Name: anova for comparing sample means
Uploaded: 2024-04-04T10:51:12.000Z
Duration: 1 min 13 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.2

CHEM.2.C

What is ANOVA?

ניתוח השונות - מקוצר כמו ANOVA - משמש כאשר האמצעים של שלוש דגימות או יותר צריכים להיבדק עבור שוויון.
לדוגמה, ANOVA יכולה לעזור לצרכן לבחור מכונית לאחר השוואת צריכת הדלק הממוצעת של מכוניות מחברות שונות.
הדגימות המשמשות לבדיקת ANOVA צריכות להיות בעלות שלושה מאפיינים חיוניים או הנחות סטטיסטיות.
ההנחה הראשונה היא שיש לשאוב דגימות מאוכלוסיות המתפלגות באופן נורמלי.
ההנחה השנייה היא שיש לבחור דגימות באופן אקראי ובלתי תלוי באוכלוסיות.
ההנחה השלישית היא שלאוכלוסיות של דגימות צריכה להיות שונות שווה.
ישנם שני סוגים נפוצים של בדיקות ANOVA: ANOVA חד-כיווני ו-ANOVA דו-כיווני.
ANOVA חד-כיווני משמש כאשר דגימות מוגדרות או מסווגות לפי גורם או טיפול אחד, ו-ANOVA דו-כיווני משמש כאשר דגימות מוגדרות או מסווגות לפי שני גורמים או טיפולים.
ANOVA יש יישום רחב במדעי החיים, זיהוי פלילי, מדעי החברה, ומנהל עסקים.

מהי anova?

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ניתוח השונות או ANOVA הוא מבחן סטטיסטי שפותח על ידי רונלד פישר בשנת 1918. הוא מבוצע על שלוש דגימות או יותר כדי לבדוק שוויון בין האמצעים שלהם.

לפני ביצוע ANOVA, יש לוודא שלדגימות המשמשות לניתוח זה יש שלושה מאפיינים מכריעים או הנחות סטטיסטיות. ההנחה הראשונה קובעת שהדגימות צריכות להילקח ממדגמים בחלוקה נורמלית, בעוד שהשנייה דורשת שכל הדגימות שנלקחו ייבחרו באופן אקראי ובלתי תלוי. ההנחה השלישית והאחרונה קובעת כי יש לשאוב את המדגמים מאוכלוסיות בעלות שונות שוות.

ישנם שני סוגים נפוצים של ANOVA: ANOVA חד כיוונית ו ANOVA דו כיוונית. ANOVA חד כיווני משמש עבור הדגימות המסווגות לפי גורם אחד, בעוד ANOVA דו כיווני משמש כאשר שני גורמים מסווגים את הדגימות.

יתר על כן, ANOVA היא שיטה מועילה שיש לה יישומים מעשיים רחבים. זה יכול לעזור לצרכן לבחור מכונת כביסה או מקרר לאחר השוואת דגמים שונים או לעזור לסוציולוג להבחין אם הכנסתו של אדם תלויה בחינוך שלו. ANOVA משמש במדעי הסביבה כדי לקבוע את השונות ברמות הזיהום הממוצעות בין מספר גופי מים. כתוצאה מכך, ANOVA ישים באופן נרחב בתחומים כמו מדעי החיים, מנהל עסקים, מדעי החברה, מדע משפטי וכו'.
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מהי ANOVA?

ניתוח השונות - מקוצר כמו ANOVA - משמש כאשר האמצעים של שלוש דגימות או יותר צריכים להיבדק עבור שוויון.
לדוגמה...

Education

JoVE Core

Analytical Chemistry

כימיה אנליטית

Unit 1

יחידה 1

Chemical Applications of Statistical Analyses

יישומים כימיים של ניתוחים סטטיסטיים

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

מונחי מפתח ומושגים

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 should have equal variances, which means the spread of the data is similar across groups.

