[Term Entry] Python statsmodels: t-tests

content/python/concepts/statsmodels/terms/t-tests/t-tests.md

@@ -0,0 +1,76 @@
+---
+Title: 't-tests'
+Description: 'Tests whether the means of one or two groups are significantly different under specified assumptions.'
+Subjects:
+  - 'Machine Learning'
+  - 'Data Science'
+Tags:
+  - 'Statistics'
+  - 'Properties'
+  - 'Models'
+  - 'Data'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/computer-science'
+---
+
+The **t-test** in Statsmodels is a statistical method to determine whether the means of one or two groups differ significantly. It is commonly used to compare the mean of a sample to a specified value, the means of two independent groups, or the means of paired data.
+
+## Syntax
+
+```pseudo
+statsmodels.stats.weightstats.ttest_ind(x1, x2, alternative='two-sided', usevar='pooled', weights=(None, None))
+```
+
+- `x1`, `x2`: Arrays containing sample data for the groups being compared.
+- `alternative`: The hypothesis to test. Options include:
+  - `'two-sided'`: Default, tests for any difference.
+  - `'larger'`: Tests if the mean of `x1` is greater than `x2`.
+  - `'smaller'`: Tests if the mean of `x1` is less than `x2`.
+- `usevar`: Assumptions about variance. Options include:
+  - `'pooled'`: Default, assumes equal variance.
+  - `'unequal'`: Does not assume equal variance.
+- `weights`: A tuple specifying weights for `x1` and `x2`, used in weighted t-tests.
+
+## Example
+
+In this example, a one-sample t-test is performed to determine whether the mean of a sample dataset is significantly different from _10_:
+
+```py
+import numpy as np
+from statsmodels.stats.weightstats import ttest_ind
+
+# Sample data
+data = np.array([9.5, 10.1, 9.8, 10.2, 9.9, 10.0, 9.7])
+
+# Hypothesized population mean
+population_mean = 10
+
+# Perform t-test
+t_stat, p_value, df = ttest_ind(
+    data,
+    np.full(len(data), population_mean),
+    alternative='two-sided'
+)
+
+# Output results
+print(f"t-statistic: {t_stat}")
+print(f"P-value: {p_value}")
+print(f"Degrees of freedom: {df}")
+
+# Interpretation
+alpha = 0.05
+if p_value < alpha:
+    print("Reject the null hypothesis: The sample mean is significantly different from 10.")
+else:
+    print("Fail to reject the null hypothesis: No significant difference from 10.")
+```
+
+The code above generates the following ouput:
+
+```shell
+t-statistic: -1.2545000963743562
+P-value: 0.23354509216171446
+Degrees of freedom: 12.0
+Fail to reject the null hypothesis: No significant difference from 10.
+```