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height of the notches is proportional to the interquartile range (IQR) of the sample and is inversely proportional to the square root of the size of the sample. However, there is an uncertainty about the most appropriate multiplier (as this may vary depending on the similarity of the variances of the samples). The width of the notch is arbitrarily chosen to be visually pleasing, and should be consistent amongst all box plots being displayed on the same page.
146:
31:
2260:, they do have a number of advantages. First, the box plot enables statisticians to do a quick graphical examination on one or more data sets. Box-plots also take up less space and are therefore particularly useful for comparing distributions between several groups or sets of data in parallel (see Figure 1 for an example). Lastly, the overall structure of histograms and kernel density estimate can be strongly influenced by the choice of
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is the number that marks one quarter of the ordered data set. In other words, there are exactly 25% of the elements that are less than the first quartile and exactly 75% of the elements that are greater than it. The first quartile value can be easily determined by finding the "middle" number between
417:
The whiskers must end at an observed data point, but can be defined in various ways. In the most straightforward method, the boundary of the lower whisker is the minimum value of the data set, and the boundary of the upper whisker is the maximum value of the data set. Because of this variability, it
901:
is the number that marks three quarters of the ordered data set. In other words, there are exactly 75% of the elements that are less than the third quartile and 25% of the elements that are greater than it. The third quartile value can be easily obtained by finding the "middle" number between the
522:
plots apply a "notch" or narrowing of the box around the median. Notches are useful in offering a rough guide of the significance of the difference of medians; if the notches of two boxes do not overlap, this will provide evidence of a statistically significant difference between the medians. The
1320:
Similarly, the minimum value in this data set is 52°F, and 1.5 IQR below the first quartile is 52.5°F. The minimum is smaller than 1.5 IQR minus the first quartile, so the minimum is also an outlier. Therefore, the lower whisker is drawn at the smallest value greater than 1.5 IQR below the first
447:
the lowest observed data point from the dataset that falls within this distance. Because the whiskers must end at an observed data point, the whisker lengths can look unequal, even though 1.5 IQR is the same for both sides. All other observed data points outside the boundary of the whiskers are
1316:
In this case, the maximum value in this data set is 89°F, and 1.5 IQR above the third quartile is 88.5°F. The maximum is greater than 1.5 IQR plus the third quartile, so the maximum is an outlier. Therefore, the upper whisker is drawn at the greatest value smaller than 1.5 IQR above the third
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Similarly, the lower whisker boundary of the box plot is the smallest data value that is within 1.5 IQR below the first quartile. Here, 1.5 IQR below the first quartile is 52.5°F and the minimum is 57°F. Therefore, the lower whisker is drawn at the value of the minimum, which is 57°F.
1286:
The upper whisker boundary of the box-plot is the largest data value that is within 1.5 IQR above the third quartile. Here, 1.5 IQR above the third quartile is 88.5°F and the maximum is 81°F. Therefore, the upper whisker is drawn at the value of the maximum, which is 81°F.
759:{\displaystyle {\begin{matrix}1.5{\text{IQR}}\cdot e^{3{\text{MC}}},&1.5{\text{ IQR}}\cdot e^{-4{\text{MC}}}{\text{ if }}{\text{MC}}\geq 0,\\1.5{\text{IQR}}\cdot e^{4{\text{MC}}},&1.5{\text{ IQR}}\cdot e^{-3{\text{MC}}}{\text{ if }}{\text{MC}}\leq 0.\end{matrix}}}
2231:
1847:
2039:
508:
first popularized this type of visual data display in 1969, several variations on the classical box plot have been developed, and the two most commonly found variations are the variable width box plots and the notched box plots shown in Figure 4.
515:
plots illustrate the size of each group whose data is being plotted by making the width of the box proportional to the size of the group. A popular convention is to make the box width proportional to the square root of the size of the group.
829:
A series of hourly temperatures were measured throughout the day in degrees
Fahrenheit. The recorded values are listed in order as follows (°F): 57, 57, 57, 58, 63, 66, 66, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 81.
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1186:
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The median is the "middle" number of the ordered data set. This means that exactly 50% of the elements are below the median and 50% of the elements are greater than the median. The median of this ordered data set is 70°F.
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Although looking at a statistical distribution is more common than looking at a box plot, it can be useful to compare the box plot against the probability density function (theoretical histogram) for a normal
382:
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1443:
563:
278:
In addition to the minimum and maximum values used to construct a box-plot, another important element that can also be employed to obtain a box-plot is the interquartile range (IQR), as denoted below:
2049:
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1857:
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792:
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Rarely, box-plot can be plotted without the whiskers. This can be appropriate for sensitive information to avoid whiskers (and outliers) disclosing actual values observed.
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the largest observed data point from the dataset that falls within this distance. Similarly, a distance of 1.5 times the IQR is measured out below the lower quartile (
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133:
in her book "Charting
Statistics" in 1952 and again in her book "Practical Charting Techniques" in 1969. The box-and-whisker plot was first introduced in 1970 by
85:(though Tukey's boxplot assumes symmetry for the whiskers and normality for their length). The spacings in each subsection of the box-plot indicate the degree of
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For a symmetrical data distribution, the medcouple will be zero, and this reduces the adjusted box-plot to the Tukey's box-plot with equal whisker lengths of
5019:
4643:
2702:
Derrick, Ben; Green, Elizabeth; Ritchie, Felix; White, Paul (September 2022). "The Risk of
Disclosure When Reporting Commonly Used Univariate Statistics".
3284:
1197:
1102:
1310:
The ordered set for the recorded temperatures is (°F): 52, 57, 57, 58, 63, 66, 66, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 89.
488:, the locations of the seven marks on the box plot will be equally spaced. On some box plots, a cross-hatch is placed before the end of each whisker.
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statistic of skewness. For a medcouple value of MC, the lengths of the upper and lower whiskers on the box-plot are respectively defined to be:
409:
with a horizontal line drawn inside it to denote the median. Some box plots include an additional character to represent the mean of the data.
73:
that differ significantly from the rest of the dataset may be plotted as individual points beyond the whiskers on the box-plot. Box plots are
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A box plot of the data set can be generated by first calculating five relevant values of this data set: minimum, maximum, median (
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In this example, only the first and the last number are changed. The median, third quartile, and first quartile remain the same.
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2226:{\displaystyle q_{n}(0.75)=x_{(18)}+(0.75\cdot 25-18)\cdot (x_{(19)}-x_{(18)})=75+(0.75\cdot 25-18)\cdot (75-75)=75^{\circ }F}
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1842:{\displaystyle q_{n}(0.5)=x_{(12)}+(0.5\cdot 25-12)\cdot (x_{(13)}-x_{(12)})=70+(0.5\cdot 25-12)\cdot (70-70)=70^{\circ }F}
418:
is appropriate to describe the convention that is being used for the whiskers and outliers in the caption of the box-plot.
