Unpaired(Independent) Parametric T-test

Statistics Series

Hello folks,
The article explains Independent(Unpaired) Parametric t-test in layman’s term without mathematical formulation which is used to test significance between two independent
Groups(samples).
We try to cover all fundamentals with example hope you like

Where We Can Apply Unpaired Prametric T-test ?

• two groups needs to be independent
• parametric assumption needs to be satisfy

Outline for performing Unpaired(independent) Parametric T-test

1. Formulate Problem statement(research question) and hypothesis
2. Import data
3. Check independent parametric t-test assumption
4. compute unpaired t-test(based on t-test selection)
5. interpret result

T-test type and selection

Two types:

1. student t-test(if assuming two group variance is equal)
2. welch t-test(if assuming two group variance is uneuqal)

we are going to implement both.. :)

Important : we used Levene’s test for variance equality check

Parametric Assumption

Assumption 1 : Are the two samples(two group) independent Assumption 2 : Are the data from each of the 2 groups follow a normal distribution?

Important : we used Shapiro-Wilk normality test for checking two group normal distribution

Shapiro-Wilk return two result first is w-value and second is p-value

Implementation section

1. Problem statement(Research Question)

we have measured the weight of 100 individuals: 50 women (group A) and 50 men (group B).
We want to know if the mean weight of women (mA) is significantly different from that of men (mB).

Bold one is problem statement

Formulate hypothesis

null hypothesis (H0): H0:mA=mB
alternative hypothesis (Ha): Ha:mA≠mB (different)

Important:two tailed hypothesis

2. Import data

In [1]:

import pandas as pd

In [2]:

data=pd.read_csv("dataset/mw.csv")
data.shape

Out[2]:

(18, 2)

In [3]:

data.shape

Out[3]:

(18, 2)

3. Parametric Assumptions

Parametric Assumption 1: Are the two samples(two group) independent?
Conclusion : Yes, since the samples from men and women are not related.

Assumtion 2: Are the data from each of the 2 groups follow a normal distribution?

step 1 : formulate hypothesis

• null hypothesis (H0): data are normaly distributed
• alternative hypothesis (Ha): note normaly distributed

step 2 : if Shapiro-Wilk test result p-values are greater then the significance p-value(0.05) then accept null hypothesis that means data is normal distributed

Conclusion:
man p-value(0.106) > 0.05 hence normal distributed
woman p-value(0.601) > 0.05 hence normal distributed

In [4]:

import scipy.stats as stats

In [5]:

man=data[data['group']!='Woman']
woman=data[data['group']=='Woman']

In [6]:

stats.shapiro(man.weight.dropna())

Out[6]:

(0.8642458319664001, 0.10660982877016068)

In [7]:

stats.shapiro(woman.weight.dropna())

Out[7]:

(0.9426567554473877, 0.6101282835006714)

Assume Equal variance t-test hence student t-test

Levene's test

Problem formulation: both group have equal variance?

step 1 : formulate hypothesis

null hypothesis (H0): both group have equal variance alternative hypothesis (Ha): both group have unequal variance

step 2 : if Levene test result p-values are greater then the significance p-value(0.05) then accept null hypothesis that means both group have equal variance

Conclusion : p-value(0.2255) > 0.05 hence both group have equal variance

In [8]:

stats.levene(man.weight.dropna(), woman.weight.dropna())

Out[8]:

LeveneResult(statistic=1.5888334612432846, pvalue=0.22556594075964187)

Parametric Normality and Equal Variance Criteria True so we apply student t-test

In [9]:

t, p = stats.ttest_ind(man.weight.dropna(), woman.weight.dropna())
t, p

Out[9]:

(2.7842353699254567, 0.013265602643801042)

Interpretation of Result

The p-value(0.013)>0.05 which is false so we accept alternate hypothesis which is We can conclude that men’s average weight is significantly different from women’s average weight

Parametric Normality and unEqual Variance Criteria True so we apply student welch-t-test

In [10]:

t, p = stats.ttest_ind(man.weight.dropna(), woman.weight.dropna(),equal_var = False)
t, p

Out[10]:

(2.7842353699254567, 0.015384235142669895)

Feel Free to ask question

Stay Tuned for next unpaired(independent) non parametric Mann- Whitney U test

Reference:

https://github.com/sanketpatel307/independent-parametric-t-test