# Methods to quantify if the sum of two variables is close to a constant

In my data set, each individual has two properties, a and b. It seems that a + b is close to 10. Which statistic method could I use to test if this is true?

 Person a   b
1   2   8
2   2   9
3   3   7
4   2   8
5   4   6
6   2   8
7   4   6
8   2   9
9   2   8
10  5   5

• "a+b close to some constant" is equivalent to testing whether $a$, $b$, and a constant (nonzero) vector are linearly dependent. Thus, your question is a special case of stats.stackexchange.com/questions/16327/…. However, it is such a straightforward problem that it admits other solutions not applicable in that thread. – whuber Mar 7 '18 at 22:22

Create a third column a+b:

10
11
10
10
10
10
10
11
10
10


Get the mean and standard deviation: $\mu=10.2$ and $\sigma=0.42$

Test whether the mean is far from 10: t-stat$: \frac{10.2-10}{0.42/\sqrt{10}}=1.5$

Since t-statistic is lower than the critical value at 95%, then we conclude that it may indeed be 10, the sum of two columns.

• Thank you! Just figured out that this question is a simple One Sample T Test. Here is the link for more details in case other people would be interested in. – Kevin Mar 8 '18 at 17:53
• yes, I forgot to divide by $\sqrt n$, corrected – Aksakal Mar 8 '18 at 20:00