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

מבחן F בודק אם ההבדל בין שתי שונות גדול מכדי להיות מוסבר על ידי שגיאה לא מוגדרת. הוא משווה את השונות של מדגם ושל אוכלוסייה או את השונות של שני מדגמים.
מבחן F מבוסס על השערת האפס, הקובעת כי שתי השונות שהושוו שוות.
סטטיסטיקת הבדיקה F מוערכת כמנת השונות, כאשר השונות מבוטאת כריבוע סטיית התקן.
השונות עם ערך גדול יותר ממוקמת בנומרטור, מה שהופך את F לגדול או שווה לאחד תמיד.
ערך F צריך להיות ערך כדי שהשערת האפס תהיה נכונה. זה הופך להיות גדול יותר מאחד עקב שגיאות לא מוגדרות ומוגדרות.
עבור מבחן חד-זנבי, ערך ה-F המתקבל מושווה לערך F המחושב ברמת ביטחון ומידת חופש נבחרת. השערת האפס נדחית כאשר ערך ה-F המתקבל נמוך מערך ה-F בטבלה במבחן חד-זנבי תחתון או גדול יותר במבחן חד-זנבי עליון.

זיהוי הבדלים מובהקים סטטיסטית: מבחן ה-f

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מבחן F משמש להשוואת שתי שונות מדגם זו לזו או להשוות את שונות המדגם לשונות האוכלוסייה. הוא משמש כדי להחליט אם שגיאה בלתי מוגדרת יכולה להסביר את ההבדל בערכים שלהם. ההנחות הבסיסיות המאפשרות את השימוש במבחן F כוללות את מערך הנתונים או את מערכי הנתונים מופצים באופן נורמאלי, ומערכי הנתונים אינם תלויים זה בזה. נתון המבחן F מחושב על ידי חלוקת שונות אחת באחרת. במילים אחרות, הריבוע של סטיית תקן אחת בריבוע של השני. כדי לקבל ערך של אחד או גדול מאחד כתוצאה מהמנה, הערך הגדול מחולק תמיד בערך הקטן יותר.

השערת האפס של מבחן F קובעת כי היחס שווה ל-1. לאחר חישוב נתון המבחן, הוא מושווה לערכי ה-F הקריטיים המוצגים בטבלה ברמת ביטחון נבחרת ובדרגת החופש המתאימה. השערת האפס מתקבלת אם נתון המבחן F קטן מערך F המופיע בטבלה. במקרה זה, ההבדל מהערך הרצוי של אחדות - אם בכלל - מוצדק בשגיאה בלתי מוגדרת, ואנו קובעים שהווריאציות אינן שונות באופן משמעותי.

זיהוי הבדלים מובהקים סטטיסטית: מבחן ה-F

מבחן F בודק אם ההבדל בין שתי שונות גדול מכדי להיות מוסבר על ידי שגיאה לא מוגדרת. הוא משווה את השונות של מדגם ו ...

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

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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key terms and concepts

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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