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I'm looking for books and information like crazy and I can not find what I need. Well the example proposed is about methods that have been used in literature students and these are the data collected:

$$ \begin{array}{rr} \text{Method 1, “X"} & \text{Method 2, “Y"} \\ 48 & 14 \\ 40 & 18 \\ 39 & 20 \\ 50 & 10 \\ 41 & 12 \\ 38 & 102 \\ 53 & 17 \end{array}$$

calculate with a level of significance of $\alpha = 0.05$ and P-Value

Hypothesis

  • $H_0 : F_{(t)} = G_{(t)}$

  • $H_0 : F_{(t)} \neq G_{(t)}$

The null hypothesis indicates that there is no difference between the reading groups X and Y.

I would like your help but as I don't understand the development well, I would ask you to do it step by step.

and I would also like to know how I solve an exercise where the samples don't have the same size

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    $\begingroup$ You need to use the self-study tag. $\endgroup$ – Michael R. Chernick Jun 3 '19 at 0:38
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    $\begingroup$ 1. What's your response variable there? 2. You ask about significance but your question contains no hypotheses; it's only a meaningful question in the presence of them. What's your null and alternative? $\endgroup$ – Glen_b Jun 3 '19 at 3:56
  • $\begingroup$ @Glen_b, edited $\endgroup$ – royer Jun 3 '19 at 16:23
  • $\begingroup$ I presume F and G represent cdfs? $\endgroup$ – Glen_b Jun 4 '19 at 1:15
  • $\begingroup$ @MichaelHardy thanks. I had to go look up how to do that in MathJax. The usual LaTex method didn't work. $\endgroup$ – Glen_b Jun 4 '19 at 1:22
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There are several possible tests for this situation.

A common choice is the two-sided two-sample Kolmogorov-Smirnov test.

Note that this assumes that the distributions are continuous; if your variables are discrete this test tends to be quite conservative (lower than desired type I error, with corresponding reduction in power)

As with the one-sample test, the test is based on the largest vertical distance between the cdfs.

This works with unequal sample sizes. There's a table of critical values at the link but any decent stats package will do it for you. You can

There's a small discrepancy between the table in Wikipedia and the p-values provided by R - the table values are large-sample, and are not exact for small samples. (You can find small sample tables fairly easily both in books and on-line.)

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