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Learning Statistics with Python

t-test Mathematically

The task of the t-test is to determine whether the difference between the two samples' means is significant. What should we take into consideration to perform it?

  • Obviously, we should consider the difference between the means itself;
  • As shown in the image below, the variance matters too;
  • Also, the size of each sample should be taken into consideration.

To account for the difference between the means, we simply calculate that difference:

The situation becomes more complex when it comes to variance. The t-test assumes that the variance is equal for both samples. We will delve deeper into this in the t-test assumptions chapter. To estimate the variance from two samples, the pooled variance formula is applied:

And to account for the size, we need sample sizes:

Let's put it all together into t statistic.

You may have noticed that sample sizes are not used in the most intuitive manner. However, this approach ensures that t follows the t-distribution, as we'll explore in the next chapter.

What sample properties does the t-test take into account?

Select a few correct answers

Everything was clear?

Section 6. Chapter 3
course content

Course Content

Learning Statistics with Python

Learning Statistics with Python

1. Basic Concepts

Sample vs PopulationTypes of StatisticsTypes of DataMean ValueMedian ValueMedian Value of the Even Number of ValuesMean or MedianMode ValueDescriptive Statistics Quiz

2. Mean, Median and Mode with Python

Examine the DatasetCalculating Mean and Median Values with PythonStatistics with pandasCalculate the Mean and Median Salary

3. Variance and Standard Deviation

Population VarianceSample VarianceCalculate Variance with PythonStandard deviationStandard Deviation with PythonCalculating Variance and Standard Deviation

4. Covariance vs Correlation

CovarianceCorrelationSelect All Possible ValuesCalculate Covariance and Correlation

5. Confidence Interval

Explore the Data SetConfidence IntervalCalculating Confidence Interval with PythonConfidence Interval Width QuizCalculate 95% Confidence IntervalAdvanced Confidence Interval Calculation with PythonMatch the Functions

6. Statistical Testing

What is t-testHypothesest-test MathematicallyOne-Tailed And Two-Tailed Testt-test AssumptionsPerforming a t-test in PythonConduct a t-testPaired t-test

t-test Mathematically

The task of the t-test is to determine whether the difference between the two samples' means is significant. What should we take into consideration to perform it?

  • Obviously, we should consider the difference between the means itself;
  • As shown in the image below, the variance matters too;
  • Also, the size of each sample should be taken into consideration.

To account for the difference between the means, we simply calculate that difference:

The situation becomes more complex when it comes to variance. The t-test assumes that the variance is equal for both samples. We will delve deeper into this in the t-test assumptions chapter. To estimate the variance from two samples, the pooled variance formula is applied:

And to account for the size, we need sample sizes:

Let's put it all together into t statistic.

You may have noticed that sample sizes are not used in the most intuitive manner. However, this approach ensures that t follows the t-distribution, as we'll explore in the next chapter.

What sample properties does the t-test take into account?

Select a few correct answers

Everything was clear?

Section 6. Chapter 3
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