When conducting an independent-samples t-test, one fundamental assumption is that the data for each group follow a normal distribution. It is crucial to recognize that the t-test relies heavily on the assumptions underlying the data distribution. The validity of the t-test results hinges on the assumption that the data meet specific criteria (Hayes, 2023). When faced with data that deviates significantly from a typical distribution, especially with limited sample sizes like 10 per group, the reliability of t-test results can be compromised. Outliers or non-normal distributions can distort the calculation of averages and spreads, potentially leading to flawed interpretations.
To address this concern, several strategies can be employed, including data trimming, outlier removal, nonparametric tests, and sample size augmentation. Trimming entails removing a specified proportion of extreme values from a data set to reduce the impact of outliers on the average (Firdose, 2023). Nevertheless, while this technique can help mitigate the influence of outliers, it may omit crucial information and be unsuitable if the outliers are significant.
Removing outliers completely can improve overall data distribution, but determining which data points are outliers can be difficult. Bias may arise when using this method if outliers are an inherent component of the population’s variation (Firdose, 2023). In contrast, nonparametric tests such as the Mann-Whitney U test can be employed because they do not depend on the normality assumption. It is important to acknowledge that nonparametric tests generally have lower statistical power than parametric tests.
Increasing the sample size can help to mitigate the impact of outliers, as supported by the central limit theorem. This theorem suggests that as the sample size increases, the sample mean will more closely approximate a normal distribution (Ganti, 2024). Nonetheless, collecting additional data can be time-consuming and expensive. The act of trimming data or removing outliers can introduce bias and reduce the quantity of data available for analysis. This problem is exacerbated when dealing with small sample sizes. It is imperative for researchers to thoughtfully evaluate the best approach given the unique research scenario and potential constraints.
References
Firdose, T. (2023). Understanding outliers: Impact, detection, and remedies. Medium.
Ganti, A. (2024). Central limit theorem (CLT): Definition and key characteristics. Investopedia.
Hayes, A. (2023). T-test: What it is with multiple formulas and when to use them. Investopedia.