# Testing for Significant Difference in one Population

I have a dataset of 60 samples and a measure in percentage and want to show that this measure is significant different between the samples.

The mentioned percentage gives me the ratio of how often the car was used on the way to work. e.g. if the measure m=60%, from 10 days of going to work 6 times the car was used and 4 times other vehicles. In the dataset there are now samples with m=60%, others with m=100% and others with 0%. Obviously they differ but how can I express this in a p-value using a test?

My first guess was to just calculate standard deviation and if the value is higher than some threshold I would say it is different. But how to obtain this threshold?

EDIT: The dataset includes 61 samples similar to the 5 below:

0.583333333 0.070866142 0.166666667 0.423529412 0.29787234

• This looks like a job for a standard t-test. Can you show us your data, maybe paste it here? – user2974951 Jan 30 '19 at 15:16
• Is it sufficient to test for normal distribution? Then I would go for shapiro-wilk – mrks Jan 31 '19 at 11:51
• t-test assumes normally distributed residuals (not normally distributed data). – user2974951 Jan 31 '19 at 12:00

You can use one-sample t-test. Here is how you can do it

> #creating random sample
> x = round(runif(60, 1, 100), 0)
>
> #summary of data
> library(psych)
> describe(x)
vars  n mean    sd median trimmed   mad min max range skew kurtosis   se
X1    1 60 42.6 28.44   38.5   40.96 33.36   2 100    98 0.36    -1.07 3.67
>
> #perform t-test now
> t.test(x)

One Sample t-test

data:  x
t = 11.602, df = 59, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
35.25261 49.94739
sample estimates:
mean of x
42.6