scholarly journals An experimental determination of the distribution of the partial correlation coefficient in samples of thirty

1920 ◽  
Vol 97 (684) ◽  
pp. 218-224 ◽  
Keyword(s):  
Correlation Coefficient ◽  
Partial Correlation ◽  
Correlation Coefficients ◽  
Small Samples ◽  
Complete Evaluation ◽  
Frequency Distributions ◽  
Zero Correlation ◽  
Suitable Form ◽  
The Mean

In 1908. “Student” dealt experimentally with the distribution of the total correlation coefficient of small samples. In particular, he dealt with values of n as low as 4 for the case of zero correlation in the sampled population. In 1913 H. E. Soper theoretically determined the mean correla­tion and the standard deviation of the distribution of correlations to second approximations. In 1915 R. A. Fisher gave an equation for the frequency distribution of r , and in 1917, as a result of a co-operative study by H. E. Soper, A. W. Young, B. M. Cave, A. Lee and K. Pearson, this was reduced to suitable form for numerical manipulation, and the frequency distributions and frequency constants for samples of size ranging from n = 3 to n = 400 were given for values of the correlation in the sampled population ranging from ρ = 0 to ρ = 0·9. The present experimental investigation was commenced in 1914, but had to be put aside during the war. It was intended to determine whether the distribution of partial correlation coefficients for samples as small as 30 showed greater dispersion than is observed for total correlation coefficients. Yule has shown that for normal distributions and large samples the standard deviations of the distributions should be of the same magnitude. The experiment can now be related to the complete evaluation of the distributions of total correlations referred to above.

scholarly journals A Quantitative Comparison of Multispectral Refraction Topography and Autorefractometer in Young Adults

2021 ◽  
Vol 8 ◽  
Author(s):  
Yunru Liao ◽  
Zhenlan Yang ◽  
Zijing Li ◽  
Rui Zeng ◽  
Jing Wang ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Pearson Correlation ◽  
Intraclass Correlation ◽  
Correlation Coefficients ◽  
Cross Sectional Study ◽  
Cross Sectional ◽  
High Agreement ◽  
Intraclass Correlation Coefficients ◽  
Repeatability And Reproducibility ◽  
The Mean

Purpose: Purpose of this study is to evaluate the measuring consistency of central refraction between multispectral refraction topography (MRT) and autorefractometry.Methods: This was a descriptive cross-sectional study including subjects in Sun Yat-sen Memorial Hospital from September 1, 2020, to December 31, 2020, ages 20 to 35 years with a best corrected visual acuity of 20/20 or better. All patients underwent cycloplegia, and the refractive status was estimated with autorefractometer, experienced optometrist and MRT. We analyzed the central refraction of the autorefractometer and MRT. The repeatability and reproducibility of values measured using both devices were evaluated using intraclass correlation coefficients (ICCs).Results: A total of 145 subjects ages 20 to 35 (290 eyes) were enrolled. The mean central refraction of the autorefractometer was −4.69 ± 2.64 diopters (D) (range −9.50 to +4.75 D), while the mean central refraction of MRT was −4.49 ± 2.61 diopters (D) (range −8.79 to +5.02 D). Pearson correlation analysis revealed a high correlation between the two devices. The intraclass correlation coefficient (ICC) also showed high agreement. The intrarater and interrater ICC values of central refraction were more than 0.90 in both devices and conditions. At the same time, the mean central refraction of experienced optometrist was −4.74 ± 2.66 diopters (D) (range −9.50 to +4.75D). The intra-class correlation coefficient of central refraction measured by MRT and subjective refraction was 0.939.Conclusions: Results revealed that autorefractometry, experienced optometrist and MRT show high agreement in measuring central refraction. MRT could provide a potential objective method to assess peripheral refraction.

