Hypothesis Testing & Statistical Analysis Markdown Table Template

When to Use This Table

Formatting This Table in Markdown

A hypothesis testing & statistical analysis table puts a few things in cells that Markdown treats as syntax. These are the ones to watch so it renders correctly on GitHub, GitLab, Obsidian and docs sites.

• Significance stars can italicize text between them

  A trailing * after a number renders literally, but an opening * and a later closing * in the same cell or paragraph turn the text between them italic, and a note line that starts with * becomes a bullet. Escape stars as \*, or use daggers (†, ‡) or a separate significance column instead of * and **.

• Keep inequalities in code spans

  A < followed by a space or digit is plain text, as in < 0.001, but a < followed by an ASCII letter can open an HTML tag: in n<m and k>2 the text between the angle brackets can be swallowed. Code spans, as in the p-value column here, remove the risk, and bold can wrap around them.

• Unicode or LaTeX for H₀, χ² and α: choose one

  This table mixes $H_0$ math with Unicode such as χ². Where math is not rendered, $H_0$ shows its dollar signs, while H₀, χ², α and ± display everywhere; use math only if every target renders it, as covered in math in tables.

• Format every value in a numeric column the same way

  Here Sample (N) sits in code spans (monospace) while degrees of freedom are plain text, so digits of the same column use different fonts. Use code spans for a whole column or for none of it, and report p-values to a fixed number of decimals so right-aligned digits stay level.

What Goes in Each Column

How to Fill It In

1. 1Write down α, the test for each hypothesis, and one- versus two-sided before looking at the data, ideally in a pre-registration or experiment plan. Copy those choices into a sentence above the table.
2. 2Run each test in your statistics package and copy the statistic, df, and p-value straight from the output. Do not round intermediate values; round only when entering them in the table.
3. 3Check the df against the design: a mismatch (for example, N − 2 reported for a chi-square test) is a fast way to spot that the wrong test or the wrong output line was copied.
4. 4If you ran several tests, apply a multiple-comparison correction such as Holm or Bonferroni and report adjusted decisions. Say which method you used.
5. 5Add effect sizes and confidence intervals, either as extra columns or in a companion table, and have someone else reproduce one row from the raw data before publishing.

Ready-to-Paste Variations

| Test | Statistic | Degrees of freedom |
| :--- | :---: | :--- |
| Two-sample t (pooled variance) | t | n₁ + n₂ − 2 |
| Welch’s t (unequal variances) | t | Welch–Satterthwaite estimate, usually non-integer |
| Paired t | t | n − 1 (number of pairs minus one) |
| One-way ANOVA, k groups | F | k − 1 and N − k |
| Chi-square test of independence | χ² | (rows − 1) × (columns − 1) |
| Pearson correlation | t | n − 2 |

| Rank | Result | Raw p | Holm threshold | Decision |
| :---: | :--- | ---: | ---: | :--- |
| 1 | R1: Parser v2 latency | < 0.001 | 0.0125 | **Reject H₀** |
| 2 | R3: Mobile bounce rate | < 0.001 | 0.0167 | **Reject H₀** |
| 3 | R4: Pipe-bug incidence | < 0.001 | 0.025 | **Reject H₀** |
| 4 | R2: Dark mode time-on-page | 0.263 | 0.05 | Fail to reject H₀ |

| Metric | Control | Variant | Difference (95% CI) | p (two-sided) |
| :--- | ---: | ---: | :--- | ---: |
| Conversion rate | 4.1% | 4.6% | +0.50 pp (−0.02 to +1.02) | 0.058 |
| Bounce rate | 38.0% | 35.5% | −2.50 pp (−3.72 to −1.28) | < 0.001 |

Common Mistakes

• Describing the p-value as the probability that the null hypothesis is true.

  A p-value is the probability, assuming H₀ and the test’s assumptions hold, of a result at least as extreme as the one observed. Phrase conclusions in those terms, and use a Bayesian analysis if you need the probability of a hypothesis.

• Writing “no difference” after a non-significant result.

  Failing to reject H₀ means the data were not strong enough to rule it out. Say “no significant difference detected” and show the confidence interval; to claim equivalence, run an equivalence test such as TOST with a pre-stated margin.

• Treating p < 0.001 as evidence of a large or important effect.

  With thousands of observations, trivial effects become significant. Report an effect size (mean difference, Cohen’s d, odds ratio) with its interval, and judge importance against what matters to the product or field.

• Choosing α or the one-sided direction after seeing the results.

  Fix α and the direction in the analysis plan before data collection. Changing them afterwards inflates the Type I error rate, which is the risk of rejecting a true H₀.

• Running many tests and reporting each at α = 0.05.

  With twenty independent tests at 0.05, roughly one false positive is expected even when every null is true. Apply Holm, Bonferroni, or a false discovery rate method and say which one.