I am quite new to statistics. I have designed an experiment where participants are supposed to tap to reproduce the tempo of some music samples. I have manipulated the music samples at tempo values at 60, 120 and 150 bpm, which is my x-variable and I have labelled it as categorical and nominal. In addition to the recorded tempo values (y-variable), I am looking at one more variable which I call the S-factor. The S-factor is a categorical variable and provides me information if the given tempo and the reproduced tempo match. For eg. If 60 bpm was perceived at 60 bpm, the label is 1 = Same. If 60 was perceived at 120 then the label is 2=Double. There are 4 labels in S-factor 0- Half, 1= Same, 2 = Double, 3 = Other. My H0 is = The perceived tempo is same as given tempo which means 60 will be perceived at 60, 120 will be perceived at 120 and 150 at 150. H1 = The perceived tempo is not same as given tempo. I have two questions: 1) Is Given tempo (60bpm, 120 bpm and 150 bpm) at which the songs are presented a categorical variable or continuous variable? Should S-factor be labelled as nominal or ordinal variable? 2) In order to test the hypothesis, should I do the chi-square test of independence since both Given Tempo and perceived tempo are categorical or Should I just go to analyse ---> Fit Model ----> Put Tempo as x-variable and S-Factor as y-variable? I do not if these are two different approaches of looking at the problem or only one of them is correct?
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