What method is recommended after outliers removal? I have a data of mice reaction times. In every session, there are some trials in which the mouse &quot;decides of a break&quot; and responds after a long time to these specific trials.
I was thinking of applying outlier removal on my data. and the data does look better (I used a Matlab function which removed all data above of below 3 IQR's above and below median).
After doing that I got a histogram which is more similar to a normal distribution (below an example picture of one of my sessions).
My question is:

After applying my outlier removal, how should I analyze the remaining data?
Should I consider the Median (together with IQR as standard error mean)?
Or should I consider the mean (together with $ \frac{\sigma}{\sqrt n}$ as standard error mean)?

Remark: I have very little knowledge in statistics, so, I there are mistakes above (for example my standard error mean definition as IQR or $ \frac{\sigma}{\sqrt n}$ is not correct), I would be grateful if you'll let me know.
Thanks!
Edit: The purpose of my analysis is to show that under certain conditions, the response times of the mice will be faster then under other conditions.
fig 1: Data before outlier removal

fig 2: Data after outlier removal
based on this information I would recommend to use


Wilcoxon signed-rank test


or


paired Student's t test


This depends on your sample size and distribution. To test if your data set is normally distributed you can use the Jarque-Bera test.

I didn't work with Matlab yet, but  I guess all the tests should be implemented in Matlab. 

From that point you could evaluate the impact of the condition on response time. 
Visualize your data (X on Y) - Scatter plot / Heatmap (if multivariate data). 

From here you could start building a model


starting with linear regression
going into more advanced models/approaches -- random forests, bootstrapping etc.


Added 

If you only have binary variables (condition / no condition) - you need to set up dummy variables to perform a regression model (1 / 0) . Data then could look like:

 obs  response-time   any_condition  condition_1   condition_2   condition_3
  1   12.54           1              1             0             0
  2   19.34           0              0             0             0
  3   13.32           1              1             1             0
  4   14.7            0              0             0             0


If you have multiple different "state" conditions, I would recommend to use a control variable ("any_condition") - to see if conditions (not specifying which, have an impact) on the response time. 

I hope that helps.