Name: interpreting correlation in calibration curves
Uploaded: 2025-05-22T09:06:07.000Z
Duration: 1 min 10 s
Channel: JoVE

معامل الارتباط هو اختبار إحصائي لتقييم درجة واتجاه الارتباط الخطي بين متغيرين.
يشيع استخدام معامل ارتباط بيرسون ، المشار إليه ب "r". هنا ، يمثل "n" العدد الإجمالي للملاحظات.
تتراوح قيمة "r" المحسوبة في منحنى المعايرة من -1 إلى +1. في حين أن القيمة الأقرب إلى +1 تشير إلى ارتباط خطي إيجابي أقوى بين المتغيرين ، فإن القيمة الأقرب إلى -1 تستنتج ارتباطا خطيا سلبيا أقوى ، وتؤكد القيمة الصفرية عدم وجود ارتباط خطي.
معامل التحديد المشار إليه ب "r2" أو "R2" هو اختبار إحصائي أفضل يخبرنا بموثوقية النموذج الرياضي في شرح التباين في البيانات.
تتراوح قيمة R2 من 0 إلى 1. تشير القيمة 0.999 إلى ملاءمة ممتازة.

منحنيات المعايرة: معامل الارتباط

<div style="direction:rtl">
في منحنى المعايرة الخطية، توجد قيمة تسمى معامل المعايرة، يُشار إليها بالرمز "r"، والتي تقيس قوة واتجاه الارتباط بين متغيرين. تتراوح قيمة معامل الارتباط من −1 إلى +1. تشير قيمة +1 إلى وجود ارتباط خطي إيجابي مثالي، وتشير −1 إلى ارتباط سلبي مثالي، ويشير 0 إلى عدم وجود ارتباط بين المتغيرين. وتنص قيمة الارتباط الإيجابية على أنه كلما زاد أحد المتغيرين، زاد الآخر، والعكس صحيح. على العكس من ذلك، تشير قيمة الارتباط السالبة إلى أنه كلما زاد أحد المتغيرين، انخفض المتغير الآخر، والعكس صحيح. يؤدي تربيع معامل الارتباط إلى الحصول على معامل التحديد، الذي يُشار إليه بـ "r2" أو "R2". تتراوح هذه القيمة من 0 إلى 1. وتشير القيمة الأقرب إلى 1، مثل 0.999، إلى توافق ممتاز، بينما تشير القيمة القريبة من 0 إلى توافق ضعيف.
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معامل الارتباط هو اختبار إحصائي لتقييم درجة واتجاه الارتباط الخطي بين متغيرين.
بيرسون ...

calibration-curves-correlation-coefficient

Education

JoVE Core

Analytical Chemistry

الكيمياء التحليلية

Unit 1

الوحدة الأولى

Chemical Applications of Statistical Analyses

التطبيقات الكيميائية للتحليلات الإحصائية

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

Calibration Curves: Correlation Coefficient

interpreting correlation in calibration curves

Calibration curves use the correlation coefficient, written as r, to show how strongly two variables are related and which direction the relationship takes. In a linear calibration curve, this value helps describe the association between the variables being compared.

The correlation coefficient ranges from -1 to +1. A value of +1 means a perfect positive linear correlation, while -1 means a perfect negative correlation. A value of 0 means there is no correlation between the two variables.

A positive correlation means that when one variable increases, the other also increases. A negative correlation means that when one variable increases, the other decreases. Squaring the correlation coefficient gives the coefficient of determination, written as r2 or R2.

The coefficient of determination ranges from 0 to 1. A value close to 1, such as 0.999, shows an excellent fit. A value close to 0 shows a poor fit.