BLOAT INVESTIGATIONS: II. A COMPARISON OF THE TRUE PROTEIN AND ELEMENT CONTENTS OF ALFALFA HAY FROM BLOATING AND NON-BLOATING FARMS

1964 ◽  
Vol 44 (2) ◽  
pp. 175-181 ◽  
Author(s):  
J. E. Miltimore ◽  
J. M. McArthur ◽  
J. L. Mason ◽  
R. B. Carson
Keyword(s):  
Correlation Coefficient ◽  
Correlation Coefficients ◽  
Nitrogen And Phosphorus ◽  
Stage Of Development ◽  
Alfalfa Hay ◽  
Calcium Magnesium ◽  
Similar Range ◽  
The Mean ◽  
True Protein ◽  
Nitrogen Phosphorus

Alfalfa samples at the hay stage of development were harvested by hand from 35 farms where bloat was a serious problem and from 38 farms where bloat did not occur even on lush legume pastures. The samples were analysed for nitrogen, phosphorus, potassium, sulphur, calcium, magnesium, and true protein. There were no differences in the mean contents of these constituents between bloating and non-bloating farms. There were wide ranges within both types of farm; true protein for example varied from 7.3 to 14.6% in alfalfa from bloating farms, with a similar range from 7.7 to 16.9% from non-bloating farms. Correlation coefficients revealed a significant association between nitrogen and phosphorus (.488) in alfalfa from non-bloating farms. There were significant associations between sulphur and nitrogen (.366) and between sulphur and protein (.707) in alfalfa from bloating farms. This correlation between sulphur and protein was the only coefficient that was significantly different from the corresponding correlation coefficient for non-bloating farms.

scholarly journals Reliability Measurement of Corneal Wavefront Aberrations using Corneal Videokeratograph Atlas 9000

2020 ◽  
Vol 18 (2) ◽  
Author(s):  
Noorshazana Mat Rejab @ Md Rejab ◽  
Mohd Radzi Hilmi ◽  
Khairidzan Mohd Kamal ◽  
Md Muziman Syah Md Mustafa
Keyword(s):  
Correlation Coefficient ◽  
Intraclass Correlation Coefficient ◽  
Spherical Aberration ◽  
Intraclass Correlation ◽  
Correlation Coefficients ◽  
Time Interval ◽  
Wavefront Aberration ◽  
Wavefront Aberrations ◽  
The Mean ◽  
Reliability Measurement

Introduction: Accurate corneal wavefront aberration measurements are essential in determining patient’s suitability, vision outcomes and patient satisfaction in laser refractive surgeries. This study aimed to evaluate the reliability measurement of higher-order aberration (HOA) using corneal videokeratograph Atlas 9000. Materials and method:  38 eyes of 19 participants were recruited in this study. Comprehensive eye examination was done to ensure all participants eligibility, and any conditions in which obstruct the central cornea were excluded. Corneal wavefront aberrations were measured based on Zernike polynomials. In assessing repeatability, three repetitive measurements in five minutes in a single session were taken by 2 experience examiners. For reproducibility measurement, similar approach was done with the time-interval between measurements was set at one week. Bland-Altman, limits of agreement (LoA) and intraclass correlation coefficients (ICCs) were used to evaluate the reliability measurement. Results: Bland-Altman and LoA findings revealed no significant differences for both repeatability and reproducibility measurement. For repeatability testing, the mean differences for vertical trefoil, oblique trefoil and spherical aberration were -0.096 ± 0.493, 0.001 ± 0.048, 0.008 ± 0.035, 0.004 ± 0.029, 0.010 ± 0.053 with LoA of 1.930, 0.188, 0.138, 0.114, and 0.208 respectively. Intraclass correlation coefficient (ICC) excellent reliability of 0.841 for all parameters. Likewise, reproducibility  testing showed similar findings  with the mean difference were -0.018 ± 0.091, 0.016 ± 0.061, -0.0004 ± 0.036, -0.002 ± 0.042, 0.003 ± 0.026, with LoA of 0.356, 0.24, 0.141,0.164, and 0.102 respectively. Intraclass correlation coefficient (ICC) shows excellent reliability of more than 0.9 for all parameters. LoA of less than 1.0 were observed in all measurements (except for repeatability of vertical trefoil) indicates high consistency of the measurements. Conclusions: Corneal videokeratograph Atlas 9000 provides excellent HOA measurement reliability.

