# Benchmarking and Statistical Difference

#### morgano

##### New Member
Hey everyone,

I have a few issues and would really appreciate your help Thank you very much !
So here it goes :

I have two levels ( A and B ), in different fiscal years ( 2007 - 2011 ) and approximately 15 variables. I would like to calculate the mean, variance, kurtosis and skewness of every variable in level A and B and in the different years, and then test if there is a statistically significant difference between the levels for every variable. How do you think I should go about it ?

Thank you very much !!

Best Morgan

#### tester1234

##### New Member
Hi morgano,

How do you think I should go about it ?

Let`s try this anyhow:

I have two levels ( A and B ), in different fiscal years ( 2007 - 2011 ) and approximately 15 variables.
So you mean A and B are the grouping factors for each year. So you do have "A" values and "B" values for each of the 15 variables for the year 2007? Same goes for the other years? How many of those "A" and "B" grouped values you do have, 1,20, 100, or more?

Further you must give us information what variable type these other 15 variables are. Are they nominal, ordinal or metric? If they are all metric (which your post indicates but we do not know for sure) you first should test if the data distribution for each year and "A" and "B" groupingvariable per variable is normally distributed or skewed or bimodal. This is important to decide for the correct test of significance.

Lets say the distribution for "A" grouping 2008 variable 12 is normally distributed and the same goes for "B" grouping variable 2008 variable 12 you may use a t-test to see if there is a significant difference in mean for both distributions.

This is cumbersome so you may try a manova but you will have to define a dependent and independent variables. Your dependent variable is the score for each year, variable and group. The independent are as named before year,variable and group.

In R language it would look like this:

Score(var1) ~ group + year
Score(var2) ~ group + year
Score(var...) ~ group + year..... (To the R-Users - i know there is a possibility to tell the modell to take all variables at one so you dont have to repeat the manova each time for a new variable but i lost it - you are free to help :yup:, something with apply or so)

If the distributions are not normally distributed (i know this is a lose word in statistics so everyone decides for his own what is "normal") you must look for so called non-parametric test.

Please look at this link - you will find infos about the test concerning the variable niveau:
http://www.ats.ucla.edu/stat/mult_pkg/whatstat/
and what test to use concerning the distribution of the variable:
http://changingminds.org/explanations/research/analysis/parametric_non-parametric.htm (you can click through via links an see what is at your disposal)

Finally give us you null hypothesis. What is to be falsified anyway?

Does this help?

Last edited:

#### morgano

##### New Member
Hi tester1234,

I am sorry for my late reply ! This helps a lot !
Thank you so much for taking the time to reply!
Best

Morgan