What Is a t-test
The t-test is a fundamental statistical method for determining whether there is a significant difference between the means of two groups.
Origin of the t-test
- Developed by William Sealy Gosset in the early 20th century;
- Published under the pseudonym "Student," leading to the name "Student's t-test";
- Created to address quality control problems at the Guinness Brewery, especially when working with small sample sizes and unknown population variances.
When to use a t-test
Use a t-test when you want to compare the means of two groups to see if they are statistically different from each other. This is especially useful in these scenarios:
- Small sample sizes;
- Unknown population standard deviation;
- Comparing test scores between two classes;
- Evaluating the effect of a treatment versus a control group;
- Analyzing results from an A/B test in product development.
123456789101112131415161718192021222324252627# Calculate the t-statistic manually for two small samples import numpy as np # Sample data: group A and group B group_a = np.array([12, 15, 14, 10, 13]) group_b = np.array([16, 18, 14, 17, 15]) # Calculate means mean_a = np.mean(group_a) mean_b = np.mean(group_b) # Calculate sample variances var_a = np.var(group_a, ddof=1) var_b = np.var(group_b, ddof=1) # Sample sizes n_a = len(group_a) n_b = len(group_b) # Calculate pooled standard deviation pooled_std = np.sqrt(((n_a - 1) * var_a + (n_b - 1) * var_b) / (n_a + n_b - 2)) # Calculate t-statistic t_stat = (mean_a - mean_b) / (pooled_std * np.sqrt(1/n_a + 1/n_b)) print("t-statistic:", round(t_stat, 3))
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The t-test is a fundamental statistical method for determining whether there is a significant difference between the means of two groups.
Origin of the t-test
- Developed by William Sealy Gosset in the early 20th century;
- Published under the pseudonym "Student," leading to the name "Student's t-test";
- Created to address quality control problems at the Guinness Brewery, especially when working with small sample sizes and unknown population variances.
When to use a t-test
Use a t-test when you want to compare the means of two groups to see if they are statistically different from each other. This is especially useful in these scenarios:
- Small sample sizes;
- Unknown population standard deviation;
- Comparing test scores between two classes;
- Evaluating the effect of a treatment versus a control group;
- Analyzing results from an A/B test in product development.
123456789101112131415161718192021222324252627# Calculate the t-statistic manually for two small samples import numpy as np # Sample data: group A and group B group_a = np.array([12, 15, 14, 10, 13]) group_b = np.array([16, 18, 14, 17, 15]) # Calculate means mean_a = np.mean(group_a) mean_b = np.mean(group_b) # Calculate sample variances var_a = np.var(group_a, ddof=1) var_b = np.var(group_b, ddof=1) # Sample sizes n_a = len(group_a) n_b = len(group_b) # Calculate pooled standard deviation pooled_std = np.sqrt(((n_a - 1) * var_a + (n_b - 1) * var_b) / (n_a + n_b - 2)) # Calculate t-statistic t_stat = (mean_a - mean_b) / (pooled_std * np.sqrt(1/n_a + 1/n_b)) print("t-statistic:", round(t_stat, 3))
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