# Which statistical test is appropriate for my data?

First 5 rows of my data are as follows:

before after    exercise_type
17.4    16.74     1
17.5    18.74     2
17.2    25.62     1
18.0    16.65     3
18.0    16.60     1


where before is the weight before the exercise, after is the weigh after the exercise and exercise_type is the exercise that was applied. I want to investigate which exercise type led to more weight lose. I have 50 observations. Which test should I use?

You should use ANOVA and a Tukey Range Test.

The top google result for ANOVA is:

https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide.php

Which is captioned with:

The one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. This guide will provide a brief introduction to the one-way ANOVA, including the assumptions of the test and when you should use this test.

This will tell you whether there is a difference in means between the treatment groups.

Then, post-hoc, you can use a Tukey Range Test, as Kevin rightly suggested in another answer, to help you determine which treatments differ.

• But my data are repeated. Does that make any difference? I suppose I should use Factorial Repeated Measures ANOVA. Am I right? – Günal Dec 30 '15 at 21:24
• Sure, you could either use repeated measures ANOVA and consider before and after $T_1$ and $T_2$ or ANOVA and consider after-before as the value. – Thomas Cleberg Dec 30 '15 at 21:29

If somebody would correct me, please do, but I believe one analysis would be Tukey's HSD. Here is a link for more information.

https://en.wikipedia.org/wiki/Tukey%27s_range_test

Basically, when you have more than two levels (exercise type), it becomes more difficult to do a proper test without taking into consideration the # of levels you have. Do you only have 3 levels?

edit @Thomas Cleberg is probably right but we'll see I guess!

• I have 5 levels. I am interested in the sharpest decrease in the weight. – Günal Dec 30 '15 at 21:23
• Actually, given that you're looking for the highest effect of exercise treatments, the answer is both ANOVA and a Tukey Range Test. That is, you'd use ANOVA to test if there is a difference and Tukey post hoc to find the highest effect. – Thomas Cleberg Dec 30 '15 at 21:38
• As answers can change position, and other answers can be added, references to answers "above" or "below" can be wrong or ambiguous. I've edited to specify the author in question. That would remain valid if there are other answers (and would only be rendered invalid if the answer was deleted). – Nick Cox Dec 31 '15 at 2:17