How to normalize acceptability scores

In acceptability judgment experiments, participants make use of an acceptability scale (most commonly the 7-point Likert scale) in various ways; some people use 1 and 7 exclusively, while other people stick to 3 through 5. In order to normalize their scores, it is common to convert raw acceptability to z-scores (standard scores). In python, I will use the scipy package to achieve this.

import pandas as pd
from scipy.stats import zscore

sample = pd.read_csv('./sampledata.csv')
sample.head(3)

	Movement	Island_Type	Island	Distance	Item	Sentence	Subj_id	List	Score
0	WH	whe	non	sh	1	Who thinks that Paul stole the necklace?	1	1	6
1	WH	whe	non	sh	2	Who thinks that Matt chased the bus?	1	1	2
2	WH	whe	non	sh	3	Who thinks that Tom sold the television?	1	1	3

sample['Z_score'] = sample.groupby('Subj_id').transform(lambda x : zscore(x,ddof=1))

sample['Score'][:5]

0    6
1    2
2    3
3    7
4    2
Name: Score, dtype: int64

sample['Z_score'][:5]

0    1.265785
1   -0.734468
2   -0.234405
3    1.765848
4   -0.734468
Name: Z_score, dtype: float64