scholarly journals Correlation and Regression using VASSARSTATS

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Suma AP ◽  
KP Suresh
Keyword(s):  
Correlation Coefficient ◽  
Partial Correlation ◽  
Rank Order ◽  
Correlation Coefficients ◽  
Regression Coefficients ◽  
Multiple Correlation ◽  
Population Correlation ◽  
Coefficient Corrélation ◽  
Sample Correlation ◽  
Simple Logistic

In a bivariate or a multivariate data, to understand the association between the variables Correlation is the best tool. It gives the degree of relationship between the variables. Regression gives the exact linear relationship between the variables. This article gives details of capabilities of Vassarstats Correlation and Regression and procedure to calculate Correlation coefficient and Regression coefficients with examples. Vassarstats Correlation and Regression can perform Linear Correlation and Regression, Intercorrelations, Multiple Correlation and Regression, Partial Correlation, 0.95 and 0.99 Confidence intervals for population correlation coefficient, Estimating the Population Value of rho, Significance of value of r, Significance of difference between two correlation coefficients, Significance of difference between sample correlation coefficient and hypothetical value of population Correlation coefficient, Rank Order Correlation, Correlation coefficient for a 2*2 contingency table, Point biserial correlation coefficient, Correlation for unordered pairs, and then Simple Logistic Regression.

scholarly journals Determination of the Dissociation Constants of Metformin from a Second Derivative UV Spectrum

2020 ◽  
Vol 11 (1) ◽  
pp. 790-796 ◽  
Author(s):  
Khalid Waleed S. Al-Janabi ◽  
Ali Khalil Mahmood ◽  
Hasan M. Luaibi
Keyword(s):  
Aqueous Solution ◽  
Dissociation Constants ◽  
Correlation Coefficients ◽  
Pharmaceutical Compounds ◽  
Second Derivative ◽  
Uv Spectrum ◽  
Established Method ◽  
Ultraviolet Spectra ◽  
The Mean

An environmentally begnin second derivative spectrometric approach was developed for the estimation of the dissociation constants pKa(s) of metformin, a common anti-diabetic drug.  The ultraviolet spectra of the aqueous solution of metformin were measured at different acidities, then the second derivative of each spectrum was graphed. The overlaid second derivative graphs exhibited two isobestic points at 225.5 nm and 244 nm pointing out to the presence of two dissociation constants for metformin pKa1 and pKa2, respectively. The method was validated by evaluating the reproducibility of the acquired results by comparing the estimated values of the dissociation constants of two different strategies that show excellent matching. As well as, the whole procedure was repeated with a new set of standard solutions and buffers for further verification. The average calculated values of pKa1 and pKa2 were found to be 2.72±0.01 and 11.61±0.08, with correlation coefficients ( R2) of 0.9916 and 0.9614, respectively. The established method was fast, affordable, reproducible, and the mean pKa values obtained were accurate and can be applied for the estimation of the dissociation constants of other active pharmaceutical compounds

scholarly journals Determination of peritoneal transport characteristics with 24-hour dialysate collections: dialysis adequacy and transport test.

1994 ◽  
Vol 5 (6) ◽  
pp. 1333-1338
Author(s):  
M V Rocco ◽  
J R Jordan ◽  
J M Burkart
Keyword(s):  
Membrane Transport ◽  
Cost Savings ◽  
Correlation Coefficients ◽  
Peritoneal Membrane ◽  
Dialysis Adequacy ◽  
Peritoneal Transport ◽  
Data Rates ◽  
The Mean

