1.21
이상치 수량화 및 거부: 그럽스 검사
때로는 자료 세트에 나머지 자료와 크게 다른 기록된 수치 관찰이 있을 수 있습니다. 자료가 정규 분포를 따른다고 가정하면 그럽스 검사라는 통계적 방법을 사용하여 관찰이 실제로 이상값인지 여부를 확인할 수 있습니다. 양측 그럽스 검사를 수행하려면 먼저 이상값과 평균 간의…
Dixon의 Q-검정과 마찬가지로 Grubbs의 검정은 정규 분포를 사용하여 데이터의 이상값을 식별하는 통계 검정입니다. 여기서 관측치의 수는 7개 이상이어야 합니다.
주어진 데이터 세트에 대해 이 테스트에는 Grubbs의 통계량 G가 포함되며, 이는 문제가 될 수 있는 값과 표본의 표준 편차에 대한 평균값 간의 절대 차이의 비율입니다.
그런 다음 계산된 G 값을 주어진 신뢰 수준 및 관측치 수에 대한 표로 작성된 G의 임계값과 비교합니다.
계산된 G 값이 G의 임계값을 초과하면 문제가 되는 관측치는 데이터의 이상치로 간주되어 기각됩니다.
또는 계산된 G 값이 G의 임계값보다 작으면 데이터는 의심스러운 관측치를 유지합니다.
View the full transcript and gain access to JoVE Core videos
Q1: What is the Grubbs test used for in analytical chemistry?
The Grubbs test is a statistical method for identifying outliers in normally distributed data sets. It determines whether a questionable observation that greatly deviates from the rest of the data is truly an outlier or should be retained. This test requires a minimum of seven observations and compares a calculated statistic against a critical value to make the rejection decision.
Q2: How do you calculate the Grubbs statistic G?
The Grubbs statistic G is calculated as the ratio of the absolute difference between the questionable value and the mean to the standard deviation of the sample. First, subtract the mean from the suspected outlier and take the absolute value. Then divide this difference by the sample's standard deviation. This G value is then compared with the tabulated critical value to determine if rejection is warranted.
Q3: When should you reject an observation using the Grubbs test?
An observation is rejected as an outlier when the calculated G value exceeds the critical value of G for your specified confidence level and number of observations. Conversely, if the calculated G value is smaller than the critical G value, the questionable observation is retained in the data set. The critical value serves as the threshold for making this rejection decision.
Q4: What are the minimum requirements for applying the Grubbs test?
The Grubbs test requires that your data set contains at least seven observations and follows a normal distribution. The test assumes the data is normally distributed before you calculate the Grubbs statistic. Meeting these prerequisites ensures the statistical validity of your outlier detection and rejection analysis.
Q5: How does the Grubbs test differ from Dixon's Q-test?
Both the Grubbs test and Dixon's Q-test are statistical methods for identifying outliers in normally distributed data. While the transcript mentions they serve similar purposes, the Grubbs test specifically calculates a ratio of the absolute difference between the questionable value and mean to the standard deviation, then compares it against tabulated critical values for a given confidence level.
Q6: What role does confidence level play in the Grubbs test?
The confidence level determines which critical value of G you use for comparison with your calculated G statistic. Different confidence levels yield different critical values from statistical tables. Your choice of confidence level affects whether a questionable observation is rejected or retained, making it a crucial parameter in the outlier detection decision.
Q7: Why is the Grubbs test limited to normally distributed data?
The Grubbs test assumes data follows a normal distribution because the statistical theory underlying the test relies on this assumption. The calculation of the Grubbs statistic and the critical values in reference tables are derived based on normal distribution properties. Applying the test to non-normally distributed data would compromise the validity of your outlier detection results.