Dear Arunanshu,

Boxplots are a means of summarising a series of ordinal or scale data values. They can be applied to normally distributed data so I don't quite understand your question.

For information on the significance of outliers in boxplots have a look here:

Dawson, R. (2011) How significant is a boxplot outlier? Journal of Statistics Education, 19(2), www.amstat.org/publications/jse/v19n2/dawson.pdf

Boxplots apply well to any continuous data, Normal or not.

Dear Mahapatro

Box plot is a convenient way of graphically depicting groups of numerical data through their quartiles. Box plots may also have lines extending vertically from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram. Outliers may be plotted as individual points. Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution. The spacing between the different parts of the box indicate the degree of dispersion (spread) and skewness in the data, and show outliers. In addition to the points themselves, they allow one to visually estimate various L-estimators, notably the interquartile range,  range, mid-range, and trim mean. Box plots can be drawn either horizontally or vertically.

Best,

Ahammad, Bangladesh

There is also a version of the box plot in which there are notches on the "boxes" for side by side plots. If the notches from different boxes do not overlap, this is equivalent to a test for the equality of several median at significance level 0.05 as a default. 

Dear Raid can you please suggest any literature for the version you have mentioned.

See the link. And note: "... if the two datasets are independent and identically distributed [...] with a normal distributional shape in the central position"

Many papers cite

McGill, R., Tukey, J.W & Larsen, W.A. Am. Stat. 32, 12–16 (1978)

Who propose the "Gaussian-based asmyptotic approximation (Kendall and Stuart 1967) of the standard deviation s of the median [...] (that) can be shown to be reasonably broadly applicable to other distributions."

Kendall and Stuart 1967: The Advanced Theory of Statistics. Vol 2, Ch. 14. New York, Hafner Publishing Co.

I find this a bit weird because the method is very bad or unsuited for "small" samples, especially when their distribution is non-gaussian(!), and in large samples it is equally correct and possibly more instructive to directly adress the expected values (means), even if their distributin is non-gaussian...

https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxkYXZpZHNzdGF0aXN0aWNzfGd4OjYxNTMzNTE4ZmY4Y2ZhNGQ

Arunashu: This is a link from SAS:

http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_boxplot_sect029.htm

Dear Jochen

Please suggest should I use this method for small data size. Some times the number  of data I am getting is not mre than 3 to 7. Please suggest ant method I can use other than this.

Thanks

Dear Arunanshu,

the boxplot is a summary representation of data. It summarizes a set of data by a groups of 5 statistics: the lower whisker, the 1st quartile, the median, the 3rd quartile, and the upper whisker.

Now think: is it sensible to summarize 3 to 7 values by 5 summary statistics?

I think: usually not. Instead I would simply show the data as it is, in a scatterplot. An example is shown in the linked figure. You can also show the median (I would not show the IQR for this few data). To my opinion showing the mean or the median and all these things is not very helpful in your case (also not in the case showin in the linked figure) because the data presents the complete information and allows the reader to draw her conclusions.

However, there is one exception where the reduction of data by showing summary statistics is appropriate even if the sample size per group is small: namely if there are many groups. Here, showing onlye the medians (or means) or the IQRs (or confidence intervals) may better visualize a general pattern over the many different groups that are shown. The second link shows a dotplot showing the mean values for a larger number of groups.

http://www.sthda.com/sthda/RDoc/figure/easy-ggplot2/ggplot2-dot-plot-demo.png

http://johncmunoz.com/wp-content/uploads/2012/04/dotplot1.png

You can try violinplot - https://seaborn.pydata.org/generated/seaborn.violinplot.html.