# How to compare means, variances and standard deviations of durations for statistical significance

I am trying to compare multiple mean values, variance and standard deviation values for statistical significance. For example I have the following data:

Data 1

• Mean: 0.01304
• Sample Variance: 0.000504324897959184
• Standard Deviation: 0.0224571792075315

Data 2

• Mean: 1.17498
• Sample Variance: 0.180901244489796
• Standard Deviation: 0.425324869352588

How can I compare them?

• Is this a question from a course or textbook? Even if not, for questions like this you should probably add the [self-study] tag & read its wiki. – gung - Reinstate Monica Apr 6 '15 at 16:25
• Using only sample statistics, you will need to make assumptions. You will also need the $n$'s from the 2 datasets. Do you have that? – gung - Reinstate Monica Apr 6 '15 at 16:45
• @gung Yes I have the n's. The n for both the above data is 50. I need to compare the information above to come to a conclusion. I just don't know how to compare them. are there any formulas or techniques? I have the entire data set from which mean, variance and standard deviation was calculated. – Lorenzo von Matterhorn Apr 6 '15 at 16:49
• Is this question from a course or textbook? What software do you have access to? You would do better to work with the full dataset rather than just the summary statistics. – gung - Reinstate Monica Apr 6 '15 at 16:50
• @gung its not from any course or textbook. I collected the data myself. The data represents HTTP requests times for 2 different web frameworks. The above means, variance and standard deviation were calculated from the data set using EXCEL. – Lorenzo von Matterhorn Apr 6 '15 at 16:56

Because your data are durations, you should use methods from survival analysis. A $t$-test is unlikely to be appropriate. I doubt this can be done in Excel. It isn't hard to do in R, however, and R is free. You should download R from here. This guide should be simple and quick enough to give you what you will need.

What you want is to use a log rank test. In R that's ?survdiff. You may also want to plot and examine the Kaplan-Meier survival curves. In R, you can use ?survfit and then plot(). Here's a quick demonstration from the R documentation:

# install.packages(survival)  # if necessary
library(survival)

leukemia.surv <- survfit(Surv(time, status) ~ x, data = aml)
windows()
plot(leukemia.surv, lty = 2:3)
legend(100, .9, c("Maintenance", "No Maintenance"), lty = 2:3)
title("Kaplan-Meier Curves\nfor AML Maintenance Study")


survdiff(Surv(time, status) ~ x, data = aml)
# Call:
#   survdiff(formula = Surv(time, status) ~ x, data = aml)
#
#                  N Observed Expected (O-E)^2/E (O-E)^2/V
# x=Maintained    11        7    10.69      1.27       3.4
# x=Nonmaintained 12       11     7.31      1.86       3.4
#
# Chisq= 3.4  on 1 degrees of freedom, p= 0.0653