7 posts
From the intuition of hypothesis testing to the meaning of the test statistic, plus null/alternative hypotheses, p-value, significance level, and critical value — all connected through a single example.
![Implementing the t-test (t test) [One, Two, Paired Samples t-test: Python feat. SciPy & Statsmodels]](assets/posts/t-test/cover.webp)
Turning the t-test theory from the previous post into SciPy code — ttest_1samp, ttest_ind (equal_var toggle), ttest_rel, with axis options. Verifying the hand-computed t and p match SciPy.
As the sample size grows, the sample mean converges to a normal distribution for any population — verified with five distributions, plus why the CLT matters for estimation and confidence intervals.
Is a difference in two group means a real difference or just variability — the rationale for the t-test, its assumptions (normality, equal variance), and worked calculations for each type.
From why confidence intervals exist, to the hypothesis-testing view, to the truth behind the common misconception that 'there's a 95% probability the mean is inside the interval.'
Why does the sample variance divide by n-1 instead of n? Two views — correcting underestimation (bias) and degrees of freedom — to get at the essence of variance.
Connecting the nature of probability through three concepts — uncertainty, variability, and variance — including the intuition for why variance is defined as 'distance from the mean.'