which kind of statistics for continous variables I have one sample composed by 18 subjects. I measured the performance of a game and the fatigue before and after going to sleep and before and after a certain wake condition. 
So, I have game scores and fatigue scores detected in 4 times. 
All variables are continous and I cannot turn them in ordinal or nominal.
I want to test the differences among the performance in each condition (1- before sleep, 2-after sleep, 3-before wake, 4-after wake) controlling for the effect of fatigue measured in these 4 conditions.
I cannot perform a repeated measure Anova because my IV is not a fixed factor. 
Which kind of statistical test is best suited for these kind of variables (i.e. continous)?
Thanks a lot!
 A: I would recommend doing a Linear Mixed-Effects Model. You would assume something like this, where $i$ is the patient and $j$ is the condition:
$$
performance_{ij} = \beta + \alpha_j + \gamma*fatigue_{ij}+\epsilon_{ij}
$$
where $\epsilon_{ij}, \alpha_j$ are normally distributed with mean 0   
the model has two types of effects (hence the word mixed):  
fixed effects: $\beta,\gamma$
random effects: $\alpha_j$
It is like a simple linear regression but there is an extra intercept $\alpha_j$ that depends on the condition, which is what you want to measure. In other words, a different intercept is assumed for each condition. In this model the conditions only determine the intercept and not the slope, however you could assume a slope for each condition too.  
After fitting the model you can use ANOVA to compare this model VS a model without random effects (i.e., a simple linear regression)
Are you familiar with R?
https://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf
Here is a simluation based on the formula above:
library(data.table)
library(magrittr)
library(lme4)

subjects <- 1:18
fatigue_effect <- -3
conditions <- c(1,2,3,4)
beta <- 10
alphas <- c(4,-2,-5,3) # this were not simulated so that you could see the actual values
set.seed(123)
fatigues <- runif(length(subjects)*length(conditions),0,2)

data <- lapply(conditions, . %>% data.table(subject=subjects,condition=.)) %>% rbindlist
data[,fatigue:=fatigues]
set.seed(123)

data[,performance:=beta+fatigue_effect*fatigue+alphas[condition]+rnorm(.N,0,2)]
model <- lmer(performance~fatigue+(1|condition),data)
coef(summary(model));ranef(model)


Here the 2 fixed effects, slope and sensitivity to fatigue are 10 and -3 respectively, and random effects by condition are: 4,-2,-5,3. The code will give the following results, pretty close to the actual values:

         Estimate Std. Error   t value
(Intercept) 10.158661  2.1848023  4.649693
fatigue     -3.089768  0.4240635 -7.286096
$condition
  (Intercept)
1    4.180160
2   -2.089153
3   -4.898196
4    2.807189

and the ANOVA test:
lreg <- lm(performance~fatigue,data)
anova(model,lreg)

refitting model(s) with ML (instead of REML)
Data: data
Models:
lreg: performance ~ fatigue
model: performance ~ fatigue + (1 | condition)
      Df    AIC    BIC  logLik deviance Chisq Chi Df Pr(>Chisq)    
lreg   3 413.31 420.14 -203.65   407.31                            
model  4 322.56 331.67 -157.28   314.56 92.75      1  < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