There are two common forms of ANOVA. One-way ANOVA is used when the samples are grouped by one factor. Two-way ANOVA is used when two factors are used to sort the samples. These forms help students see how one variable or two variables can affect group means.

ANOVA has many practical uses. A consumer can compare washing machine or refrigerator models with it. A sociologist can use it to study whether income depends on upbringing. In environmental science, it can help compare average pollution levels among several water bodies. ANOVA is also useful in life science, business administration, social science, and forensic science.

ANOVA for Comparing Sample Means

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...

statistical analysis: overview

Mean, Median, Range, Precision & Accuracy

Statistical analysis helps compare repeated measurements and judge how good the results are. When the same sample is measured again and again, small differences can appear. These differences are called errors. Researchers use statistics to describe the data and to decide whether a method is suitable. The mean and median are common ways to find the central value of a data set. The mean is the sum of all results divided by the total number of results. The median is the middle value after the...

types of errors: detection and minimization

types-of-errors-detection-and-minimization

Measurement Errors: Sources and Examples

Measurement errors are the differences between an obtained result and the true value or estimated central value. They can be written as absolute error or relative error. Absolute error is the numerical difference from the true or central value. Relative error compares that difference to the true or central value and is often shown as a percentage. Errors can also be grouped by their source, magnitude, and sign. In many experiments, the main categories are systematic, random, and gross errors.

systematic error: methodological and sampling errors

systematic-error-methodological-and-sampling-errors

Reducing Bias in Measurement Errors

Systematic errors are bias in measurement, and their sources can often be identified and reduced. In this topic, the main categories are sampling, instrumental, methodological, and personal errors. Each one comes from a different part of the experiment, so each one needs a different fix. Sampling errors happen when the sampling method is poor or when the wrong population is chosen. These errors can be reduced by improving the sampling strategy. Better sample selection helps the results...

random error

Random Error in Measurements

Random error in measurements comes from uncontrollable variables that affect data from one trial to the next. These variables can include changes in the environment, imperfections in an instrument, or the natural variation of the thing being measured. Because the direction and size of the error can change from one measurement to the next, random error is hard to predict, estimate, or describe directly. Although random error is difficult to remove, its overall effect can be studied in a large...

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...

introduction to z scores

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...

propagation of uncertainty from random error

propagation-of-uncertainty-from-random-error

How Uncertainty Changes in Calculations

Uncertainty changes as measurements move through calculations. In a multi-step experiment, each measurement adds some uncertainty. Because the steps happen one after another, the uncertainty from one step carries into the next step and affects the final result. The way uncertainty is combined depends on the math operation. For addition and subtraction, the final result is reported with absolute uncertainty. Absolute uncertainty is found as the square root of the sum of the absolute...

propagation of uncertainty from systematic error

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Atomic Mass Uncertainty in Isotope Samples

Atomic mass can vary because different samples contain different isotope ratios. For oxygen, the measured atomic mass is a weighted average of the isotopic masses in that sample. A single sample may not match the true atomic mass of oxygen found across all oxygen molecules on Earth. That creates sampling error, which is a type of systematic error. This kind of uncertainty is not random. It is tied to the system being measured. Within the uncertainty range, the chance of finding a particular...

uncertainty: confidence intervals

Confidence Intervals and Sample Size

Confidence intervals show a range of values around a sample mean that may contain the true mean. They are written as a probability percentage. A 95% confidence interval means the statistician is 95% confident that the true mean lies within that range. The two ends of the range are called confidence limits. These limits are estimated from the sample mean, the standard deviation, and the statistical factor t, or t-score. The t-score depends on the number of degrees of freedom and the confidence...

significance testing: overview

Significance Testing in Analytical Chemistry

Significance testing helps analytical chemists decide whether a difference is meaningful or just caused by random error. It is used to test whether a claim about a parameter is valid. In analytical chemistry, it mainly helps determine whether a change between two values comes from determinate error or indeterminate error. A determinate error has a clear source. It may come from a change in the measurement protocol, the analyst, or the sample itself. These changes can create a deviation from...

