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I have two observations for each row of my dataset:

My Dataset looks like this:

 Company1 |  2016 |    x1 | y1 
 Company1 |  2017 |    x2 | y2 
 Company2 |  2016 |    x3 | y3 
 Company2 |  2017 |    x4 | y4 
 ... 

I want to prove with a statistical test, that the $X$ values are significantly larger than the $Y$ values. Meaning, that the difference $X$ - $Y$ is tendencially positive.

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2 Answers 2

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If you assume each row is independent to each other, you could just calculate the difference of X - Y, and perform the paired sample t-test on these differences to see if they are greater than zero or not. However, it looks like you repeated measure each company twice (2016 & 2017) so it violates the independent assumption of t test. You may need to use the repeated measure ANOVA instead. This link might be helpful: https://statistics.laerd.com/statistical-guides/repeated-measures-anova-statistical-guide.php

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The RV $X$ being larger than the RV $Y$ is referred to as $X$ being stochastically greater than $Y$. The Mann-Whitney U Test tests this very hypothesis.

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    $\begingroup$ The form of the data suggests you ought to control for year. $\endgroup$
    – whuber
    Dec 27, 2017 at 23:42

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