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Data Basics
Percentile Rank
It does not make sense for a researcher to find the percentile rank using the z-score and
the standard normal distribution table if the empirical frequency distribution is extremely non-
normal. Calculating percentiles with z-scores assumes a normal distribution, as z-scores are often
linked to normal curves (Warner, 2020). Suppose data is extremely non-normal; using z-scores is
inappropriate as the z-score calculation assumptions are violated (Siebert & Siebert, 2018). In
such cases, percentiles should be directly computed from observed data without assuming
normality. In extremely non-normal cases, researchers should avoid normality assumptions and
opt for nonparametric methods that do not make normality assumptions (Warner, 2020).
Bimodal Distributions
Bimodal distributions have two distinct peaks or modes, indicating the presence of two
different groups or subpopulations within the data. Bimodal distributions can occur when two
underlying processes or groups are being measured. For example, if a researcher measures the
heights of a population, including adults and children, they might observe a bimodal distribution.
Bimodal distributions have a significant number of their observations far from the center. They
also have more negative kurtosis values than heavy-tailed distributions like the t distribution.
Bimodal distributions occur in research when studying phenomena divided into distinct groups,
such as high and low-income ranges, males versus females, young versus old, and other such
phenomena.
Skewed Distribution
Skewed distributions are asymmetrical and have a long tail on one side due to data points
that are unevenly distributed around the central point. One side has a longer tail, while the other
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has a shorter tail (Warner, 2020). Negative (left) skew indicates a longer, thinner tail on the left
side of the distribution, whereas positive (right) skew refers to a longer or thinner tail on the
right. These skews describe the direction and weight of the distribution. Skewed distributions
occur in research when studying events or behaviors that have many responses, such as the
number of states people have visited, how many siblings a person has, or how many pairs of
shoes a person owns. The variables in these scenarios can range from the lowest value of 0 to
large numbers that would result in a skewed distribution shape (Warner, 2020).
Absence of Data Screening
Recognizing and addressing errors is crucial in the scientific process, leading to the
principle that science corrects itself (Brown et al., 2018). Conversely, if errors are not
acknowledged and rectified, science cannot genuinely embody this self-correcting principle,
which has been extensively debated. Some argue that errors are necessary for the progress of
science, as adhering strictly to established thinking and methods constrains the growth of
knowledge. One of the most significant issues that stem from an absence of data screening is
missing outliers. An outlier is an erroneous or significantly skewed sample that significantly
deviates from most samples in the calibration set (Menezes et al., 2009). Without proper
screening, erroneous or outlying data points may go unnoticed, leading to inaccuracies in the
dataset.
The data might have missing values or inconsistencies, affecting its overall quality.
Unidentified outliers can distort statistical analyses, influencing central tendency and dispersion
measures. Skewed or non-normally distributed data may violate assumptions of specific
statistical tests, affecting the validity of the results (Knief & Forstmeier, 2021). Flawed data can
lead to incorrect conclusions and interpretations, undermining the reliability of the study's
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findings (Brown et al., 2018). In extreme cases, it may result in misidentifying trends or
relationships within the data.
Quantitative Rule for Univariate Outliers
The legitimacy of an outlier case can be assessed using the Interquartile Range (IQR), which
measures its distance from the central or middle value. The 1.5(IQR) Rule classifies an outlier as
a univariate outlier if its value falls at least 1.5 times the length of the IQR box beyond either
side of the box's edge (Mowbray et al., 2018). If a case value falls between 1.5 and 3 times
beyond the length of the IQR in either direction, it is considered a mild outlier. In contrast, any
value surpassing three times the length of the IQR box is identified as an extreme outlier.
Established guidelines for managing errors, genuine missing data, and extreme values are
integral to best practices (Van den Broeck et al., 2005).
Degrees of Freedom refers to a researcher's ability to determine how they want to analyze
their data, manage errors, and address missing data. This analysis can include deleting or
omitting a case/participant for the sake of their research (Leys et al., 2019). Degrees of freedom
allow researchers to modify their data if they have cases where a value significantly deviates
from the overall pattern (an extreme outlier). Extreme outliers may be candidates for removal,
especially if they are suspected to be due to errors or anomalies (Frost, 2019). If outliers violate
assumptions and alternative methods are not appropriate, excluding outliers may be considered.
Removing cases may be justified in maintaining data integrity if there is evidence of data
entry mistakes that cannot be corrected and will influence the analysis. If participants fail to
adhere to the study protocol and their data is deemed unreliable or invalid due to non-
compliance, excluding their data may be justified (McCoy, 2017). While there are circumstances
where deleting a case is justified, it is essential to exercise caution and transparency in such
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References
Brown, A. W., Kaiser, K. A., & Allison, D. B. (2018). Issues with data and analyses: Errors,
underlying themes, and potential Solutions. Proceedings of the National Academy of
Sciences, 115(11), 2563–2570. https://doi.org/10.1073/pnas.1708279115
Frost, J. (2019, October 23). Guidelines for Removing and Handling Outliers in Data - Statistics
By Jim. Statistics by Jim. https://statisticsbyjim.com/basics/remove-outliers/
Knief, U., & Forstmeier, W. (2021). Violating the normality assumption may be the lesser of two
evils. Behavior Research Methods, 53. https://doi.org/10.3758/s13428-021-01587-5
Leys, C., Delacre, M., Mora, Y. L., Lakens, D., & Ley, C. (2019). How to classify, detect, and
manage univariate and multivariate outliers, with emphasis on pre-
registration. International Review of Social Psychology, 32(1).
https://doi.org/10.5334/irsp.289
McCoy, E. (2017). Understanding the Intention-to-treat principle in randomized controlled
trials. Western Journal of Emergency Medicine, 18(6), 1075–1078.
https://doi.org/10.5811/westjem.2017.8.35985
Menezes, J. C., Ferreira, A. P., Rodrigues, L. O., Brás, L. P., & Alves, T. P. (2009). Chemometrics
role within the PAT context: Examples from primary pharmaceutical
manufacturing. Comprehensive Chemometrics, 313–355. https://doi.org/10.1016/b978-
044452701-1.00012-0
Mowbray, F. I., Fox-Wasylyshyn, S. M., & El-Masri, M. M. (2018). Univariate outliers: A
conceptual overview for the nurse researcher. Canadian Journal of Nursing
Research, 51(1), 31–37. https://doi.org/10.1177/0844562118786647
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Siebert, C. F., & Siebert, D. C. (2018). Data analysis with small samples and non-normal data:
Nonparametric and other strategies. Oxford University Press.
Van den Broeck, J., Argeseanu Cunningham, S., Eeckels, R., & Herbst, K. (2005). Data cleaning:
Detecting, diagnosing, and editing data abnormalities. PLoS Medicine, 2(10), e267.
https://doi.org/10.1371/journal.pmed.0020267
Warner, R. M. (2020). Applied Statistics I (3rd ed.). SAGE Publications, Inc. (US).
https://mbsdirect.vitalsource.com/books/9781506352817
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