Although the 24-hour collection of dialysate provides a very accurate measure of the adequacy of dialysis, it is not known if it can also determine peritoneal membrane transport characteristics. In this prospective study, 101 24-hour dialysate collections were immediately followed by a standard peritoneal equilibration test (PET). Four- and 24-h dialysate-to-plasma (D/P) ratios were determined for creatinine and urea. The correlation coefficients between these two tests were 0.86 for the adjusted D/P creatinine and 0.71 for the D/P urea, whereas the standard errors of estimate were 0.054 and 0.060, respectively. Patients were classified into one of four transport groups on the basis of the mean and standard deviation of the adjusted D/P creatinine values, and these values were similar to those generated from the PET data. Rates of ultrafiltration were also defined for patients undergoing 2.0- and 2.5-L dwells. A survey of a subset of these patients demonstrated that the 24-h collection was preferred to the PET for determining transport characteristics. Therefore, the 24-h dialysate collection can be used to monitor both peritoneal membrane transport characteristics and adequacy. This technique, which has been named the "dialysis adequacy and transport test," has the potential for significant cost savings when it is used for the routine follow-up of both peritoneal transport and adequacy of dialysis.

scholarly journals Megha-Tropiques/SAPHIR measurements of humidity profiles: validation with AIRS and global radiosonde network

2013 ◽  
Vol 6 (6) ◽  
pp. 11405-11437 ◽  
Author(s):  
K. V. Subrahmanyam ◽  
K. K. Kumar
Keyword(s):  
Regression Analysis ◽  
North America ◽  
East Asia ◽  
Correlation Coefficient ◽  
Correlation Coefficients ◽  
The Mean ◽  
Level 1 ◽  
Level 2 ◽  
Humidity Profiles ◽  
Dry Bias

Abstract. The vertical profiles of humidity measured by SAPHIR (Sondeur Atmospherique du Profil d' Humidité Intropicale par Radiométrie) on-board Megha-Tropiques satellite are validated using Atmosphere Infrared Sounder (AIRS) and ground based radiosonde observations during July–September 2012. SAPHIR provides humidity profiles at six pressure layers viz., 1000–850 (level 1), 850–700 (level 2), 700–550 (level 3), 550–400 (level 4) 400–250 (level 5) and 250–100(level 6) hPa. Segregated AIRS observations over land and oceanic regions are used to assess the performance of SAPHIR quantitatively. The regression analysis over oceanic region (125° W–180° W; 30° S–30° N) reveal that the SAPHIR measurements agrees very well with the AIRS measurements at levels 3, 4, 5 and 6 with correlation coefficients 0.79, 0.88, 0.87 and 0.78 respectively. However, at level 6 SAPHIR seems to be systematically underestimating the AIRS measurements. At level 2, the agreement is reasonably good with correlation coefficient of 0.52 and at level 1 the agreement is very poor with correlation coefficient 0.17. The regression analysis over land region (10° W–30° E; 8° N–30° N) revealed an excellent correlation between AIRS and SAPHIR at all the six levels with 0.80, 0.78, 0.84, 0.84, 0.86 and 0.65 respectively. However, again at levels 5 and 6, SAPHIR seems to be underestimating the AIRS measurements. After carrying out the quantitative comparison between SAPHIR and AIRS separately over land and ocean, the ground based global radiosonde network observations of humidity profiles over three distinct geographical locations (East Asia, tropical belt of South and North America and South Pacific) are then used to further validate the SAPHIR observations as AIRS has its own limitations. The SAPHIR observations within a radius of 50 km around the radiosonde stations are averaged and then the regression analysis is carried out at the first five levels of SAPHIR. The comparison is not carried out at sixth level due to inaccuracies of radiosonde measurements of humidity at this level. From the regression analysis, it is found that the SAPHIR observations agree very well with the radiosonde observations at all the five levels with correlation coefficients 0.65, 0.72, 0.84, 0.88 and 0.78 respectively. Among the three regions considered for the present study, the correlation was poor at the first level over East Asia. Further, statistical analysis showed that at first level the SAPHIR observations have wet bias at low humidity magnitudes and dry bias at high humidity magnitudes. The humidity magnitude at which wet bias changes to dry bias varied from one level to the other. The mean bias between the radiosonde and the SAPHIR observations are also estimated separately for the three regions. The mean bias profiles showed that SAPHIR has wet bias at all the five levels over South/North America and South Pacific regions. However, the results showed dry bias at all the levels except 2nd and 3rd levels, where it showed wet bias, over East Asia. In a nutshell, the results indicated that SAPHIR has wet bias over dry regions and dry bias over wet regions. The important outcome of the present study is the quantitative validation of the SAPHIR humidity observations using both space and ground based measurements. The present results are very encouraging and envisage the great potential of SAPHIR observations for meteorological applications especially in understanding the hydrological cycle at shorter temporal and spatial scales in the Tropics.

