Name: using the q test to flag outlier data
Uploaded: 2024-04-04T10:51:12.000Z
Duration: 1 min
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.2

CHEM.2.C

Detection of Gross Error: The Q Test

חריגים הם נקודות נתונים שונות מאוד משאר ערכת הנתונים.
מבחן Q של דיקסון הוא מבחן מובהקות המסייע לקבוע אם לשמור או לדחות נקודות נתונים לא עקביות אלה במערך הנתונים.
מבחינה מתמטית, סטטיסטיקת מבחן Q היא היחס בין ההפרש המוחלט בין החריג לנקודת הנתונים הקרובה ביותר שלו לבין טווח האוכלוסייה.
לאחר מכן, משווים את הסטטיסטיקה של מבחן Q או את מנת הדחייה לערך Q הקריטי עבור רמת מובהקות מסוימת ודרגות חופש מסוימות.
כאשר מנת הדחייה שווה או גדולה מהערך הטבול, השערת האפס נדחית, וניתן לדחות את החריגה החשודה.
נהפוך הוא, השערת האפס מתקבלת כאשר ערך הניסוי קטן מערך Q הטבול. לאחר מכן, יש לשמור את החריגה החשודה בערכת הנתונים.

איתור שגיאה גסה: מבחן ה-q

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כאשר נקודת נתונים אחת או יותר מופיעות רחוק משאר הנתונים, יש צורך לקבוע האם הן חריגות והאם יש לבטל אותן ממערך הנתונים כדי להבטיח ייצוג מדויק של הערך הנמדד. במקרים רבים, חריגים נובעים מטעויות גסות (או טעויות אנוש) ואינן משקפות במדויק את התופעה הבסיסית. עם זאת, במקרים מסוימים, החריגים לכאורה הללו משקפים הבדלים פנומנולוגיים אמיתיים. במקרים אלה, אנו יכולים להשתמש בשיטות סטטיסטיות כדי לעזור לקבוע אם לשמור על החריג. שיטה סטטיסטית שיכולה לעזור לנו לשמר או לדחות חריגים נקראת מבחן Q. כדי לבצע את מבחן ה-Q, תחילה אנו מסדרים את הערכים במערך נתונים לפי סדר הגדלה של הערך. לאחר מכן, אנו מחשבים את ערך Q על ידי נטילת היחס בין ההפרש המוחלט בין נקודת נתונים לנקודת הנתונים הסמוכה לה. ערך Q זה מושווה לאחר מכן עם ערך ה-Q הקריטי המוצג בטבלה ברמת מובהקות נבחרת ובדרגות חופש מתאימות. אם ערך ה-Q שווה או עולה על ערך ההתייחסות Q בטבלה, נקודת הנתונים נחשבת חריגה ולכן נדחתה ממערך הנתונים. כאן, סביר להתעלם מנקודת הנתונים כחריגה מכיוון שלא ניתן להסביר באופן הגיוני את גודל הסטייה על ידי שגיאות אקראיות (בלתי מוגדרות). מצד שני, אם ערך ה-Q קטן מערך הייחוס בטבלה, יש לשמור את נקודת הנתונים, והפרשנות היא שההבדל בין נקודת הנתונים הזו לשאר הנתונים הוא בגדר ציפייה סבירה (סטטיסטית).
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איתור שגיאה גסה: מבחן ה-Q

חריגים הם נקודות נתונים שונות מאוד משאר ערכת הנתונים.
מבחן Q של דיקסון הוא מבחן מובהקות המסייע לקבוע אם ...

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

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 be kept or rejected. The Q test provides that check by comparing a suspect point with the rest of the ordered data.

To perform the Q test, the values are first arranged in increasing order. Next, the Q value is calculated as the ratio of the absolute difference between a data point and its adjacent data point. That Q value is then compared with the tabulated critical Q value for a chosen significance level and the correct degrees of freedom.

If the calculated Q value is equal to or greater than the table value, the point is treated as an outlier and rejected from the data set. In that case, the deviation is considered too large to be explained by random, indeterminate errors. If the Q value is smaller than the reference value, the point is retained because the difference is within normal statistical expectation.

Using the Q Test to Flag Outlier Data

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detection of gross error: the q test

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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key terms and concepts

Learn how the Q test helps students identify outlier data, compare a suspected value to a critical table value, and decide whether to keep or reject it.

Using the Q Test to Flag Outlier Data | JoVE K12

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Using the Q Test to Flag Outlier Data

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