Running head: DATA SCREENING
Data Screening
Belinda Richard
School of Community Care and Counseling- Traumatology
Liberty University
DATA SCREENING BASICS 2
Data Screening – Non-normal distributions
Frequency distributions, when graphed, show the shape of the data. One of many ways of
visualizing these is by graphing data points using histograms or bar charts, depending on the type
of data. It is fair to note that the normal distribution is the most well-known, and is more taught
than others in Statistics. In reality however, statistical data can take many other forms aside from
the normal distribution. In fact, Bono et al. in a study of distributions found that “only 5.5% of
the distributions [observed] were close to the expected values under normality” (2017, p. 2). A
few examples of non-normal distributions that researchers can encounter include the uniform,
exponential, binomial, Poisson, and triangular distributions.
There are several other distributions in existence, we’ve just named a few of those that
are well-known. Each of these distributions are extremely useful for modeling different real-life
scenarios, and statisticians need to be careful while working with them. A researcher must make
sure the data matches the model they’re working with. According to Krithikadatta (2014), tests
such as the Shapiro-Wilk, Anderson-Darling, or the Kolmogonov-Smirnov can be used to
determine if data is normally distributed (p. 96). If the data fails the tests mentioned prior, there’s
still hope of using the normal distribution to describe the data. Sainani notes that non-normal
data can be transformed in many ways. An example of this would be taking a log transformation
or a square root of the data, leading it to it satisfying the assumptions for normalcy. Sainani
writes: “For example, for skewed distributions, taking a natural log is often sufficient to remove
the right or left tail (because logs rein in extreme values)” (2012, p. 1003). A log transformation
could fix skewness! In such an instance, researchers can still use z scores and the standard
normal distribution to model the data even though it’s technically not normal.
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Researchers don’t always carry out the tests mentioned in the previous paragraph. A large
number of statistical practitioners suggest visualizing the data first. If the data gathered appears
normal when graphed, then a normal distribution is assumed to describe the population; If the
data is not normal and is maybe uniform, then a uniform distribution and its assumptions should
be used (or whatever distribution the data seems to follow). In practice, one simply cannot take a
population that is uniformly distributed for example, and treat it like a normal distribution. In the
absence of transformations, this would result in the population being misrepresented, and the
inferences made from such analyses would be misleading. Therefore, it does not make sense for
a researcher to use z scores and standard normal tables for data that follows another distribution;
that defeats the whole purpose of performing this type of analysis which per Warren is to
“generalize the results obtained from a sample to make inferences about outcomes that might
conceivably occur in some larger population.” (2013, p.2).
One of the aforementioned distributions, the uniform distribution, is quite common. As
an example of this, Warner says “the distribution of number of births across days of the week…
is approximately uniform” (2013, p. 14). We do not expect more children to be born on
particular days of the week, since the day a Child comes out is quite random and unpredictable;
this is something beyond our control. In a world with 8 billion people, we cannot expect to see
significant differences in births on certain days of the week. The uniform distribution is best
visualized in a bar chart and is shown to have a flat shape with each bar roughly the same height,
unlike the bell-shaped normal distribution.
Fig 1 in the appendix is the result of simulating a die roll 10,000 times in Excel. A
uniform distribution can be generated by simply using Excel’s RANDBETWEEN function. “For
example, to generate a population between 120 and 180, use RANDBETWEEN(120, 180)”
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(Sethi, 2015, p.3). Fig 1 was created using the same method stated by Sethi, Excel was used to
simulate a random number between 1 and 6. This was done 10,000 times, then a count was taken
for each occurrence and graphed. As one can observe from the graph, each outcome has roughly
an equal probability of occurring. When a 6-sided die is rolled, the probability of getting any roll
between 1 through 6 is equal with every roll (1/6), this explains the flat nature of the distribution.
Another common, yet interesting distribution to touch on is the binomial distribution.
Anderson et al. (2020), describe this distribution as one which has “n” independent trials, each of
which has the same possible two outcomes, a probability of success (p) and a probability of
failure (1-p) (p. 242). The most frequently utilized example of a binomial distribution is a coin
toss. There are only two possible outcomes: head or tail. Here, the researcher gets to define either
of the outcomes as a success or a failure and then performs the trials. With each independent
trial, the probability of the coin landing on either side is ½. Knowledge of this distribution could
come in handy for certain games in casinos, for example.
Data Screening – Non-normal distributions
In practice, data collection is often a tedious undertaking for a myriad of reasons. Human
error and other unusual circumstances could cause issues with the data such as incorrect
information, missing values, outliers, and more. Data screening is an extremely important aspect
of the data analysis process. According to Warner, individuals conducting research “should
conduct thorough preliminary data screening to identify and remedy potential problems with
their data prior to running the data analyses that are of primary interest” (2013, p. 168). In other
words, these issues need to be resolved or else they could misconstrue the interpretation of data,
thereby making it not representative of the population.