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2034:{\displaystyle q_{n}(0.25)=x_{(6)}+(0.25\cdot 25-6)\cdot (x_{(7)}-x_{(6)})=66+(0.25\cdot 25-6)\cdot (66-66)=66^{\circ }F}
61:) extending from the box indicating variability outside the upper and lower quartiles, thus, the plot is also called the
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Another popular choice for the boundaries of the whiskers is based on the 1.5 IQR value. From above the upper quartile (
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The unusual percentiles 2%, 9%, 91%, 98% are sometimes used for whisker cross-hatches and whisker ends to depict the
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is a method for demonstrating graphically the locality, spread and skewness groups of numerical data through their
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the minimum and the median. For the hourly temperatures, the "middle" number found between 57°F and 70°F is 66°F.
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The minimum is the smallest number of the data set. In this case, the minimum recorded day temperature is 57°F.
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The maximum is the largest number of the data set. In this case, the maximum recorded day temperature is 81°F.
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Frigge, Michael; Hoaglin, David C.; Iglewicz, Boris (February 1989). "Some
Implementations of the Boxplot".
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An additional example for obtaining box-plot from a data set containing a large number of data points is:
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Above is an example without outliers. Here is a followup example for generating box-plot with outliers:
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median and the maximum. For the hourly temperatures, the "middle" number between 70°F and 81°F is 75°F.
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There are other representations in which the whiskers can stand for several other things, such as:
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1656:= 24), one can calculate the median, first and third quartile either mathematically or visually.
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The interquartile range, or IQR, can be calculated by subtracting the first quartile value (
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A box-plot usually includes two parts, a box and a set of whiskers as shown in Figure 2.
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2628:"The shifting boxplot. A boxplot based on essential summary statistics around the mean"
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137:, who later published on the subject in his book "Exploratory Data Analysis" in 1977.
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One convention for obtaining the boundaries of these notches is to use a distance of
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2272:) distribution and observe their characteristics directly (as shown in Figure 7).
1276:{\displaystyle Q_{1}-1.5{\text{ IQR}}=66^{\circ }F-13.5^{\circ }F=52.5^{\circ }F.}
1181:{\displaystyle Q_{3}+1.5{\text{ IQR}}=75^{\circ }F+13.5^{\circ }F=88.5^{\circ }F.}
825:
Figure 5. The generated boxplot figure of the example on the left with no outliers
165:: the minimum, the maximum, the sample median, and the first and third quartiles.
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452:. The outliers can be plotted on the box-plot as a dot, a small circle, a star,
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1018:{\displaystyle {\text{IQR}}=Q_{3}-Q_{1}=75^{\circ }F-66^{\circ }F=9^{\circ }F.}
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distributions, which cannot be observed from the original classical box-plot.
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57:. In addition to the box on a box plot, there can be lines (which are called
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2809:; Vandervieren, E. (2008). "An adjusted boxplot for skewed distribution".
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Figure 4. Four box plots, with and without notches and variable width
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430:), a distance of 1.5 times the IQR is measured out and a whisker is drawn
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572:
106:
90:
54:
2706:. Lecture Notes in Computer Science. Vol. 13463. pp. 119â129.
1303:
Figure 6. The generated boxplot of the example on the left with outliers
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4907:
2937:
2901:
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2612:
2450:
Statistical
Methods in Practice : for Scientists and Technologists
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821:
161:
A boxplot is a standardized way of displaying the dataset based on the
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70:
17:
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3105:
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206:
2954:- superimposing a frequency-jittered stripchart on top of a box plot
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2604:
1087:{\displaystyle 1.5{\text{IQR}}=1.5\cdot 9^{\circ }F=13.5^{\circ }F.}
804:
and the bean plots can show the difference between single-modal and
157:
Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value
97:. In addition, the box-plot allows one to visually estimate various
2558:
Holmes, Alexander; Illowsky, Barbara; Dean, Susan (31 March 2015).
2274:
2239:
1298:
820:
152:
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29:
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377:{\displaystyle {\text{IQR}}=Q_{3}-Q_{1}=q_{n}(0.75)-q_{n}(0.25)}
5017:
4584:
4331:
3630:
3400:
3017:
2961:
2744:; Larsen, Wayne A. (February 1978). "Variations of Box Plots".
202:: the highest data point in the data set excluding any outliers
1528:{\displaystyle {\text{with }}k={\text{ and }}\alpha =p(n+1)-k}
186:: the lowest data point in the data set excluding any outliers
2957:
1570:
stands for the general ordering of the data points (i.e. if
121:. Box plots can be drawn either horizontally or vertically.
2410:"Procedures for Detecting Outlying Observations in Samples"
2279:
Figure 8. Box-plots displaying the skewness of the data set
1438:{\displaystyle q_{n}(p)=x_{(k)}+\alpha (x_{(k+1)}-x_{(k)})}
558:{\displaystyle \pm {\frac {1.58{\text{ IQR}}}{\sqrt {n}}}}
473:
The 2nd percentile and the 98th percentile of the data set
470:
The 9th percentile and the 91st percentile of the data set
288: : the distance between the upper and lower quartiles
274:(0.75), it is the median of the upper half of the dataset.
246:(0.25), it is the median of the lower half of the dataset.
149:
Figure 2. Box-plot with whiskers from minimum to maximum
2880:
Benjamini, Y. (1988). "Opening the Box of a
Boxplot".
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techniques and the choice of bandwidth, respectively.
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532:
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Autoregressive conditional heteroskedasticity (ARCH)
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93:of the data, which are usually described using the
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1652:Using the above example that has 24 data points (
81:without making any assumptions of the underlying
2252:Although box plots may seem more primitive than
4418:Multivariate adaptive regression splines (MARS)
2632:International Journal of Psychological Research
1333:General equation to compute empirical quantiles
2973:
129:The range-bar method was first introduced by
8:
2916:(1999). "The Bagplot: A Bivariate Boxplot".
2393:: CS1 maint: multiple names: authors list (
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2811:Computational Statistics and Data Analysis
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77:: they display variation in samples of a
495:
467:above and below the mean of the data set
2351:
4944:KaplanâMeier estimator (product limit)
2626:Marmolejo-Ramos, F.; Tian, S. (2010).
2386:
1191:1.5 IQR below the first quartile is:
1096:1.5 IQR above the third quartile is:
7:
5254:
4954:Accelerated failure time (AFT) model
2528:
2526:
2248:(pdf) of a Normal N(0,1Ï) Population
34:Figure 1. Box plot of data from the
5266:
4549:Analysis of variance (ANOVA, anova)
2533:Wickham, Hadley; Stryjewski, Lisa.
2362:Graphical exploratory data analysis
4644:CochranâMantelâHaenszel statistics
3270:Pearson product-moment correlation
2560:"Introductory Business Statistics"
2408:Grubbs, Frank E. (February 1969).
