Paired t-test

The following function conducts a paired t-test:

python
ttest_rel(a, b, alternative='two-sided')

This process resembles the one used for independent samples, but here we do not need to check the homogeneity of variance. The paired t-test explicitly does not assume that variances are equal.

Keep in mind that for a paired t-test, it's crucial that the sample sizes are equal.

With this information in mind, you can proceed to the task of conducting a paired t-test.

Here, you have data regarding the number of downloads for a particular app. Take a look at the samples: the mean values are nearly identical.

import pandas as pd

import matplotlib.pyplot as plt

# Read the data

before = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/before.csv').squeeze()

after = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/after.csv').squeeze()

# Plot histograms

plt.hist(before, alpha=0.7)

plt.hist(after, alpha=0.7)

# Plot the means

plt.axvline(before.mean(), color='blue', linestyle='dashed')

plt.axvline(after.mean(), color='gold', linestyle='dashed')


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import pandas as pd
import matplotlib.pyplot as plt

# Read the data
before = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/before.csv').squeeze()
after = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/after.csv').squeeze()
# Plot histograms
plt.hist(before, alpha=0.7)
plt.hist(after, alpha=0.7)
# Plot the means
plt.axvline(before.mean(), color='blue', linestyle='dashed')
plt.axvline(after.mean(), color='gold', linestyle='dashed')

Compito

Swipe to start coding

Hypotheses are established:

H₀: The mean number of downloads before and after the changes is the same;
Hₐ: The mean number of downloads is greater after the modifications.

Conduct a paired t-test with this alternative hypothesis, using before and after as the samples.

Soluzione

import scipy.stats as st

import pandas as pd

before = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/before.csv').squeeze()

after = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/after.csv').squeeze()

stats, pvalue = st.ttest_rel(after, before, alternative='greater')

# Check the null hypothesis

if pvalue > 0.05:

print("We support the null hypothesis, the mean values are equal")

# Check the alternative hypothesis

else:

print("We reject the null hypothesis, the mean values are different")

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Sezione 6. Capitolo 8

import scipy.stats as st

import pandas as pd

before = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/before.csv').squeeze()

after = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/after.csv').squeeze()

stats, pvalue = ___(___)

# Check the null hypothesis

if pvalue > 0.05:

print("We support the null hypothesis, the mean values are equal")

# Check the alternative hypothesis

else:

print("We reject the null hypothesis, the mean values are different")

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