One-Sample t-Test Algorithm

A One-Sample t-Test Algorithm is a statistical hypothesis testing algorithm that can be implemented by a one-sample t-test system (to solve a one-sample t-test task).

• Context:
  • It can (typically) calculate a One-Sample t-Test Statistic.
  • It can range from being a Composite One-Sample t-Test Algorithms to being a Singular One-Sample t-Test Algorithm.
  • It can also include the calculation of the p-value.
• Example(s):
  • the algorithm followed by SciPy.stats' stats.ttest_1samp()
• Counter-Example(s):
  • Independent Two-Sample t-Test Algorithm.
  • Paired Samples t-Test System.
• See: One-Sample t-Test Task, Parametric Statistical Test, Computing System, Parameter Optimization System.

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References

2017a

• (Scipy docs, 2017) ⇒ https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_1samp.html
  • scipy.stats.ttest_1samp(a, popmean, axis=0, nan_policy='propagate')

Calculates the T-test for the mean of ONE group of scores.

This is a two-sided test for the null hypothesis that the expected value (mean) of a sample of independent observations a is equal to the given population mean, popmean.

2017b

• (Varoquaux, 2017) ⇒ Retrieved on 2017-02-16 from "Statistics in Python" http://www.scipy-lectures.org/packages/statistics/index.html#student-s-t-test-the-simplest-statistical-test
  • QUOTE: scipy.stats.ttest_1samp() tests if the population mean of data is likely to be equal to a given value (technically if observations are drawn from a Gaussian distributions of given population mean). It returns the T statistic, and the p-value (see the function’s help):

>>>
>>> stats.ttest_1samp(data['VIQ'], 0) 
(...30.088099970..., 1.32891964...e-28)

With a p-value of 10^-28 we can claim that the population mean for the IQ (VIQ measure) is not 0.

2015

• (Hamelg, 2015) ⇒ Retrieved on 2017-02-26 from "Python for Data Analysis Part 24: Hypothesis Testing and the T-Test", http://hamelg.blogspot.ca/2015/11/python-for-data-analysis-part-24.html
  • A one-sample t-test checks whether a sample mean differs from the population mean. (...) To conduct a one sample t-test, we can the stats.ttest_1samp() function:

stats.ttest_1samp(a= minnesota_ages, popmean= population_ages.mean())
# (Sample data, Pop mean)

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