2305:Data and information visualization
1641:{\displaystyle x_{(i)}<x_{(k)}}
218:: the middle value in the data set
25:
914:) from the third quartile value (
5265:
5253:
5241:
5228:
5227:
2704:Privacy in Statistical Databases
787:{\displaystyle 1.5{\text{ IQR}}}
5294:Statistical charts and diagrams
4903:Least-squares spectral analysis
571:plots are intended to describe
3884:Mean-unbiased minimum-variance
2426:10.1080/00401706.1969.10490657
2204:
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2012:
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1:
5197:Geographic information system
4413:Simultaneous equations models
2499:Practical charting techniques
2497:Spear, Mary Eleanor. (1969).
1325:In the case of large datasets
4380:Coefficient of determination
3991:Uniformly most powerful test
2482:Spear, Mary Eleanor (2024).
2246:probability density function
4949:Proportional hazards models
4893:Spectral density estimation
4875:Vector autoregression (VAR)
4309:Maximum posterior estimator
3541:Randomized controlled trial
2712:10.1007/978-3-031-13945-1_9
2486:. McGraw Hill. p. 166.
5315:
4709:Multivariate distributions
3129:Average absolute deviation
2833:10.1016/j.csda.2007.11.008
2359:C., Dutoit, S. H. (2012).
889:The third quartile value (
873:The first quartile value (
5223:
5026:
5013:
4697:Structural equation model
4605:
4580:
4351:
4327:
4059:
4033:Score/Lagrange multiplier
3639:
3626:
3448:Sample size determination
3409:
3396:
3026:
3013:
2995:
2918:The American Statistician
2882:The American Statistician
2857:Exploratory Data Analysis
2747:The American Statistician
2592:The American Statistician
2501:. New York: McGraw-Hill.
2453:. John Wiley & Sons.
2310:Exploratory data analysis
2244:Figure 7. Box-plot and a
1321:quartile, which is 57°F.
1317:quartile, which is 79°F.
443:) and a whisker is drawn
5192:Environmental statistics
4714:Elliptical distributions
4507:Generalized linear model
4436:Simple linear regression
4206:HodgesâLehmann estimator
3663:Probability distribution
3572:Stochastic approximation
3134:Coefficient of variation
2782:"R: Box Plot Statistics"
2447:Richard., Boddy (2009).
2262:number and width of bins
2258:kernel density estimates
817:Example without outliers
798:Other kinds of box plots
504:Since the mathematician
83:statistical distribution
4852:Cross-correlation (XCF)
4460:Non-standard predictors
3894:LehmannâScheffĂ© theorem
3567:Adaptive clinical trial
1563:{\displaystyle x_{(k)}}
851:), and third quartile (
575:, and they rely on the
67:box-and-whisker diagram
5248:Mathematics portal
5069:Engineering statistics
4977:NelsonâAalen estimator
4554:Analysis of covariance
4441:Ordinary least squares
4365:Pearson product-moment
3769:Statistical functional
3680:Empirical distribution
3513:Controlled experiments
3242:Frequency distribution
3020:Descriptive statistics
2669:Dekking, F.M. (2005).
2535:"40 years of boxplots"
2280:
2249:
2227:
2035:
1843:
1642:
1590:
1589:{\displaystyle i<k}
1564:
1529:
1439:
1304:
1277:
1182:
1088:
1019:
826:
788:
760:
559:
501:
395:The box is drawn from
378:
158:
150:
79:statistical population
43:descriptive statistics
38:
5164:Population statistics
5106:System identification
4840:Autocorrelation (ACF)
4768:Exponential smoothing
4682:Discriminant analysis
4677:Canonical correlation
4541:Partition of variance
4403:Regression validation
4247:(JonckheereâTerpstra)
4146:Likelihood-ratio test
3835:Frequentist inference
3747:Locationâscale family
3668:Sampling distribution
3633:Statistical inference
3600:Cross-sectional study
3587:Observational studies
3546:Randomized experiment
3375:Stem-and-leaf display
3177:Central limit theorem
2677:. Springer. pp.
2645:10.21500/20112084.823
2278:
2243:
2228:
2036:
1844:
1643:
1591:
1565:
1530:
1440:
1302:
1295:Example with outliers
1278:
1183:
1089:
1020:
824:
789:
761:
560:
499:
456:(see example below).
379:
156:
148:
33:
5299:Statistical outliers
5087:Probabilistic design
4672:Principal components
4515:Exponential families
4467:Nonlinear regression
4446:General linear model
4408:Mixed effects models
4398:Errors and residuals
4375:Confounding variable
4277:Bayesian probability
4255:Van der Waerden test
4245:Ordered alternative
4010:Multiple comparisons
3889:RaoâBlackwellization
3852:Estimating equations
3808:Statistical distance
3526:Factorial experiment
3059:Arithmetic-Geometric
2330:Seven-number summary
2050:
1858:
1666:
1600:
1574:
1541:
1452:
1341:
1198:
1103:
1032:
930:
773:
586:
530:
486:normally distributed
482:seven-number summary
296:
262:: also known as the
234:: also known as the
200:or 100th percentile)
63:box-and-whisker plot
36:Michelson experiment
5159:Official statistics
5082:Methods engineering
4763:Seasonal adjustment
4531:Poisson regressions
4451:Bayesian regression
4390:Regression analysis
4370:Partial correlation
4342:Regression analysis
3941:Prediction interval
3936:Likelihood interval
3926:Confidence interval
3918:Interval estimation
3879:Unbiased estimators
3697:Model specification
3577:Up-and-down designs
3265:Partial correlation
3221:Index of dispersion
3139:Interquartile range
2484:Charting Statistics
2320:Five-number summary
899:or 75th percentile)
883:or 25th percentile)
842:), first quartile (
794:for both whiskers.
565:around the median.
284:Interquartile range
260:or 75th percentile)
232:or 25th percentile)
216:or 50th percentile)
163:five-number summary
103:interquartile range
95:five-number summary
5179:Spatial statistics
5059:Medical statistics
4959:First hitting time
4913:Whittle likelihood
4564:Degrees of freedom
4559:Multivariate ANOVA
4492:Heteroscedasticity
4304:Bayesian estimator
4269:Bayesian inference
4118:KolmogorovâSmirnov
4003:Randomization test
3973:Testing hypotheses
3946:Tolerance interval
3857:Maximum likelihood
3752:Exponential family
3685:Density estimation
3645:Statistical theory
3605:Natural experiment
3551:Scientific control
3468:Survey methodology
3154:Standard deviation
2325:Functional boxplot
2281:
2250:
2223:
2031:
1839:
1638:
1586:
1560:
1525:
1435:
1305:
1273:
1178:
1084:
1015:
827:
784:
756:
754:
573:skew distributions
555:
513:Variable width box
502:
484:. If the data are
465:standard deviation
374:
159:
151:
131:Mary Eleanor Spear
39:
27:Data visualization
5281:
5280:
5219:
5218:
5215:
5214:
5154:National accounts
5124:Actuarial science
5116:Social statistics
5009:
5008:
5005:
5004:
5001:
5000:
4936:Survival function
4921:
4920:
4783:Granger causality
4624:Contingency table
4599:Survival analysis
4576:
4575:
4572:
4571:
4428:Linear regression
4323:
4322:
4319:
4318:
4294:Credible interval
4263:
4262:
4046:
4045:
3862:Method of moments
3731:Parametric family
3692:Statistical model
3622:
3621:
3618:
3617:
3536:Random assignment
3458:Statistical power
3392:
3391:
3388:
3387:
3237:Contingency table
3207:
3206:
3074:Generalized/power
2817:(12): 5186â5201.
