Question

For the following data, please calculate and interpret the IQV (Indices of Qualitative variation). Ensure that you show your work. Primary Social Networking Site Observed frequency Facebook 15 LinkedIn 3 Twitter 12 Reddit 5 Google+ 1 Total 36

Answer 1

Index of Qualitative Variation (IQV):
IQV is a measure of variability for nominal variables (data) such as race, gender, ethnicity, (here) networking sites etc. It is based on the ratio of the total number of differences in the distribution to the maximum number of possible differences within the same distribution.

Formula:
IQV = K (100^2 - Σ(p^2)) / 100^2 (K-1)
where,
K= the number of categories
N= the total number of cases in the distribution
Σ(p^2)= the sum of all squared percentages

Steps to calculate IQV:
-Construct a percentage distribution.
-Square the percentages for each category.
-Sum the squared percentages.
-Calculate the IQV using the formula above.

Note that:
• The IQV is a single number that expresses the diversity of a distribution.
• The IQV ranges from 0 to 1
• An IQV of 0 would indicate that the distribution has NO diversity (variation) at all, that means all the cases are in one category.
• When the cases in the distribution are distributed evenly across the categories, then there is maximum variation/diversity and hence the IQV is 1.

Here,K=5,N=36, Σ(p^2)=3117.28

Primary Social Networking Site	Observed Frequency	Proportion		Percentage		p^2
Facebook	15	(15/36)	0.42	(15/36)*100	41.67	1736.11
LinkedIn	3	(3/36)	0.08	(3/36)*100	8.33	69.44
Twitter	12	(12/36)	0.33	(12/36)*100	33.33	1111.11
Reddit	5	(5/36)	0.14	(5/36)*100	13.89	192.90
Google	1	(1/36)	0.03	(1/36)*100	2.78	7.72
TOTAL	36		1		100	3117.28

IQV = 5*(100^2 - 3117.28)/ (100^2*(5-1))
IQV= 0.86034

Here, IQV=0.86034, this means that we have a distribution that do not consists entirely of particular social networking site. Infact 0.86 is closer to 1, which indicates more variation in the data.