DATA SCREENING BASICS 5
Per Mowbray, “A univariate outlier is a case with an extreme value that falls outside the
expected population values for a single variable” (2019, p. 21). An outlier is typically far away
from the central tendency of the data, and thus isn’t a good proxy to include while trying to
represent the population. Leys et al. (2019) outline that the cutoff for determining outliers in
psychological studies is to look for numbers that are more than 3 standard deviations away from
the mean. According to Leys et al., “99.7% of observations fall within 3 standard deviations” (p.
4). This does not only apply in psychological studies, but in all types of statistical analyses under
the normal distribution.
Contrary to Leys et al., Kwak & Kim find the 3 standard deviation cutoffs to be
inadequate, since the standard deviation and mean are both impacted by the presence of the
outliers. In other words, these outliers were inputs while calculating both values, and thus the
values do not provide an accurate representation. They believe that “the median and quartile
range are more useful because these statistics are less sensitive to outliers” (2017, p. 409). Lastly,
the authors suggest visualizing the data using boxplots in order to get a clear view of outliers that
fall outside the quartile ranges. They are right in the sense that outliers are represented as
individual points separate from the rest of the data.
Aside from outliers, dealing with missing values is a constantly recurring phenomenon
that researchers often face. There are several ways in which missing values occur. They could
occur as a result of survey participants accidentally or purposely not filling out information, or
due to loss of data from mishandling, corruption of files, and more. According to Rustum et al.
(2007), missing values can be replaced by using the mean/median of the data or running a linear
regression and using that to fill in the values. However, these estimators only work when there
are a few missing values (p. 910). The last statement reiterates a point that was emphasized in
DATA SCREENING BASICS 6
earlier class discussions about the importance of sample size. With large sample sizes, the
researcher doesn’t face much pressure to deal with outliers in a certain way. A large enough
sample size could allow researchers to eliminate both outliers and missing values without any
noticeable tradeoffs.
At this stage of the research, a lot of decisions fall to the discretion of the researcher.
Whether to delete, replace, or transform the data entirely to account for outliers depends on a
number of factors. Again, with a large enough sample, it’s not even worth the hassle to try and
fix outliers or even missing data, since the impact of a few points would be infinitesimal.
However, when the luxury of an excessively large sample size isn’t there, it is still sometimes
necessary to delete participants when their responses don’t make sense. This is true because
statistical analyses are only as good as the data used to obtain them.
Warner provides an example of a research question where there are four possible answers
on a scale (1,2,3,4). If a respondent inputs a number higher than 4 in this case, it could be argued
that this data needs to be removed (p. 178). This makes sense, because there may be no way to
know why a higher number was entered, and it doesn’t correspond to any of the values allowed.
In fact, Mowbray says the safest way to handle outliers is by eliminating the particular response,
or the entire variable in cases where numerous bad responses exist (p. 35).
In certain instances, for outliers, using trimmed means (dropping a fixed percentage of
data from each end of the data prior to calculating the mean) to describe the central tendency,
and other estimators of dispersion such as the MAD is a good fix (p. 910). This supports Kwak &
Kim in their assertion that the 3 standard deviation rule is not reliable. Trimming off the outliers
eliminates the opportunity for non-representative data to influence the study in anyway;
however, it could be tricky to determine how much to trim. The truth is, there is no universal rule
DATA SCREENING BASICS 7
that works for every single scenario. Statisticians need to sit down and rationalize why a certain
approach should be taken, while taking every bit of detail into consideration.
Managing outliers and missing values is a tricky endeavor that requires researchers to
take a close look at the impact based on the sample size, how representative/nonrepresentative
the outlier is, and the overall validity of the entire undertaking.
DATA SCREENING BASICS 8
References
Warner, R. M. (2013). Applied statistics: From bivariate through Multivariate Techniques.
SAGE Publications.
Bono, R., Blanca, M. J., Arnau, J., & Gómez-Benito, J. (2017). Non-normal distributions
commonly usedvin health, education, and social sciences: A systematic
review.NFrontiers in psychology,N8, 1602.
Krithikadatta, J. (2014). Normal distribution.NJournal of conservative dentistry: JCD,N17(1), 96.
Sethi, A. P. (2015). Use of Excel in statistics: Problem solving vs. problem
understanding.NInternational Journal on Integrating Technology in Education,N4(4).
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., Fry, M. J., &
Ohlmann, J. W. (2020). Essentials of modern business statistics with Microsoft Excel (8th
ed.). Cengage.
Mowbray, F. I., Fox-Wasylyshyn, S. M., & El-Masri, M. M. (2019). Univariate outliers: a
conceptual overview for the nurse researcher. Canadian Journal of Nursing Research,
51(1), 31-37.
Kwak, S. K., & Kim, J. H. (2017). Statistical data preparation: management of missing values
and outliers.NKorean journal of anesthesiology,N70(4), 407-411.
Rustum, R., & Adeloye, A. J. (2007). Replacing outliers and missing values from activated
sludge data using Kohonen self-organizing map.NJournal of Environmental
Engineering,N133(9), 909-916.
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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.NInternational Review of Social Psychology,N32(1).
Sainani, K. L. (2012). Dealing with non-normal data.NPm&r,N4(12), 1001-1005.
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Appendix
Fig 1:
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Simulation (10,000 rolls of a Die)
Die Roll
# of Occurrences