2721:978-3-031-13944-4
2460:978-0-470-74664-6
2372:978-1-4612-9371-2
2300:Candlestick chart
1493:
1458:
1220:
1125:
1041:
936:
782:
744:
739:
732:
713:
698:
682:
661:
656:
649:
630:
615:
599:
553:
552:
545:
302:
16:(Redirected from
5306:
5269:
5268:
5257:
5256:
5246:
5245:
5231:
5230:
5134:Crime statistics
5028:
5015:
4932:
4898:Fourier analysis
4885:Frequency domain
4865:
4812:
4778:Structural break
4738:
4687:Cluster analysis
4634:Log-linear model
4607:
4582:
4523:
4497:Homoscedasticity
4353:
4329:
4248:
4240:
4232:
4231:(KruskalâWallis)
4216:
4201:
4156:Cross validation
4141:
4123:AndersonâDarling
4070:
4057:
4028:Likelihood-ratio
4020:Parametric tests
3998:Permutation test
3981:1- & 2-tails
3872:Minimum distance
3844:Point estimation
3840:
3791:Optimal decision
3742:
3641:
3628:
3610:Quasi-experiment
3560:Adaptive designs
3411:
3398:
3275:Rank correlation
3037:
3028:
3015:
2982:
2975:
2968:
2959:
2952:Beeswarm Boxplot
2941:
2910:Rousseeuw, P. J.
2905:
2876:
2860:
2837:
2836:
2826:
2803:
2797:
2796:
2794:
2792:
2778:
2772:
2771:
2740:McGill, Robert;
2737:
2726:
2725:
2699:
2693:
2692:
2676:
2666:
2660:
2659:
2657:
2647:
2623:
2617:
2616:
2586:
2580:
2579:
2577:
2575:
2566:. Archived from
2555:
2549:
2548:
2546:
2544:
2539:
2530:
2521:
2520:
2494:
2488:
2487:
2479:
2473:
2472:
2444:
2438:
2437:
2405:
2399:
2398:
2392:
2384:
2356:
2232:
2230:
2229:
2224:
2219:
2218:
2155:
2154:
2136:
2135:
2090:
2089:
2062:
2061:
2040:
2038:
2037:
2032:
2027:
2026:
1963:
1962:
1944:
1943:
1898:
1897:
1870:
1869:
1848:
1846:
1845:
1840:
1835:
1834:
1771:
1770:
1752:
1751:
1706:
1705:
1678:
1677:
1647:
1645:
1644:
1639:
1637:
1636:
1618:
1617:
1595:
1593:
1592:
1587:
1569:
1567:
1566:
1561:
1559:
1558:
1534:
1532:
1531:
1526:
1494:
1491:
1459:
1456:
1444:
1442:
1441:
1436:
1431:
1430:
1412:
1411:
1381:
1380:
1353:
1352:
1282:
1280:
1279:
1274:
1266:
1265:
1250:
1249:
1234:
1233:
1221:
1218:
1210:
1209:
1187:
1185:
1184:
1179:
1171:
1170:
1155:
1154:
1139:
1138:
1126:
1123:
1115:
1114:
1093:
1091:
1090:
1085:
1077:
1076:
1061:
1060:
1042:
1039:
1024:
1022:
1021:
1016:
1008:
1007:
992:
991:
976:
975:
963:
962:
950:
949:
937:
934:
793:
791:
790:
785:
783:
780:
765:
763:
762:
757:
755:
745:
742:
740:
737:
735:
734:
733:
730:
714:
711:
701:
700:
699:
696:
683:
680:
662:
659:
657:
654:
652:
651:
650:
647:
631:
628:
618:
617:
616:
613:
600:
597:
564:
562:
561:
556:
554:
548:
547:
546:
543:
537:
383:
381:
380:
375:
364:
363:
342:
341:
329:
328:
316:
315:
303:
300:
21:
5314:
5313:
5309:
5308:
5307:
5305:
5304:
5303:
5284:
5283:
5282:
5277:
5240:
5211:
5173:
5110:
5096:quality control
5063:
5045:Clinical trials
5022:
4997:
4981:
4969:Hazard function
4963:
4917:
4879:
4863:
4826:
4822:BreuschâGodfrey
4810:
4787:
4727:
4702:Factor analysis
4648:
4629:Graphical model
4601:
4568:
4535:
4521:
4501:
4455:
4422:
4384:
4347:
4346:
4315:
4259:
4246:
4238:
4230:
4214:
4199:
4178:Rank statistics
4172:
4151:Model selection
4139:
4097:Goodness of fit
4091:
4068:
4042:
4014:
3967:
3912:
3901:Median unbiased
3829:
3740:
3673:Order statistic
3635:
3614:
3581:
3555:
3507:
3462:
3405:
3403:Data collection
3384:
3296:
3251:
3225:
3203:
3163:
3115:
3032:Continuous data
3022:
3009:
2991:
2986:
2948:
2930:10.2307/2686061
2908:
2894:10.2307/2685133
2879:
2873:
2849:
2846:
2844:Further reading
2841:
2840:
2805:
2804:
2800:
2790:
2788:
2780:
2779:
2775:
2760:10.2307/2683468
2739:
2738:
2729:
2722:
2701:
2700:
2696:
2689:
2668:
2667:
2663:
2625:
2624:
2620:
2605:10.2307/2685173
2588:
2587:
2583:
2573:
2571:
2570:on 27 July 2020
2557:
2556:
2552:
2542:
2540:
2537:
2532:
2531:
2524:
2509:
2496:
2495:
2491:
2481:
2480:
2476:
2461:
2446:
2445:
2441:
2407:
2406:
2402:
2385:
2373:
2358:
2357:
2353:
2348:
2295:Contour boxplot
2286:
2238:
2210:
2140:
2121:
2075:
2053:
2048:
2047:
2018:
1948:
1929:
1883:
1861:
1856:
1855:
1826:
1756:
1737:
1691:
1669:
1664:
1663:
1622:
1603:
1598:
1597:
1572:
1571:
1544:
1539:
1538:
1492: and
1450:
1449:
1416:
1391:
1366:
1344:
1339:
1338:
1335:
1327:
1297:
1257:
1241:
1225:
1201:
1196:
1195:
1162:
1146:
1130:
1106:
1101:
1100:
1068:
1052:
1030:
1029:
999:
983:
967:
954:
941:
928:
927:
921:
912:
896:
880:
858:
849:
840:
819:
814:
771:
770:
753:
752:
718:
