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Multivariate Analysis of Variance
Published in Jhareswar Maiti, Multivariate Statistical Modeling in Engineering and Management, 2023
The quality control engineer of the plant initially uses graphical plots such as box plots to extract the pattern in the data. The box plot is shown in Figure 7.1. A box plot is a powerful tool that depicts the central tendency, spread, and skewness of a given univariate data set. It also shows outliers, if any, in the data set. A box plot contains a box in the middle and two whiskers at the two ends. The box length, i.e., the distance between the top and bottom horizontal lines of the box, represents the inter-quartile range (IQR) and the horizontal line in the middle of the box represents median of the data set. The two vertical lines at the bottom and top of the box are whiskers. The whiskers’ lengths are the lines emanating from the top and bottom of the box and terminating at the points of maximum and minimum, respectively. Alternatively, a whisker’s length is 1.5 IQR. Any observation beyond the whisker’s length (1.5 IQR) is suspected as being an outlier. The mean of the observed data can also be added in the box plot (see the small circle within the box). For a symmetric data, both mean and median coincide. From Figure 7.1, it can be seen that the steel washer quality varies from process to process. The mean OD for the three processes differs. We will conceptualize this as an ANOVA model below.
Experimental study of the perception of body position in space
Published in Steve Haake, The Engineering of Sport, 2020
Ingo Kobenz, Trevor T. J. DeVaney, Wolfram Mütter, Walter Habermann, Michael Samastur
We call p-values smaller than 0.05 significant and p-values smaller than 0.01 highly significant. A common form to show results graphically is the box plot-form. It is used to show the median* and the interquartile range (IQR=upper quartile** - lower quartile***), further the outliers and the extreme values. 50% of all values are within the box. Extreme values are bigger than the upper quartile plus 3 times the IQR, and the outliers are the upper quartile plus 1.5-3 times the IQR. Statistical analysis was performed with the Statistical Package of the Social Sciences (SPSS 6.0 for Windows). 50% of all data are lower and 50% are bigger than the median.75% of all data are lower and 25% are bigger than the upper quartile.25% of all data are lower and 75% are bigger than the lower quartile.
Probability and Mathematical Statistics Problems
Published in Dingyü Xue, YangQuan Chen, Scientific Computing with MATLAB®, 2018
The concept of median value, also known as the second quartile q2, of the vector v was discussed earlier. With the concept median value in mind, the original data vector can further be divided into two halves, one with data smaller than the median value, denoted as v1, and the other, denoted by v3. The median values, q1 and q3, of the two vectors can also be obtained. The three median values are denoted as quartiles, and can be obtained with q = (v,3), where q = [q1, q2, q3]. The quartiles q1 and q3 are referred to the first and third quartiles of the data set. The interquartile range (IQR) is defined as the distance between the first and third quartiles, IQR = q3− q1, and the data fall 1.5 × IQR above q3 or below q1 are considered the outliers.
Wind speed forecasting using deep learning and preprocessing techniques
Published in International Journal of Green Energy, 2023
It is important to identify outliers in a time series since outliers can influence the performance of the forecast model and reduce its accuracy and reliability. For outlier detection, the statistical methods are the most common and can be divided into density-based, distance-based, correlation-based, and image-based (Zou and Djokic 2020). In this case, Interquartile Range (IQR) will be used to detect outliers. Figure 20 illustrates the IQR boundaries of the data (Frost 2021). Q1 is the first quartile and refers to 24.65% of the data that lies between minimum and Q1. Q3 is the third quartile with almost 75%. The difference between Q3 and Q1 is referred to as Inter-Quartile Range (IQR). Outliers can be identified as 1.5 times IQR or 3 times IQR from the central 50% of data. The 1.5 × IQR refers to minor outliers and 3 × IQR to major outliers. For this case study, the 3 × IQR will be used which detects the major outliers.
Maneuver-based deep learning parameter identification of vehicle suspensions subjected to performance degradation
Published in Vehicle System Dynamics, 2023
Yongjun Pan, Yu Sun, Chuan Min, Zhixiong Li, Paolo Gardoni
We used box plots, shown in Figure 7, to describe the absolute percentage errors between the DNN results and the reference data. The elements in the box plots include the median, mean, and lower and upper quartiles. The median is the middle value of the DNN results when arranged either in descending or ascending order. The mean is the average of the DNN results. Quartiles are the partitioned values, which divide the whole series into four equal parts. The difference between the upper quartile and the lower quartile is known as the interquartile range (IQR). They clearly depict the data dispersion and the bias of the data and can be used to describe the discrete distribution of data. Figure 7 shows the centre position and spreading range of the data distribution. The height of the box reflects the fluctuation of the data to a certain extent. The percentage absolute errors of more than 90% of the DNN results are very small.
Statistics of Atterberg limit values of some pure kaolinitic clays
Published in Geomechanics and Geoengineering, 2023
Giovanni Spagnoli, Satoru Shimobe
Figure 3(A and B) shows the box plots and the dot plots of the Atterberg limits listed in Table 1, respectively. From Figure 3A, a relatively high dispersion of LL values is observed with respect to PL and PI. However, a higher range of values are observed with respect to the average values observed by Holtz and Kovacs (1981), developed on the data of Mitchell (1976) for kaolinitic clays. In box plots, the box represents the interquartile range (IQR) where the bottom and top of the box are the 25th and 75th percentiles, respectively. The whiskers extend to the last data value inside the inner fence, which represent 1.5 times the IQR from the edge of the box. In Figure 3A, some points are identified as ‘suspected outliers’, which are those falling within the inner fence. Figure 3B simply shows the shape of the data, with seem to be fairly normal, at least visually.