Name: comparing variance with the f-test
Uploaded: 2024-04-04T10:51:12.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.2

CHEM.2.C

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

Identifying Statistically Significant Differences: The F-Test

F-критерий проверяет, не слишком ли велика разница между двумя вариациями, чтобы ее можно было объяснить неопределенной ошибкой. Он сравнивает дисперсию выборки и популяции или дисперсию двух выборок.
F-критерий основан на нулевой гипотезе, которая гласит, что две сравниваемые дисперсии равны.
Тестовая статистика F оценивается как частное дисперсии, где дисперсия выражается как квадрат стандартного отклонения.
Дисперсия с большим значением помещается в числитель, что делает F больше или равно единице всегда.
Значение F должно быть равно единице, чтобы нулевая гипотеза была верна. Она становится больше единицы из-за неопределенных и определенных ошибок.
Для одностороннего теста полученное значение F сравнивается с табличным значением F при выбранном уровне достоверности и степени свободы. Нулевая гипотеза отвергается, когда полученное значение F меньше табличного значения F в тесте с низким одним хвостом или больше в тесте с одним верхним хвостом.

Выявление статистически значимых различий: f-тест

F-тест используется для сравнения двух выборочных дисперсий друг с другом или сравнения выборочной дисперсии с генеральной дисперсией. Он используется для того, чтобы решить, может ли неопределенная ошибка объяснить разницу в их значениях. Основные предположения, которые позволяют использовать F-тест, включают в себя то, что набор или наборы данных нормально распределены, а наборы данных независимы друг от друга. Тестовая статистика F рассчитывается путем деления одной дисперсии на другую. Другими словами, квадрат одного стандартного отклонения на квадрат другого. Чтобы получить значение единицы или больше единицы в результате отношения, большее значение всегда делится на меньшее значение.

Нулевая гипотеза F-теста утверждает, что соотношение равно 1. После расчета статистики теста она сравнивается с табличными критическими значениями F при выбранном уровне достоверности и соответствующей степени свободы. Нулевая гипотеза принимается, если тестовая статистика F меньше табличного значения F. В этом случае отличие от желаемого значения единицы – если оно вообще имеется – оправдывается неопределенной ошибкой, и мы утверждаем, что изменения существенно не отличаются.

Выявление статистически значимых различий: F-тест

F-критерий проверяет, не слишком ли велика разница между двумя вариациями, чтобы ее можно было объяснить неопределенной ошибкой. Он сравнивает дисперсию выборки и...

Education

JoVE Core

Analytical Chemistry

Аналитическая химия

Unit 1

Раздел 1

Chemical Applications of Statistical Analyses

Применение статистического анализа в химии

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 by another. That means one standard deviation is squared and divided by the square of the other standard deviation. To get a value of one or greater than one, the larger variance is always divided by the smaller variance.

The null hypothesis for the F-test states that the ratio is equal to 1. After the test statistic is calculated, it is compared with tabulated critical F values at a chosen confidence level and the correct degree of freedom. If the test statistic F is smaller than the tabulated F value, the null hypothesis is rejected. In that case, any difference from unity is explained by indeterminate error, and the variations are not considered significantly different.

Comparing Variance with the F-Test

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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...

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Learn how the F-test compares variances, checks normality and independence, and uses critical F values to judge whether differences are significant.

Comparing Variance with the F-Test | JoVE K12

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Comparing Variance with the F-Test

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