Interpreting Correlation in Calibration Curves

interpreting-correlation-in-calibration-curves

si units: 2019 redefinition

SI Units in Chemistry Measurements

SI units give chemistry measurements a common standard. A measurement has two parts: a number that shows magnitude and a unit that gives the comparison scale. Using the same unit system helps keep results consistent and reduces mistakes in scientific communication. The Système International d'Unités, or SI units, includes both fundamental units and derived SI units. Fundamental units describe base physical quantities such as mass, distance, temperature, time, electric current, luminous...

degrees of freedom

Degrees of Freedom in Statistical Calculations

Degrees of freedom describe how many values in a statistical calculation are free to vary. They represent the minimum number of independent numbers needed to determine a statistic. In a data set, some values may be independent while others depend on them. A simple example uses three unknown numbers with a mean of 10. The first two numbers can be chosen freely. The last number cannot be chosen on its own because it must keep the mean at 10. In that case, the data set has two degrees of freedom.<br...

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Mean, Median, Range, Precision & Accuracy

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Measurement Errors: Sources and Examples

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systematic error: methodological and sampling errors

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Reducing Bias in Measurement Errors

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random error

Random Error in Measurements

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standard deviation of calculated results

Reading Data Spread with Standard Deviation

Standard deviation describes how spread out data are around the mean. It helps show how tightly values cluster near the center and how far they sit from that central value. Many large data sets follow a Gaussian distribution, also called a normal distribution. A Gaussian distribution has a bell-shaped curve. The mean, or central value, appears in the middle, where the most frequent values are found. As data points move farther from the center, deviation increases and frequency decreases. The...

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Reading z Scores for Outliers

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uncertainty: overview

Measuring and Reporting Uncertainty

Uncertainty is part of analytical chemistry measurement. When repeated measurements are taken, random errors can cause the results to differ in small ways. These repeated values are compared with the estimated or expected value to judge how much uncertainty is present. Uncertainty is usually written after the estimated or expected value. It should also be reported with the correct number of significant figures, which are the digits needed to show a precise result. The possible variation from...

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How Uncertainty Changes in Calculations

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propagation of uncertainty from systematic error

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Confidence Intervals and Sample Size

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Significance Testing in Analytical Chemistry

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identifying statistically significant differences: the f-test

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Comparing Variance with the F-Test

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comparing experimental results: student's t-test

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Student's t-Test for Significance Checks

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detection of gross error: the q test

Using the Q Test to Flag Outlier Data

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calibration curves: linear least squares

Using a Calibration Line to Find Unknowns

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calibration curves: correlation coefficient

Calibration curves use the correlation coefficient, written as r, to show how strongly two variables are related and which direction the relationship takes. In a linear calibration curve, this value helps describe the association between the variables being compared. The correlation coefficient ranges from -1 to +1. A value of +1 means a perfect positive linear correlation, while -1 means a perfect negative correlation. A value of 0 means there is no correlation between the two variables. A...

correlation and regression

Using Regression to Measure Variable Links

Correlation and regression are used to study the relationship between two variables. Correlation shows how strongly the variables are associated. Regression helps describe that relationship with a line that can be used for prediction. In linear regression, the relationship is written as a correlation coefficient. This coefficient is shown as r and ranges from -1 to +1. A positive value means the variables move in the same direction. A negative value means they move in opposite directions. <br...

difference from background: limit of detection

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Limit of Detection and Quantification

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quantifying and rejecting outliers: the grubbs test

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Grubbs Test for Spotting Data Outliers

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ANOVA for Comparing Sample Means

ANOVA, or Analysis of Variance, is a statistical test used to compare the means of three or more samples. It was developed by Ronald Fisher in 1918. In high school statistics, ANOVA helps determine whether group averages are equal or whether at least one group is different. Before ANOVA is used, the samples should meet three key assumptions. The data should come from normally distributed samples. The samples should also be randomly and independently selected. In addition, the populations...

key terms and concepts

Learn how the correlation coefficient r and coefficient of determination r2 describe linear calibration curves, including positive, negative, and no correlation.

Interpreting Correlation in Calibration Curves | JoVE K12

analytical chemistry

JoVE Core Analytical Chemistry simplifies complex chemical principles by breaking them down into clear, engaging animations, making topics from SI Units to NMR spectroscopy more accessible and straightforward. Additionally, the scientist-in-action videos highlight the application of these concepts in real-world research conducted in laboratories globally.

Interpreting Correlation in Calibration Curves

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