Testing for treatment differences in a problem involving repeated measures I am having trouble choosing the right statistical test for my data analysis.
Every patient undergoes a stress condition and other five normal conditions. For each patient and for each condition I measure the blood flow velocity. The measures are thus repeated.
Which statistic test should be used to compare the difference between different normal conditions and between all conditions?
Currently, I have observed values for 7 patients, but the study is undergoing and the number of patients will likely increase.
 A: Since the patients in each treatment cohort are identical, I don't think you need a mixed model (as opposed to utobi's answer). Instead you can simply perform pairwise one-sample t-test between the treatments (even this is not my favourite solution). But I would simply use the lm() function to estimate each treatments expected value of the target and then considering the confidence intervals I would compare the groups using the GGally package. Here is how I do it:
# nr. of patients
N <- 30

# --- using a modified version of the simulated data by utobi
set.seed(1)
bfv_stress <- rnorm(N,50, sd=10)
bfv_rest1 <- rnorm(N,2, sd=7)
bfv_rest2 <- rnorm(N,3, sd=10)
bfv_rest3 <- rnorm(N,0, sd=15)
bfv_rest4 <- rnorm(N,0, sd=16)
bfv_rest5 <- rnorm(N,-1, sd=17)

my_long_data <- data.frame(bfv = c(bfv_stress,bfv_rest1,
                                   bfv_rest2,bfv_rest3,
                                   bfv_rest4,bfv_rest5),
                           treatment = c(rep("stress", N),
                                         rep("rest1", N),
                                         rep("rest2", N),
                                         rep("rest3", N),
                                         rep("rest4", N),
                                         rep("rest5", N)
                           ))
my_long_data$patient_id <- rep(1:N, 6)


# Fitting the model
lm.fit = lm(bfv ~ -1 + treatment, data = my_long_data)

# Visualising the results
GGally::ggcoef_model(lm.fit)   

And here is the resulting plot:

From this plot you can see that the stress treatment is significantly different than the rest. Their confidence intervals do not overlap and if you perform a hypothesis test you will get significant result for $\alpha = 5\%$.