705:
687:
673:
672:
635:
622:
604:
584:
583:
538:
528:
527:
494:
441:
428:
415:
408:
401:
393:
355:
333:
320:
307:
294:
293:
273:
259:
245:
231:
215:
199:
179:
143:
127:
28:
23:
22:
15:
12:
11:
5:
5312:
5310:
5302:
5301:
5296:
5286:
5285:
5279:
5278:
5276:
5275:
5263:
5251:
5237:
5224:
5221:
5220:
5217:
5216:
5213:
5212:
5210:
5209:
5204:
5199:
5194:
5189:
5183:
5181:
5175:
5174:
5172:
5171:
5166:
5161:
5156:
5151:
5146:
5141:
5136:
5131:
5126:
5120:
5118:
5112:
5111:
5109:
5108:
5103:
5098:
5089:
5084:
5079:
5073:
5071:
5065:
5064:
5062:
5061:
5056:
5051:
5042:
5040:Bioinformatics
5036:
5034:
5024:
5023:
5018:
5011:
5010:
5007:
5006:
5003:
5002:
4999:
4998:
4996:
4995:
4989:
4987:
4983:
4982:
4980:
4979:
4973:
4971:
4965:
4964:
4962:
4961:
4956:
4951:
4946:
4940:
4938:
4929:
4923:
4922:
4919:
4918:
4916:
4915:
4910:
4905:
4900:
4895:
4889:
4887:
4881:
4880:
4878:
4877:
4872:
4867:
4859:
4854:
4849:
4848:
4847:
4845:partial (PACF)
4836:
4834:
4828:
4827:
4825:
4824:
4819:
4814:
4806:
4801:
4795:
4793:
4792:Specific tests
4789:
4788:
4786:
4785:
4780:
4775:
4770:
4765:
4760:
4755:
4750:
4744:
4742:
4735:
4729:
4728:
4726:
4725:
4724:
4723:
4722:
4721:
4706:
4705:
4704:
4694:
4692:Classification
4689:
4684:
4679:
4674:
4669:
4664:
4658:
4656:
4650:
4649:
4647:
4646:
4641:
4639:McNemar's test
4636:
4631:
4626:
4621:
4615:
4613:
4603:
4602:
4585:
4578:
4577:
4574:
4573:
4570:
4569:
4567:
4566:
4561:
4556:
4551:
4545:
4543:
4537:
4536:
4534:
4533:
4517:
4511:
4509:
4503:
4502:
4500:
4499:
4494:
4489:
4484:
4479:
4477:Semiparametric
4474:
4469:
4463:
4461:
4457:
4456:
4454:
4453:
4448:
4443:
4438:
4432:
4430:
4424:
4423:
4421:
4420:
4415:
4410:
4405:
4400:
4394:
4392:
4386:
4385:
4383:
4382:
4377:
4372:
4367:
4361:
4359:
4349:
4348:
4345:
4344:
4339:
4333:
4332:
4325:
4324:
4321:
4320:
4317:
4316:
4314:
4313:
4312:
4311:
4301:
4296:
4291:
4290:
4289:
4284:
4273:
4271:
4265:
4264:
4261:
4260:
4258:
4257:
4252:
4251:
4250:
4242:
4234:
4218:
4215:(MannâWhitney)
4210:
4209:
4208:
4195:
4194:
4193:
4182:
4180:
4174:
4173:
4171:
4170:
4169:
4168:
4163:
4158:
4148:
4143:
4140:(ShapiroâWilk)
4135:
4130:
4125:
4120:
4115:
4107:
4101:
4099:
4093:
4092:
4090:
4089:
4081:
4072:
4060:
4054:
4052:Specific tests
4048:
4047:
4044:
4043:
4041:
4040:
4035:
4030:
4024:
4022:
4016:
4015:
4013:
4012:
4007:
4006:
4005:
3995:
3994:
3993:
3983:
3977:
3975:
3969:
3968:
3966:
3965:
3964:
3963:
3958:
3948:
3943:
3938:
3933:
3928:
3922:
3920:
3914:
3913:
3911:
3910:
3905:
3904:
3903:
3898:
3897:
3896:
3891:
3876:
3875:
3874:
3869:
3864:
3859:
3848:
3846:
3837:
3831:
3830:
3828:
3827:
3822:
3817:
3816:
3815:
3805:
3800:
3799:
3798:
3788:
3787:
3786:
3781:
3776:
3766:
3761:
3756:
3755:
3754:
3749:
3744:
3728:
3727:
3726:
3721:
3716:
3706:
3705:
3704:
3699:
3689:
3688:
3687:
3677:
3676:
3675:
3665:
3660:
3655:
3649:
3647:
3637:
3636:
3631:
3624:
3623:
3620:
3619:
3616:
3615:
3613:
3612:
3607:
3602:
3597:
3591:
3589:
3583:
3582:
3580:
3579:
3574:
3569:
3563:
3561:
3557:
3556:
3554:
3553:
3548:
3543:
3538:
3533:
3528:
3523:
3517:
3515:
3509:
3508:
3506:
3505:
3503:Standard error
3500:
3495:
3490:
3489:
3488:
3483:
3472:
3470:
3464:
3463:
3461:
3460:
3455:
3450:
3445:
3440:
3435:
3433:Optimal design
3430:
3425:
3419:
3417:
3407:
3406:
3401:
3394:
3393:
3390:
3389:
3386:
3385:
3383:
3382:
3377:
3372:
3367:
3362:
3357:
3352:
3347:
3342:
3337:
3332:
3327:
3322:
3317:
3312:
3306:
3304:
3298:
3297:
3295:
3294:
3289:
3288:
3287:
3282:
3272:
3267:
3261:
3259:
3253:
3252:
3250:
3249:
3244:
3239:
3233:
3231:
3230:Summary tables
3227:
3226:
3224:
3223:
3217:
3215:
3209:
3208:
3205:
3204:
3202:
3201:
3200:
3199:
3194:
3189:
3179:
3173:
3171:
3165:
3164:
3162:
3161:
3156:
3151:
3146:
3141:
3136:
3131:
3125:
3123:
3117:
3116:
3114:
3113:
3108:
3103:
3102:
3101:
3096:
3091:
3086:
3081:
3076:
3071:
3066:
3064:Contraharmonic
3061:
3056:
3045:
3043:
3034:
3024:
3023:
3018:
3011:
3010:
3008:
3007:
3002:
2996:
2993:
2992:
2987:
2985:
2984:
2977:
2970:
2962:
2956:
2955:
2947:
2946:External links
2944:
2943:
2942:
2924:(4): 382â387.
2906:
2888:(4): 257â262.
2877:
2871:
2863:Addison-Wesley
2851:Tukey, John W.
2845:
2842:
2839:
2838:
2824:10.1.1.90.9812
2798:
2773:
2742:Tukey, John W.