scholarly journals Statistical Relations of the Qualitative Attributes of Real Properties Subject to Mass Appraisal

2019 ◽  
Vol 19 (2) ◽  
pp. 25-37
Author(s):  
Krzysztof Dmytrów ◽  
Anna Gdakowicz ◽  
Ewa Putek-Szeląg
Keyword(s):  
Real Estate ◽  
Correlation Coefficient ◽  
Partial Correlation ◽  
Rank Correlation ◽  
Correlation Coefficients ◽  
Qualitative Properties ◽  
Real Estate Appraisal ◽  
Attribute Weights ◽  
Actual Direction ◽  
Kendall Correlation

Abstract Research background: Every real estate may be described with a multitude of attributes. In the process of real estate appraisal only those properties are taken into account that significantly affect its value. Mass appraisal involves a simultaneous valuation of many similar real properties, carried out in the same manner and at the same time. The algorithm applied to mass appraisal ought to ensure a uniform approach to the valuation of all real estate of the same type in an objective fashion. Purpose: The purpose of the paper is to define the weights of attributes in the process of real estate mass appraisal on the basis of relationships between unit property value and the values of attributes. Research methodology: The weights were defined on the grounds of partial correlation coefficients for the qualitative properties (Spearman rank correlation coefficient and τB Kendall correlation coefficient). Results: The signs of certain correlation coefficients were discordant with the actual direction of the relations between the analysed properties. The problem was avoided by employing partial correlation coefficients. On the basis of the calculated partial correlation coefficients the weights of individual attributes were calculated. Of all analysed coefficients the partial τB Kendall correlation coefficient is methodologically the most suitable one. Novelty: The use of partial correlation coefficients for determining attribute weights is an innovative approach and is applied in the article.

scholarly journals Assessing the shared variation among high-dimensional data matrices: a modified version of the Procrustean correlation coefficient

2019 ◽  
Author(s):  
E. Coissac ◽  
C. Gonindard-Melodelima
Keyword(s):  
Correlation Coefficient ◽  
Partial Correlation ◽  
High Dimensional Data ◽  
Correlation Coefficients ◽  
R Package ◽  
High Dimensional ◽  
Data Sets ◽  
High Dimension Data ◽  
Correct Estimation ◽  
Shared Variation

AbstractMotivationMolecular biology and ecology studies can produce high dimension data. Estimating correlations and shared variation between such data sets are an important step in disentangling the relationships between different elements of a biological system. Unfortunately, classical approaches are susceptible to producing falsely inferred correlations.ResultsHere we propose a corrected version of the Procrustean correlation coefficient that is robust to high dimensional data. This allows for a correct estimation of the shared variation between two data sets and the partial correlation coefficients between a set of matrix data.AvailabilityThe proposed corrected coefficients are implemented in the ProcMod R package available on CRAN. The git repository is hosted at https://git.metabarcoding.org/lecasofts/[email protected]

scholarly journals HORMONAL IMMUNOASSAYS

2015 ◽  
Vol 22 (05) ◽  
pp. 648-655
Author(s):  
Bashir Elfatih Abdalla ◽  
Abedelmula M. Abdealla
Keyword(s):  
Correlation Coefficients ◽  
Strong Relationship ◽  
Detection Technology ◽  
Accuracy And Precision ◽  
Significant Difference ◽  
Postgraduate Studies ◽  
The Mean ◽  
Tsh Levels ◽  
Made In

