cautioned against their use. Contents move to sidebar hide. Article Talk.

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Download as PDF Printable version. Definition [ edit ] Assume there are two characteristics — x and y — that can be observed for each sampled element in the data set. On a method of bias reduction in ratio estimation.

ACM Transactions on Modeling and Computer Simulation - TOMACS 9 4 doi : Springer, §7. Comparison of Some Ratio Estimators. Journal of the American Statistical Association, 60 , — Selecting a calculation method to estimate sediment and nutrient loads in streams: Application to the Beaurivage River Québec, Canada.

Journal of Hydrology, 1—4 , — Select the Water-Cement Ratio Range 3. Estimate the Water Content 4. Adjust Water Content 5. Weigh Cement 6. Determine the aggregate size 7.

Calculate Water-Cement ratio How to Test the Water-Cement Ratio? Slump Test 2. Compressive Strength Test 3. Durability Testing FAQs How is the concrete strength affected by the water-cement ratio? What are the advantages of a low water-cement ratio? How can we reduce the water-cement ratio in concrete?

What is Water-Cement Ratio? Importance of Water-Cement Ratio The water-cement ratio in concrete directly affects its durability and strength. How to Calculate Water-Cement Ratio in Concrete?

Below is a comprehensive guide on how to find the water-cement ratio that is appropriate for your concrete mix: 1. Determine the Required Strength Before calculating the water-cement ratio, identify the required strength of the concrete.

Select the Water-Cement Ratio Range Based on the required strength and the specific conditions of the project, determine an initial range. Estimate the Water Content Calculate the estimated water content required for a given volume of concrete mix.

Weigh Cement Weigh the cement required for the concrete mix. Determine the aggregate size Per IS , the maximum water content in a concrete mix may also depend on the aggregate size. Refer to the table below: Nominal Maximum Size of Aggregate in mm Maximum Water Content per Cubic Metre of Concrete 10 50 40 7.

Calculate Water-Cement ratio Finally, divide the weight of water by the weight of cement to obtain the ratio. The following methods can be used to test the water-cement ratio: 1. Slump Test Conduct a slump test to evaluate the workability of the concrete. Compressive Strength Test Perform a compressive strength test on cured concrete samples to ensure that the achieved strength meets the design requirements.

Durability Testing Assess the durability properties of the concrete, such as permeability, resistance to chemical attack, and freeze-thaw resistance. Check out our superior-quality cement for all types of construction.

FAQs How is the concrete strength affected by the water-cement ratio? Previous: What is M20 Concrete Ratio. Next: What is Concrete Used For?

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The results from the case study suggest that at least in some cases the resistivity of the mud Rm produce a better estimate of the resistivity of water Rw in the fully flushed zone than an estimate using the resistivity of the mud filtrate Rmf.

The ratio method can be easily used to estimate ground-water resistivity and total dissolved solids concentration of the formation water based only on data from resistivity logs. The advantage of the method is that data on porosity, cementation exponent, temperature, and volume of clay are not required.

The method, which has been used by the oil industry to crudely estimate water resistivity, is based in part on the ratio of the resistivity of a fully water-saturated formation to the resistivity of the fully flushed zone adjacent to the annulus in a mud-filled borehole.

The method, which is very robust, requires only an estimate of the resistivity of a fully water-saturated formation from a deep looking induction or resistivity log, an estimate of the resistivity of the fully flushed zone from a microresistivity or short normal log, and a measurement of resistivity of the mud or mud filtrate and its temperature.

By joining you are opting in to receive e-mail. Promoting, selling, recruiting, coursework and thesis posting is forbidden. Students Click Here. Eng-Tips Posting Policies Contact US.

Forum Search FAQs Links MVPs. Menu Forum Search FAQs Links MVPs. Known: Sand Wt: 13, lb's 4. of H2O added at plant: 1, of H2O added onsite: is this correct? It's been a long time since I was involved with mix design, but I would think the water in the sand would just be calculated as x.

So I get about 0. You have to consider the absorption of the aggregate. Assuming the fine aggregate absorption to be about 0. The calculate as hokie66 stated. Is there any truth in that? I have been peeling throught ACI I appreciate all of your responses. ASTM C, "Standard Test Method for Total Evaporable Moisture Content of Aggregate by Drying," should be followed when determining the aggregate moisture content.

This is due to bleeding effects and presence of aggregates that increases the heterogeneity of the concrete microstructure. However, the results tend to converge when a representative number of images are analysed and averaged Fig.

The results show a good agreement between the measured and actual values. The errors do not appear to be influenced by either the mix proportion or curing age. The method is based on measuring the volume fractions of unreacted cement, hydration products and capillary pores in the concrete using backscattered electron microscopy.

