# How to use R to determine if a value is statistically LARGER than an average?

So I have daily temperature data for each day of the year going back up to 100 years for different locations. With this, I have created a mean value for each day of the year and a 95th percentile again for each day of the year.

I am comparing these values to the daily readings for a specific year (e.g.2016). However, I am only interested if the 2016 values are greater than the daily mean/95th percentile.

Is there a way to determine if the values are significantly greater than the mean/95th percentile?

In essence, there are 366 values for each column (one for each day of the year), and the mean/95th percentile and the 2016 data would be paired.

A rough idea of what my data looks like:

DAY OF YEAR: 1, 2, 3

MEAN TEMP: 12, 10, 11

2016 Temp: 17, 20.6, 13

Then:

DAY OF YEAR: 1, 2, 3

95th Percentile: 16, 14, 13

2016 Temp: 17, 20.6, 13

Apologies if the formatting is confusing.

So, all the 2016 values are larger than they 'should' be, but is this significant?

Is there a way to determine if the values are significantly greater than the mean/95th percentile, not just statistically different?

The short answer: yes, there is. Are you familiar with a t-test? I assume that's what you're referring to when you say you don't want something 'statistically different' but rather significantly greater. The thing you might be looking for is a one-sided t-test. However, that's fallen out of fashion in the scientific community because it can inflate your false-positive rate when combined with other data analysis practices.

If you have more questions, I can be more helpful if you include a reprex.

Having read the post a little more deeply. I think it's also important to pair your samples, considering they're from the same days. Of course, I'd like to know exactly what data you have and what you're trying to show, because there are nuances in the tests that can matter a lot.

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