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Learn Paired t-test | Statistical Testing
Learning Statistics with Python

bookPaired t-test

The following function conducts a paired t-test:

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.

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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')
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Task

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You are testing whether a change has increased the average number of downloads.

Two datasets are provided β€” before and after β€” representing the number of downloads before and after the changes.

The hypotheses are:

  • Hβ‚€: 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 using these samples and the corresponding alternative hypothesis.

  1. Use the st.ttest_rel() function to perform a paired t-test.
  2. Pass after and before as the first two arguments in this order.
  3. Set the argument alternative='greater' to test if the mean after is greater than before.
  4. Store the results in the variables stats and pvalue.
  5. Use the pvalue to determine whether to support or reject the null hypothesis.

Solution

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SectionΒ 6. ChapterΒ 8
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bookPaired t-test

Swipe to show menu

The following function conducts a paired t-test:

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.

123456789101112
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')
copy
Task

Swipe to start coding

You are testing whether a change has increased the average number of downloads.

Two datasets are provided β€” before and after β€” representing the number of downloads before and after the changes.

The hypotheses are:

  • Hβ‚€: 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 using these samples and the corresponding alternative hypothesis.

  1. Use the st.ttest_rel() function to perform a paired t-test.
  2. Pass after and before as the first two arguments in this order.
  3. Set the argument alternative='greater' to test if the mean after is greater than before.
  4. Store the results in the variables stats and pvalue.
  5. Use the pvalue to determine whether to support or reject the null hypothesis.

Solution

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SectionΒ 6. ChapterΒ 8
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