Unpaired(Independent) Non Parametric Two-sample Mann–Whitney U test

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Where We Can Apply Unpaired Non Parametric Two-sample Mann–Whitney U test ?

• two groups needs to be independent

Outline for performing Unpaired Non Parametric Two-sample Mann–Whitney U test

1. Formulate Problem statement(research question) and hypothesis(two different type)
2. Import data
3. Check Appropriate data
4. compute Mann–Whitney U test
5. interpret result

Implementation section

1. Problem statement(Research Question)

Are Pooh's scores significantly different from those of Piglet?.

Formulate hypothesis

Two types:

If the distributions of the two groups are similar in shape and spread:
• Null hypothesis: The medians of values for each group are equal.
• Alternative hypothesis (two-sided): The medians of values for each group are not equal.

If the distributions of the two groups are not similar in shape and spread:
• Null hypothesis: The two groups exhibit stochastic equality.
• Alternative hypothesis (two-sided): The two groups do not exhibit stochastic equality.

Important:two tailed hypothesis

2. Import data

import pandas as pd

data=pd.read_csv("dataset/mwt.csv", skipinitialspace= True )
data['Speaker'] = data['Speaker'].map(lambda x: x.strip())

data.shape

(20, 2)

data.shape

(20, 2)

3. Appropriate data

• Two-sample data. That is, one-way data with two groups only
• Dependent variable is ordinal, interval, or ratio
• Independent variable is a factor with two levels. That is, two groups
• Observations between groups are independent. That is, not paired or repeated measures data
• In order to be a test of medians, the distributions of values for each group need to be of similar shape and spread; outliers affect the spread. Otherwise the test is a test of stochastic equality.

import scipy.stats as stats
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
plt.style.use('bmh')
plt.style.use('ggplot')
plt.rcParams['figure.figsize'] = 20, 10

Pooh=data[data['Speaker'] == 'Pooh']
Piglet=data[data['Speaker'] == 'Piglet']

Pooh.hist(figsize=(5, 5), bins=5, xlabelsize=8, ylabelsize=8);
Piglet.hist(figsize=(5, 5), bins=5, xlabelsize=8, ylabelsize=8);
    

Likert is the dependent variable and Speaker is the independent variable. **
** Shape and distribution is not same so second hypothesis will used here.

stats.mannwhitneyu(Pooh.Likert, Piglet.Likert)

MannwhitneyuResult(statistic=5.0, pvalue=0.00023567203407747563)

Interpretation of Result

The p-value(0.00023)>0.05 which is false so we accept alternate hypothesis which is The two groups do not exhibit stochastic equality.