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Biostatistics and Bioaerosols
Published in Harriet A. Burge, Bioaerosols, 2020
Lynn Eudey, H. Jenny Su, Harriet A. Burge
One simple measure of the dispersion in the data is the range. The range is the number of units needed to span the data. As this is easily influenced by either extremely high or extremely low values, a more reliable measure is the inner quartile range (IQR) which is the number of units needed to span the middle 50% of the data. Note that, for either of these measures, we need to first order the data (as we did for the median). A percentile is a way to locate a data value relative to the rest of the data set or relative to another data set. For example, 95% of the data lies at or below the 95th percentile. The median is the 50th percentile, and the 25th, 50th, 75th percentiles are called the 1st, 2nd, and 3rd quartiles, respectively because they divide the data set into quarters. So now we can define the inner quartile range as: IQR = 3rd quartile – 1st quartile. The box plot (Figure 13.5) shows (from inside to outside) the median, the first and third quartile (within the box), the range of data falling within the inner fence (the whiskers), and data falling beyond the inner fence (open circles). The box part is drawn from the first quartile to the third quartile. The inner fences are a distance of 1.5 IQRs out from the quartiles.
Statistics for Quality
Published in K. S. Krishnamoorthi, V. Ram Krishnamoorthi, Arunkumar Pennathur, A First Course in Quality Engineering, 2018
K. S. Krishnamoorthi, V. Ram Krishnamoorthi, Arunkumar Pennathur
The S&L diagram drawn as above helps in identifying the ordered rank of values in the data, the rank of a value when the data are ordered in an ascending order and makes it easy to compute the percentiles of the distribution. A percentile is the value below which a certain percentage of the data lies. We denote the p-th percentile by Xp to indicate that p% of the data lies below Xp. Thus, X25 and X75 represent the 25th and 75th percentiles, respectively, below which 25% and 75% of the data lie. The following names and notations are also used for these percentiles: X25 is called the “first quartile” and is denoted as Q1.X50 is called the “second quartile” or “median” and is denoted as Q2 or X˜.X75 is called the “third quartile” and is denoted as Q3.
Research Methods in Human Factors
Published in Robert W. Proctor, Van Zandt Trisha, Human Factors in Simple and Complex Systems, 2018
Robert W. Proctor, Van Zandt Trisha
As implied by the name, descriptive statistics describe or summarize the results of research. One concept that is fundamental to descriptive statistics is that of the frequency distribution. When we obtain many measurements of a variable, we can organize and plot the frequencies of the observed values. For example, if we have a group of people estimate the mental workload imposed by a task on a scale of 1–7, we can record the number of people who responded with each value. This record of the frequency with which each score occurred is a frequency distribution. A frequency distribution often is plotted in the form of a frequency polygon, as is shown in Figure 2.3. A relative frequency distribution, also shown in the figure, displays the same plot on the scale of the proportion (or percentage) of times that each score was observed. We can describe a score in terms of its percentile rank in the distribution. A percentile is a point on a measurement scale below which a specified percentage of scores falls. The percentile rank is the percentage of scores that falls below that percentile. We use percentile ranks for, among other things, creating tables of anthropometric data and applying these data in the design of equipment for human use.
DDoS Attacks Detection in 5G Networks: Hybrid Model with Statistical and Higher-Order Statistical Features
Published in Cybernetics and Systems, 2023
Percentile (Esmael et al. 2012): In statistics, a percentile is a score below which a given percentage of scores in its frequency distribution falls or a score at or below which a given percentage falls. This gives technique of “how the data values are spread over the interval from the smallest value to the largest value”. A little over % of data values fall beneath the percentile, but around of data values surpass the percentile. denotes percentile characteristics. depicts higher order statistical feature, and this was provided by Eq. (7).
Measures, Metrics, and Indicators for Evaluating Technology-Based Interventions
Published in International Journal of Human–Computer Interaction, 2023
Eva L. Baker, Harold F. O’Neil
This approach to quantification was developed early in the 20th century as early statistical approaches were developed for NRTs, including standard scores and percentiles (Spearman, 1904). This method was sensible for the purposes of the measures developed at that time. For the most part, measures were used to identify (or select) individuals who were unsuitable for immigration or likely to be acceptable for military service (Baker et al., 2016). The method persists with measures of selection or assignment to program, including the SAT, the ACT, and the Armed Services Vocational Aptitude Battery (ASVAB), all of which use norm-referenced methods for interpreting scores. When converted to percentiles, the respondent knows explicitly how their score compares to others, e.g., a percentile score of 72 means one has a score higher than 72% of the distribution. For the most part, the field of psychometrics has been focused on normative approaches.
4D dynamic system for visual-motor integration analysis
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
In this study, we conducted three tests sequentially according to the detailed guidelines presented and scored the test results by referring to the scoring criteria. The scoring criteria are different for each figure, and if applicable, it is scored one point plus for each figure. From each of the three tests, we can get a raw score, and also a standard and percentile score based on the raw score. The raw score refers to the number of figures scored and ranges in [0, 30] including scores of scribble and imitating tasks. Additionally, the standard score is obtained by transforming the distribution of the raw score with an average of 100 and a standard deviation of 15. It indicates how far the subject is from the average of the standardized group in the same age category. It is divided into five categories: low, slightly low, average, slightly high, and high. Lastly, the percentile score refers to the proportion of people who scored lower than the subjects in a standardized group in the same age category. The lower percentile score means that subject has a lower raw score compared to people of the same age group (Hwang et al. 2016).