2727:
2720:
2694:
2687:
2661:
2618:
2581:
2550:
2522:
2507:
2489:
2474:
2459:
2439:
2400:
2371:
2350:
2349:
2347:
2344:
2343:
2342:
2337:
2332:
2327:
2322:
2317:
2312:
2307:
2302:
2297:
2292:
2285:
2282:
2237:
2234:
2222:
2217:
2213:
2209:
2206:
2203:
2200:
2197:
2194:
2191:
2188:
2185:
2182:
2179:
2176:
2173:
2170:
2167:
2164:
2161:
2158:
2153:
2150:
2147:
2143:
2139:
2134:
2131:
2128:
2124:
2120:
2117:
2114:
2111:
2108:
2105:
2102:
2099:
2096:
2093:
2088:
2085:
2082:
2078:
2074:
2071:
2068:
2065:
2060:
2056:
2044:Third quartile
2030:
2025:
2021:
2017:
2014:
2011:
2008:
2005:
2002:
1999:
1996:
1993:
1990:
1987:
1984:
1981:
1978:
1975:
1972:
1969:
1966:
1961:
1958:
1955:
1951:
1947:
1942:
1939:
1936:
1932:
1928:
1925:
1922:
1919:
1916:
1913:
1910:
1907:
1904:
1901:
1896:
1893:
1890:
1886:
1882:
1879:
1876:
1873:
1868:
1864:
1852:First quartile
1838:
1833:
1829:
1825:
1822:
1819:
1816:
1813:
1810:
1807:
1804:
1801:
1798:
1795:
1792:
1789:
1786:
1783:
1780:
1777:
1774:
1769:
1766:
1763:
1759:
1755:
1750:
1747:
1744:
1740:
1736:
1733:
1730:
1727:
1724:
1721:
1718:
1715:
1712:
1709:
1704:
1701:
1698:
1694:
1690:
1687:
1684:
1681:
1676:
1672:
1650:
1649:
1635:
1632:
1629:
1625:
1621:
1616:
1613:
1610:
1606:
1585:
1582:
1579:
1557:
1554:
1551:
1547:
1535:
1524:
1521:
1518:
1515:
1512:
1509:
1506:
1503:
1500:
1497:
1489:
1486:
1483:
1480:
1477:
1474:
1471:
1468:
1465:
1462:
1446:
1445:
1434:
1429:
1426:
1423:
1419:
1415:
1410:
1407:
1404:
1401:
1398:
1394:
1390:
1387:
1384:
1379:
1376:
1373:
1369:
1365:
1362:
1359:
1356:
1351:
1347:
1334:
1331:
1326:
1323:
1296:
1293:
1284:
1283:
1272:
1269:
1264:
1260:
1256:
1253:
1248:
1244:
1240:
1237:
1232:
1228:
1224:
1216:
1213:
1208:
1204:
1189:
1188:
1177:
1174:
1169:
1165:
1161:
1158:
1153:
1149:
1145:
1142:
1137:
1133:
1129:
1121:
1118:
1113:
1109:
1083:
1080:
1075:
1071:
1067:
1064:
1059:
1055:
1051:
1048:
1045:
1037:
1026:
1025:
1014:
1011:
1006:
1002:
998:
995:
990:
986:
982:
979:
974:
970:
966:
961:
957:
953:
948:
944:
940:
919:
910:
894:
878:
856:
847:
838:
818:
815:
813:
810:
800:, such as the
778:
767:
766:
751:
748:
738: if
728:
725:
721:
717:
709:
706:
704:
694:
690:
686:
678:
675:
674:
671:
668:
665:
655: if
645:
642:
638:
634:
626:
623:
621:
611:
607:
603:
595:
592:
591:
551:
541:
535:
493:
490:
475:
474:
471:
468:
439:
426:
414:
411:
406:
399:
392:
389:
385:
384:
373:
370:
367:
362:
358:
354:
351:
348:
345:
340:
336:
332:
327:
323:
319:
314:
310:
306:
290:
289:
276:
275:
269:
264:upper quartile
257:
251:Third quartile
247:
241:
236:lower quartile
229:
223:First quartile
219:
213:
203:
197:
187:
177:
142:
139:
126:
123:
101:, notably the
75:non-parametric
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5311:
5300:
5297:
5295:
5292:
5291:
5289:
5274:
5273:
5264:
5262:
5261:
5252:
5250:
5249:
5244:
5238:
5236:
5235:
5226:
5225:
5222:
5208:
5205:
5203:
5202:Geostatistics
5200:
5198:
5195:
5193:
5190:
5188:
5185:
5184:
5182:
5180:
5176:
5170:
5169:Psychometrics
5167:
5165:
5162:
5160:
5157:
5155:
5152:
5150:
5147:
5145:
5142:
5140:
5137:
5135:
5132:
5130:
5127:
5125:
5122:
5121:
5119:
5117:
5113:
5107:
5104:
5102:
5099:
5097:
5093:
5090:
5088:
5085:
5083:
5080:
5078:
5075:
5074:
5072:
5070:
5066:
5060:
5057:
5055:
5052:
5050:
5046:
5043:
5041:
5038:
5037:
5035:
5033:
5032:Biostatistics
5029:
5025:
5021:
5016:
5012:
4994:
4993:Log-rank test
4991:
4990:
4988:
4984:
4978:
4975:
4974:
4972:
4970:
4966:
4960:
4957:
4955:
4952:
4950:
4947:
4945:
4942:
4941:
4939:
4937:
4933:
4930:
4928:
4924:
4914:
4911:
4909:
4906:
4904:
4901:
4899:
4896:
4894:
4891:
4890:
4888:
4886:
4882:
4876:
4873:
4871:
4868:
4866:
4864:(BoxâJenkins)
4860:
4858:
4855:
4853:
4850:
4846:
4843:
4842:
4841:
4838:
4837:
4835:
4833:
4829:
4823:
4820:
4818:
4817:DurbinâWatson
4815:
4813:
4807:
4805:
4802:
4800:
4799:DickeyâFuller
4797:
4796:
4794:
4790:
4784:
4781:
4779:
4776:
4774:
4773:Cointegration
4771:
4769:
4766:
4764:
4761:
4759:
4756:
4754:
4751:
4749:
4748:Decomposition
4746:
4745:
4743:
4739:
4736:
4734:
4730:
4720:
4717:
4716:
4715:
4712:
4711:
4710:
4707:
4703:
4700:
4699:
4698:
4695:
4693:
4690:
4688:
4685:
4683:
4680:
4678:
4675:
4673:
4670:
4668:
4665:
4663:
4660:
4659:
4657:
4655:
4651:
4645:
4642:
4640:
4637:
4635:
4632:
4630:
4627:
4625:
4622:
4620:
4619:Cohen's kappa
4617:
4616:
4614:
4612:
4608:
4604:
4600:
4596:
4592:
4588:
4583:
4579:
4565:
4562:
4560:
4557:
4555:
4552:
4550:
4547:
4546:
4544:
4542:
4538:
4532:
4528:
4524:
4518:
4516:
4513:
4512:
4510:
4508:
4504:
4498:
4495:
4493:
4490:
4488:
4485:
4483:
4480:
4478:
4475:
4473:
4472:Nonparametric
4470:
4468:
4465:
4464:
4462:
4458:
4452:
4449:
4447:
4444:
4442:
4439:
4437:
4434:
4433:
4431:
4429:
4425:
4419:
4416:
4414:
4411:
4409:
4406:
4404:
4401:
4399:
4396:
4395:
4393:
4391:
4387:
4381:
4378:
4376:
4373:
4371:
4368:
4366:
4363:
4362:
4360:
4358:
4354:
4350:
4343:
4340:
4338:
4335:
4334:
4330:
4326:
4310:
4307:
4306:
4305:
4302:
4300:
4297:
4295:
4292:
4288:
4285:
4283:
4280:
4279:
4278:
4275:
4274:
4272:
4270:
4266:
4256:
4253:
4249:
4243:
4241:
4235:
4233:
4227:
4226:
4225:
4222:
4221:Nonparametric
4219:
4217:
4211:
4207:
4204:
4203:
4202:
4196:
4192:
4191:Sample median
4189:
4188:
4187:
4184:
4183:
4181:
4179:
4175:
4167:
4164:
4162:
4159:
4157:
4154:
4153:
4152:
4149:
4147:
4144:
4142:
4136:
4134:
4131:
4129:
4126:
4124:
4121:
4119:
4116:
4114:
4112:
4108:
4106:
4103:
4102:
4100:
4098:
4094:
4088:
4086:
4082:
4080:
4078:
4073:
4071:
4066:
4062:
4061:
4058:
4055:
4053:
4049:
4039:
4036:
4034:
4031:
4029:
4026:
4025:
4023:
4021:
4017:
4011:
4008:
4004:
4001:
4000:
3999:
3996:
3992:
3989:
3988:
3987:
3984:
3982:
3979:
3978:
3976:
3974:
3970:
3962:
3959:
3957:
3954:
3953:
3952:
3949:
3947:
3944:
3942:
3939:
3937:
3934:
3932:
3929:
3927:
3924:
3923:
3921:
3919:
3915:
3909:
3906:
3902:
3899:
3895:
3892:
3890:
3887:
3886:
3885:
3882:
3881:
3880:
3877:
3873:
3870:
3868:
3865:
3863:
3860:
3858:
3855:
3854:
3853:
3850:
3849:
3847:
3845:
3841:
3838:
3836:
3832:
3826:
3823:
3821:
3818:
3814:
3811:
3810:
3809:
3806:
3804:
3801:
3797:
3796:loss function
3794:
3793:
3792:
3789:
3785:
3782:
3780:
3777:
3775:
3772:
3771:
3770:
3767:
3765:
3762:
3760:
3757:
3753:
3750:
3748:
3745:
3743:
3737:
3734:
3733:
3732:
3729:
3725:
3722:
3720:
3717:
3715:
3712:
3711:
3710:
3707:
3703:
3700:
3698:
3695:
3694:
3693:
3690:
3686:
3683:
3682:
3681:
3678:
3674:
3671:
3670:
3669:
3666:
3664:
3661:
3659:
3656:
3654:
3651:
3650:
3648:
3646:
3642:
3638:
3634:
3629:
3625:
3611:
3608:
3606:
3603:
3601:
3598:
3596:
3593:
3592:
3590:
3588:
3584:
3578:
3575:
3573:
3570:
3568:
3565:
3564:
3562:
3558:
3552:
3549:
3547:
3544:
3542:
3539:
3537:
3534:
3532:
3529:
3527:
3524:
3522:
3519:
3518:
3516:
3514:
3510:
3504:
3501:
3499:
3498:Questionnaire
3496:
3494:
3491:
3487:
3484:
3482:
3479:
3478:
3477:
3474:
3473:
3471:
3469:
3465:
3459:
3456:
3454:
3451:
3449:
3446:
3444:
3441:
3439:
3436:
3434:
3431:
3429:
3426:
3424:
3421:
3420:
3418:
3416:
3412:
3408:
3404:
3399:
3395:
3381:
3378:
3376:
3373:
3371:
3368:
3366:
3363:
3361:
3358:
3356:
3353:
3351:
3348:
3346:
3343:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3325:Control chart
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3307:
3305:
3303:
3299:
3293:
3290:
3286:
3283:
3281:
3278:
3277:
3276:
3273:
3271:
3268:
3266:
3263:
3262:
3260:
3258:
3254:
3248:
3245:
3243:
3240:
3238:
3235:
3234:
3232:
3228:
3222:
3219:
3218:
3216:
3214:
3210:
3198:
3195:
3193:
3190:
3188:
3185:
3184:
3183:
3180:
3178:
3175:
3174:
3172:
3170:
3166:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3127:
3126:
3124:
3122:
3118:
3112:
3109:
3107:
3104:
3100:
3097:
3095:
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3075:
3072:
3070:
3067:
3065:
3062:
3060:
3057:
3055:
3052:
3051:
3050:
3047:
3046:
3044:
3042:
3038:
3035:
3033:
3029:
3025:
3021:
3016:
3012:
3006:
3003:
3001:
2998:
2997:
2994:
2990:
2983:
2978:
2976:
2971:
2969:
2964:
2963:
2960:
2953:
2950:
2949:
2945:
2939:
2935:
2931:
2927:
2923:
2919:
2915:
2911:
2907:
2903:
2899:
2895:
2891:
2887:
2883:
2878:
2874:
2872:9780201076165
2868:
2864:
2859:
2858:
2852:
2848:
2847:
2843:
2834:
2830:
2825:
2820:
2816:
2812:
2808:
2802:
2799:
2787:
2783:
2777:
2774:
2769:
2765:
2761:
2757:
2753:
2749:
2748:
2743:
2736:
2734:
2732:
2728:
2723:
2717:
2713:
2709:
2705:
2698:
2695:
2690:
2688:1-85233-896-2
2684:
2680:
2675:
2674:
2665:
2662:
2656:
2651:
2646:
2641:
2637:
2633:
2629:
2622:
2619:
2614:
2610:
2606:
2602:
2598:
2594:
2593:
2585:
2582:
2569:
2565:
2561:
2554:
2551:
2536:
2529:
2527:
2523:
2518:
2514:
2510:
2504:
2500:
2493:
2490:
2485:
2478:
2475:
2470:
2466:
2462:
2456:
2452:
2451:
2443:
2440:
2435:
2431:
2427:
2423:
2419:
2415:
2414:Technometrics
2411:
2404:
2401:
2396:
2390:
2382:
2378:
2374:
2368:
2364:
2363:
2355:
2352:
2345:
2341:
2338:
2336:
2333:
2331:
2328:
2326:
2323:
2321:
2318:
2316:
2313:
2311:
2308:
2306:
2303:
2301:
2298:
2296:
2293:
2291:
2288:
2287:
2283:
2277:
2273:
2271:
2265:
2263:
2259:
2255:
2247:
2242:
2236:Visualization
2235:
2233:
2220:
2215:
2211:
2207:
2201:
2198:
2195:
2189:
2183:
2180:
2177:
2174:
2171:
2165:
2162:
2159:
2148:
2141:
2137:
2129:
2122:
2115:
2109:
2106:
2103:
2100:
2097:
2091:
2083:
2076:
2072:
2066:
2058:
2054:
2045:
2041:
2028:
2023:
2019:
2015:
2009:
2006:
2003:
1997:
1991:
1988:
1985:
1982:
1979:
1973:
1970:
1967:
1956:
1949:
1945:
1937:
1930:
1923:
1917:
1914:
1911:
1908:
1905:
1899:
1891:
1884:
1880:
1874:
1866:
1862:
1853:
1849:
1836:
1831:
1827:
1823:
1817:
1814:
1811:
1805:
1799:
1796:
1793:
1790:
1787:
1781:
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5239:
5232:
5144:Econometrics
5094: /
5077:Chemometrics
5054:Epidemiology
5047: /
5020:Applications
4862:ARIMA model
4809:Q-statistic
4758:Stationarity
4654:Multivariate
4597: /
4593: /
4591:Multivariate
4589: /
4529: /
4525: /
4299:Bayes factor
4198:Signed rank
4110:
4084:
4076:
4064:
3759:Completeness
3595:Cohort study
3493:Opinion poll
3428:Missing data
3415:Study design
3370:Scatter plot
3319:
3292:Scatter plot
3285:Spearman's Ï
3247:Grouped data
2921:
2917:
2914:Tukey, J. W.