identifying statistically significant differences: the f-test

identifying-statistically-significant-differences-the-f-test

Comparing Variance with the F-Test

The F-test compares variance in two data sets or compares a sample variance with a population variance. It helps decide whether an indeterminate error can explain a difference in the values. In statistics, variance shows how spread out the data are. The test assumes that the data set or sets are normally distributed. It also assumes that the data sets are independent of each other. These conditions must be met before the F-test is used. The F test statistic is found by dividing one variance...

comparing experimental results: student's t-test

comparing-experimental-results-student-s-t-test

Student's t-Test for Significance Checks

Student's t-test is a statistical tool for checking whether two means are different in a meaningful way. It can compare a sample mean with a population mean, or it can compare the means from two data sets. The test uses the mean, standard deviation, and number of measurements, along with a chosen confidence interval. The test statistic is then compared with a table of critical values at that confidence level. If the test statistic is smaller than the critical value, the null hypothesis is...

detection of gross error: the q test

Using the Q Test to Flag Outlier Data

The Q test helps identify outlier data points that sit far from the rest of a data set. In high school lab work, this can help students decide whether an unusual value should stay in the data or be removed. Outliers often come from gross errors, or human mistakes, and may not reflect the real result being measured. Some points that look like outliers may still reflect a true difference in the phenomenon being studied. In those cases, a statistical test can help judge whether the value should...

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Using a Calibration Line to Find Unknowns

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calibration curves: correlation coefficient

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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...

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

difference-from-background-limit-of-detection

Limit of Detection and Quantification

The limit of detection, or LOD, is the smallest amount of analyte that can be distinguished from background noise. In measurement science, background noise is the natural signal in a sample that can interfere with the analyte signal. The LOD helps show whether a substance is present, but it does not usually give a reliable amount. The LOD is set at the concentration where the analyte signal is three times larger than the standard deviation of the blank signal. A blank is a sample without the...

quantifying and rejecting outliers: the grubbs test

quantifying-and-rejecting-outliers-the-grubbs-test

Grubbs Test for Spotting Data Outliers

The Grubbs test is a statistical way to spot a possible outlier in a data set. It is used when the data is assumed to follow a normal distribution. A Grubbs test helps decide whether one unusual numerical value should be treated as a true outlier. To run a two-tailed Grubbs test, first find the absolute difference between the questionable value and the mean. Then divide that difference by the sample standard deviation. The result is the Grubbs statistic, or G. Next, compare the calculated G...

what is anova?

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 ANOVA compares the means of three or more samples, the assumptions it needs, and the difference between one-way and two-way ANOVA.

ANOVA for Comparing Sample Means | JoVE K12

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Systematic errors, depending on their source, are of four types &#8211; sampling, instrumental, method, and personal errors.
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Random Error

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Since these errors can neither be predicted nor ...

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The uncertainty reflects the possible range of values in which the result of a measurement can exist.
However, uncertainty varies from error, which is the ...

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CHEM.2.B

SI Units: 2019 Redefinition

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An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...

Standard Deviation of Calculated Results

A plot of relative deviation from the mean and its frequency of occurrence appears as a Gaussian curve. This probability distribution curve of a ...

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Is the difference between the two values due to an unexplainable random error or a systematic error that can be rationalized by a hypothetical model?
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The influence of changing the method, the sample, or the analyst on the analysis results is studied by altering only one in a pair of experiments.
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The analysis of variance&#8212;abbreviated as ANOVA &#8212;is used when the means of three or more samples need to be tested for equality.
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Scientific and engineering practices. The student analyzes and interprets data to derive meaning, identify features and patterns, and discover relationships or correlations to develop evidence-based arguments or evaluate designs. The student is expected to:

ANOVA for Comparing Sample Means

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