Objectives: several improvements have been made in the design of immunoassayssuch as method of antibody production, labeling, automation and detection technology. The aim ofthe present study was to compare the accuracy and precision of enzyme linked immunofloriscenceassay (ELFA) and electrochemiluminescence assay (ECL), with Elisa for determination of serum TSHlevels. Period: Feb 2014 to Nov 2014. Setting: College of postgraduate studies, University of Al-Neelain, Khartoum, Sudan. Material and Methods: Three commercial control materials low, normaland high levels of TSH, were used for imprecision studies of immunofloriscence assay (ELFA) andelectrochemiluminescence assay (ECL) methods and 120 patients samples including low (20%),normal (50%), and high (30%) TSH levels, were measured by the two methods, and used for methodscomparison. In addition to six assigned prepared pool serum used for linearity evaluation of the twomethods. Results: Inter- and intra-assay CV% for ECL and ELFA was significantly low compared withthe required by the manufacture. (Intraassay CV% for ECL was 2.9%, 2.74%, and 2.55% for low,normal, and high respectively of TSH levels of the control sera. Intraassay CV% for ELFA was 3.95%,3.75%, and 5.73% for low, normal, and high respectively of TSH levels of the control sera. InterassayCV% for ECL was 3.0%, 2.75%, and 2.81% for low, normal, and high respectively of TSH levels ofthe control sera. Intraassay CV% for ELFA was 4.26%, 4.0% , and 5.75% for low, normal , and highrespectively of TSH levels of the control sera. Although the mean TSH levels of the three levels of thecontrol sera measured by ECL & ELFA methods, is significantly difference from assigned TSH meanvalues( low 0.488+/-0.078,normal 6.016+/- 0.952,high 33.651+/-5.39) , but the measured values iswithin the mean range of the assigned means values. ECL; low (0.611 +/- 0.018. p ≤ 0.001), normal(6.6785 +/- 0.183. p ≤ 0.00), high (35.0485 +/- 0.894. p ≤ 0.02). ELFA low (0.50545 +/- 0.020. p ≤0.00) , normal (6.5395 +/- 0.244. p ≤ 0.00), high (31.0350 +/- 1.779. p ≤0.001).The mean TSH levelsof the 120 patients samples measured by ECL & ELFA , is significantly difference , for ECL (15.74+/-1.181 . p ≤ 0.00) when compared with the mean TSH value (14.56 +/- 1.65) of the patients samples.For ELFA method also there is significant difference (13.76 +/- 1.59 , p ≤ 0.00) when comparedwith mean of the assigned TSH values(14.56 +/- 1.65) of the patients samples, but within the targetvalues of the means .The study showed strong relationship between the two TSH levels measuredby ECL( mean 15.74 mIU/L, slope 0.67 , correlation coefficients 0.991, p ≤ 0.00) and by ELFA (mean 13.76 mIU/L, slope 0.54, correlation coefficients 0.995, p ≤ 0.00) with the assigned values(14.56 ) of 120 patients sample .The results illustrates no significant difference of TSH mean level insix prepared pool samples measured by ECL(22.63 mIU/l +/- 1.12 , p ≤ 0.1) and ELFA(19.87mIU/l+/- 1.15 , p ≤ 0.11) when compared with the TSH assigned values(22.54 mIU/l +/-0.96), and withstrong correlation between the two TSH levels measured by ECL(22.63 mIU/l, slope 0.79, correlationcoefficients 0.999, p ≤ 0.00) and ELFA ( mean 19.87mIU, slope 0.68, correlation coefficients 0.985,p ≤ 0.00), with the assigned TSH values (22.54 mIU/l +/-0.96).of the six prepared pool samples.Conclusion: Considerable significant precision and accuracy was manifested by both ECL and ELFAmethods in estimation of TSH levels, but ECL is more precise than ELFA especially in the lower TSHconcentration.

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