Question

Writing in what ways are box-whisker plots and hypothesis tests alike, and in what ways are they different?

Explain detail, please.

Answer 1

Box plots or box-whisker plots or box-and-whisker diagrams are a method of graphically presenting the statistical data making it easy to visualize than the descriptive statistics and provides more information about the data than a bar graph can.

Here the sample data is presented as a box. The spacings between the different parts of the box help indicate the degree of dispersion or the spread and skewness in the data, and also identifies outliers. A box plot shows a 5-number data summary: (i) minimum, (ii) first or lower quartile, (iii) median, (iv) third or upper quartile, and (v) maximum. The box is divided at the median. The length of the box depicts the interquartile range (IQR) with the 1st quartile being the bottom line and 3rd quartile the top line. This is used for a single set of data.

A paired hypothesis test compares two different measures taken from the same data set whereas hypothesis test for independent samples compares the mean of two samples. It is used for comparing two sample means and considers that each dataset is taken from a normal distribution for the starting cases, but there are other methods as well. The consideration or assumptions come in this testing which was not there in the box-whisker plot. We can use a one‐tailed test when we have a reason convincing enough to expect that the difference between the two samples will be in a particular direction. If the difference between the two samples could go in either direction, then we do a two-tailed test, using the assumption

H0: (null hypothesis): The samples' means are equal.

Ha: The means are the two samples are different.

They can be represented as curves or bar diagram but a pictorial data analysis as easily depicted as box-whisker plot is not possible.