2912:; Ruts, I.;
2885:
2881:
2856:
2814:
2810:
2801:
2789:. Retrieved
2785:
2776:
2754:(1): 12â16.
2751:
2745:
2703:
2697:
2672:
2664:
2638:(1): 37â46.
2635:
2631:
2621:
2599:(1): 50â54.
2596:
2590:
2584:
2572:. Retrieved
2568:the original
2563:
2553:
2543:December 24,
2541:. Retrieved
2498:
2492:
2483:
2477:
2449:
2442:
2417:
2413:
2403:
2365:. Springer.
2361:
2354:
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828:
802:violin plots
797:
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569:Adjusted box
568:
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99:L-estimators
66:
62:
58:
50:
46:
40:
5272:WikiProject
5187:Cartography
5149:Jurimetrics
5101:Reliability
4832:Time domain
4811:(LjungâBox)
4733:Time-series
4611:Categorical
4595:Time-series
4587:Categorical
4522:(Bernoulli)
4357:Correlation
4337:Correlation
4133:JarqueâBera
4105:Chi-squared
3867:M-estimator
3820:Asymptotics
3764:Sufficiency
3531:Interaction
3443:Replication
3423:Effect size
3380:Violin plot
3360:Radar chart
3340:Forest plot
3330:Correlogram
3280:Kendall's Ï
2420:(1): 1â21.
2340:Violin plot
520:Notched box
448:plotted as
5288:Categories
5139:Demography
4857:ARMA model
4662:Regression
4239:(Friedman)
4200:(Wilcoxon)
4138:Normality
4128:Lilliefors
4075:Student's
3951:Resampling
3825:Robustness
3813:divergence
3803:Efficiency
3741:(monotone)
3736:Likelihood
3653:Population
3486:Stratified
3438:Population
3257:Dependence
3213:Count data
3144:Percentile
3121:Dispersion
3054:Arithmetic
2989:Statistics
2807:Hubert, M.
2655:10819/6492
2508:0070600104
2381:1019645745
2346:References
2254:histograms
1457:with
806:multimodal
492:Variations
182:percentile
135:John Tukey
87:dispersion
4520:Logistic
4287:posterior
4213:Rank sum
3961:Jackknife
3956:Bootstrap
3774:Bootstrap
3709:Parameter
3658:Statistic
3453:Statistic
3365:Run chart
3350:Pie chart
3345:Histogram
3335:Fan chart
3310:Bar chart
3192:L-moments
3079:Geometric
2819:CiteSeerX
2517:924909765
2469:940679163
2434:0040-1706
2389:cite book
2335:Sina plot
2315:Fan chart
2216:∘
2199:−
2190:⋅
2181:−
2175:⋅
2138:−
2116:⋅
2107:−
2101:⋅
2024:∘
2007:−
1998:⋅
1989:−
1983:⋅
1946:−
1924:⋅
1915:−
1909:⋅
1832:∘
1815:−
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1797:−
1791:⋅
1754:−
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1723:−
1717:⋅
1520:−
1496:α
1414:−
1386:α
1263:∘
1247:∘
1239:−
1231:∘
1219: IQR
1212:−
1168:∘
1152:∘
1136:∘
1124: IQR
1074:∘
1058:∘
1050:⋅
1005:∘
989:∘
981:−
973:∘
952:−
781: IQR
747:≤
724:−
716:⋅
712: IQR
685:⋅
664:≥
641:−
633:⋅
629: IQR
602:⋅
577:medcouple
544: IQR
534:±
353:−
318:−
115:mid-range
55:quartiles
5234:Category
4927:Survival
4804:Johansen
4527:Binomial
4482:Isotonic
4069:(normal)
3714:location
3521:Blocking
3476:Sampling
3355:QâQ plot
3320:Box plot
3302:Graphics
3197:Skewness
3187:Kurtosis
3159:Variance
3089:Heronian
3084:Harmonic
2853:(1977).
2786:R manual
2574:29 April
2564:OpenStax
2284:See also
2046: :
1854: :
1662: :
1596:, then
812:Examples
450:outliers
413:Whiskers
141:Elements
107:midhinge
91:skewness
71:Outliers
65:and the
59:whiskers
47:box plot
5260:Commons
5207:Kriging
5092:Process
5049:studies
4908:Wavelet
4741:General
3908:Plug-in
3702:L space
3481:Cluster
3182:Moments
3000:Outline
2938:2686061
2902:2685133
2791:26 June
2768:2683468
2613:2685173
2290:Bagplot
1028:Hence,
445:down to
191:Maximum
180:or 0th
171:Minimum
125:History
119:trimean
51:boxplot
18:Boxplot
5129:Census
4719:Normal
4667:Manova
4487:Robust
4237:2-way
4229:1-way
4067:-test
3738:
3315:Biplot
3106:Median
3099:Lehmer
3041:Center
2936:
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2681:â238.
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1660:Median
207:Median
117:, and
4753:Trend
4282:prior
4224:anova
4113:-test
4087:-test
4079:-test
3986:Power
3931:Pivot
3724:shape
3719:scale
3169:Shape
3149:Range
3094:Heinz
3069:Cubic
3005:Index
2934:JSTOR
2898:JSTOR
2764:JSTOR
2609:JSTOR
2538:(PDF)
1537:Here
432:up to
286:(IQR)
111:range
4986:Test
4186:Sign
4038:Wald
3111:Mode
3049:Mean
2867:ISBN
2793:2011
2716:ISBN
2683:ISBN
2576:2020
2545:2020
2513:OCLC
2503:ISBN
2465:OCLC
2455:ISBN
2430:ISSN
2395:link
2377:OCLC
2367:ISBN
2268:N(0,
2172:0.75
2098:0.75
2067:0.75
1980:0.25
1906:0.25
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454:etc.
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4161:AIC
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