Two sample t-test for every individual row in Python

Question

I am trying to do a two sample t test to check if there is significant difference in mean between two datasets.

I have two datasets and each dataset has 5 trials and each Trial has 3 features. Every Trial has different unique label but the 3 features(X1,X2,X3 are same across all). On every individual Trial we are measuring the 3 features and the measurement values are displayed below. I am trying to calculate the mean difference for each feature across both the datasets.

This is how my data looks after when i get it from SQL.

Data Set 1:

T1  X1   0.93
T1  X2   0.3
T1  X3   -2.9
T2  X1   1.3
T2  X2   0.8
T2  X3   1.9
T3  X1   2.3
T3  X2   -1.8
T3  X3   0.9
T4  X1   0.3
T4  X2   0.8
T4  X3   0.9
T5  X1   0.3
T5  X2   0.8
T5  X3   0.9

Data Set 2:

T10 X1  1.3
T10 X2  -2.8
T10 X3  0.09
T11 X1  3.3
T11 X2  0.8
T11 X3  1.9
T12 X1  0.3
T12 X2  -4.8
T12 X3  2.9
T13 X1  1.3
T13 X2  2.8
T13 X3  0.19
T14 X1  2.3
T14 X2  0.08
T14 X3  -0.9

This is how i want my output to look, where i want the ttest to be applied to each Feature, so I can get the p value for each feature

Feature  Mean-DataSET1  Mean-DataSET2  P-value 
X1
X2
X3  

when i do stats.ttest_ind(set1['value'], set2['value']).pvalue, I am getting one single pvalue

Thanks!

Answer 1

If I understand you question correctly you can get the mean for each feature using Groupby, and then get the p-value for each feature all in one dataset. so first I would create the dataset,

a = {'Feature': ['X1','X2','X3','X4','X5']}
Results = pd.DataFrame(data = a)
Results.set_index('Feature')

Then to get the mean of your features, you can use group by and send the result to this new dataset,

Results['Mean-DataSET1'] = df1.groupby('feature')['value'].transform('mean')
Results['Mean-DataSET2'] = df2.groupby('feature')['value'].transform('mean')

Now as far as I know p-tests returns the value of the whole column so I would get both my value columns in one place and then split my data into temporary datasets and get the p-value of those,

df['value2'] = df2['value']

xone = df[(df['col2'] == 'X1')]
xtwo = df[(df['col2'] == 'X2')] 
xthree = df[(df['col2'] == 'X3')] 
xfour = df[(df['col2'] == 'X4')] 
xfive = df[(df['col2'] == 'X5')] 

This way you can preform the same function as before and get all the values like so,

p_vals = ttest_ind(xone['value'], xone['value2']).pvalue, ttest_ind(xtwo['value'], xtwo['value2']).pvalue, ttest_ind(xthree['value'], xthree['value2']).pvalue, ttest_ind(xfour['value'], xfour['value2']).pvalue, ttest_ind(xfive['value'], xfive['value2']).pvalue

Results['P_value'] = p_vals

So a sample output on a subset of your data would like like:

    Feature mean1   mean2   P_value
    X1  1.510000    1.633333    0.905175
    X2  -0.233333   -2.266667   0.326891
    X3  -0.033333   1.630000    0.377542

It's not the most graceful answer but it should be ok for now as you only have small datasets!

Answer 2

I written your output above to two tab delimited files, and I read it in below, and add a column to indicate the dataframe or table it is from:

import pandas as pd
from scipy.stats import ttest_ind
t1 = pd.read_csv("../t1.csv",names=['V1','V2','V3'],sep="\t")
t1['data'] = 'data1'
t2 = pd.read_csv("../t2.csv",names=['V1','V2','V3'],sep="\t")
t2['data'] = 'data2'

    V1  V2  V3  data
0   T1  X1  0.93    data1
1   T1  X2  0.30    data1
2   T1  X3  -2.90   data1
3   T2  X1  1.30    data1

Then we concatenate them and calculating the mean is straight forward:

df = pd.concat([t1,t2])
res = df.groupby("V2").apply(lambda x:x['V3'].groupby(x['data']).mean())
data    data1   data2
V2      
X1  1.026   1.700
X2  0.180   -0.784
X3  0.340   0.836

p.value requires a bit more coding within the apply:

res['pvalue'] = df.groupby("V2").apply(lambda x:
                                       ttest_ind(x[x['data']=="data1"]["V3"],x[x['data']=="data2"]["V3"])[1])
data    data1   data2   pvalue
V2          
X1  1.026   1.700   0.316575
X2  0.180   -0.784  0.521615
X3  0.340   0.836   0.657752

You can always choose to do res.reset_index() to get a table..