By plotting a forecast on both rate and ratio data, the slope dependencies can be used to match historical data on both the rate and ratio trends.

These interpretations are less likely to show personal bias, as the forecast would only look reasonable if it matched both trends. cumulative oil. These may guide the user in which plot to select, but both should be considered uncertain. An oil rate forecast is calculated by combining the ratio forecast with a total fluid rate.

By joining you are opting in to receive e-mail. Promoting, selling, recruiting, coursework and thesis posting is forbidden. Students Click Here. Eng-Tips Posting Policies Contact US.

Forum Search FAQs Links MVPs. Menu Forum Search FAQs Links MVPs. Known: Sand Wt: 13, lb's 4. of H2O added at plant: 1, of H2O added onsite: is this correct? It's been a long time since I was involved with mix design, but I would think the water in the sand would just be calculated as x.

So I get about 0. You have to consider the absorption of the aggregate. Assuming the fine aggregate absorption to be about 0.

The calculate as hokie66 stated. Is there any truth in that? I have been peeling throught ACI I appreciate all of your responses. ASTM C, "Standard Test Method for Total Evaporable Moisture Content of Aggregate by Drying," should be followed when determining the aggregate moisture content.

The ratio estimator is a statistical estimator for the ratio of means of two random variables. Ratio estimates are biased and corrections must be made when they are used in experimental or survey work. The ratio estimates are asymmetrical and symmetrical tests such as the t test should not be used to generate confidence intervals.

Therefore, the estimator is approximately unbiased for large sample sizes. Assume there are two characteristics — x and y — that can be observed for each sampled element in the data set.

The ratio R is. where θ x is the corresponding value of the x variate. θ y is known to be asymptotically normally distributed. That the ratio is biased can be shown with Jensen's inequality as follows assuming independence between x and y :.

An upper bound on the relative bias of the estimate is provided by the coefficient of variation the ratio of the standard deviation to the mean.

The correction methods, depending on the distributions of the x and y variates, differ in their efficiency making it difficult to recommend an overall best method. Because the estimates of r are biased a corrected version should be used in all subsequent calculations.

A correction of the bias accurate to the first order is [ citation needed ]. where m x is the mean of the variate x and s xy is the covariance between x and y. To simplify the notation s xy will be used subsequently to denote the covariance between the variates x and y.

Another estimator based on the Taylor expansion is [3]. where n is the sample size, N is the population size, m x is the mean of the x variate and s x 2 and s y 2 are the sample variances of the x and y variates respectively.

where N is the population size, n is the sample size, m x is the mean of the x variate and s x 2 and s y 2 are the sample variances of the x and y variates respectively.

These versions differ only in the factor in the denominator N - 1. For a large N the difference is negligible. If x and y are unitless counts with Poisson distribution a second-order correction is [4]. Other methods of bias correction have also been proposed.

To simplify the notation the following variables will be used. Pascual's estimator: [5]. Beale's estimator: [6].

Tin's estimator: [7]. Sahoo's estimator: [8]. Sahoo has also proposed a number of additional estimators: [9]. An asymptotically correct estimator is [3]. A jackknife estimate of the ratio is less biased than the naive form.

A jackknife estimator of the ratio is. where n is the size of the sample and the r i are estimated with the omission of one pair of variates at a time. Then the estimator. Other estimators based on the division of the sample into g groups are: [12].

where r i ' is the value of the sample ratio with the i th group omitted. Other methods of estimating a ratio estimator include maximum likelihood and bootstrapping. where s x 2 and s y 2 are the variances of the x and y variates respectively, m x and m y are the means of the x and y variates respectively and s xy is the covariance of x and y.

Although the approximate variance estimator of the ratio given below is biased, if the sample size is large, the bias in this estimator is negligible. where N is the population size, n is the sample size and m x is the mean of the x variate.

Another estimator of the variance based on the Taylor expansion is. where n is the sample size and N is the population size and s xy is the covariance of x and y.

where r i is the ratio with the i th pair of variates omitted and r J is the jackknife estimate of the ratio. where m x is the mean of the x variate, s x 2 and s y 2 are the sample variances of the x and y variates respectively and s xy is the covariance of x and y.

The skewness and the kurtosis of the ratio depend on the distributions of the x and y variates. Estimates have been made of these parameters for normally distributed x and y variates but for other distributions no expressions have yet been derived.

It has been found that in general ratio variables are skewed to the right, are leptokurtic and their nonnormality is increased when magnitude of the denominator's coefficient of variation is increased. For normally distributed x and y variates the skewness of the ratio is approximately [7].