Your first analysis, end-to-end

We will answer a real question with a real dataset, in fifteen lines of code, with proper margins of error. Nothing about this is fake.

The question

The Fisher iris dataset is a 150-row table of measurements of three species of iris flower (setosa, versicolor, virginica). For each flower we have sepal length, sepal width, petal length, petal width, and the species name.

Question: Are setosa flowers’ petals shorter than virginica flowers’ petals, and by how much?

This is a difference-of-means question. Two groups, one numeric outcome, you want a number with error bars.

Step 1: Load the data

from morie.fn import dnorm  # any morie import warms the package
import sqlite3
import pandas as pd

# MORIE ships with the iris dataset in its built-in database.
from morie.data import morie_builtin_db
conn = sqlite3.connect(morie_builtin_db())
iris = pd.read_sql("SELECT * FROM iris", conn)
conn.close()

print(iris.head())
#    sepal_length  sepal_width  petal_length  petal_width    species
# 0           5.1          3.5           1.4          0.2     setosa
# 1           4.9          3.0           1.4          0.2     setosa
# ...

If you’ve never seen import, =, or from, the Python tutorial has a one-page introduction. Five minutes is enough.

Step 2: Pick the right tool

The question is “are petal lengths different between two groups?”. That maps to a two-sample t-test (with a robust alternative when the data is skewed) — which lives at morie.fn.t2smp.

You can find this by:

  • MORIE Inference Engine — methods reference.

  • The cheatsheet helper at the terminal:

    from morie.cheatsheet import cheatsheet
print(cheatsheet("t2smp"))

    That prints a whole help card: when to use, the formula reference, and a quote because it is more fun to learn that way.

Step 3: Run the test

import numpy as np
from morie.fn.t2smp import t2smp  # if t2smp ships a module of the same name

setosa_petal     = iris.loc[iris.species == "setosa",     "petal_length"].to_numpy()
virginica_petal  = iris.loc[iris.species == "virginica",  "petal_length"].to_numpy()

result = t2smp(setosa_petal, virginica_petal, alternative="two-sided")
# result is a dict; keys depend on the exact fn.

The exact key names will be whatever the fn returns; the cheatsheet will tell you. In general expect:

  • estimate — the difference of means

  • statistic — the t-statistic

  • p_value — the p-value

  • ci — a 95% confidence interval

Step 4: Read the output honestly

Three numbers matter:

  1. The estimate. How big is the difference? If the difference is 4 cm but petals are around 1–6 cm long, that’s enormous. If the difference is 0.04 cm in the same range, that’s basically nothing — even if the p-value is tiny.

  2. The confidence interval. Where could the truth plausibly be, given this much data? A CI of (3.8, 4.2) cm means “I’m pretty sure the real difference is somewhere in there”. A CI of (-0.5, 4.5) cm with the same point estimate of 2.0 means “I have no idea, the data is too thin”.

  3. The p-value. How surprising would the data be if the truth really is “no difference”? A p of 0.001 means “very surprising, probably a real difference”. A p of 0.4 means “not surprising, could easily be noise”. The p-value is not the probability the difference is real — it’s the probability of the data given no difference. Those are different statements.

Step 5: What to do when the data is messy

The t-test assumes both groups are roughly normal. Real data isn’t. For petal length on iris this is fine — but for income, time-on-page, hospital cost, whatever the heck “engagement” means in your A/B test, it usually isn’t.

When the data is skewed or has extreme values, use the robust alternatives in the RobustRegression and RobustWeight families. The cheatsheet for any of them tells you when to reach for it.

Where to go next

  • Statistical Methods — full statistical-methods reference, sorted by question. Start here for the catalogue of estimators and which one fits which design.

  • Causal Inference — once your question is causal (“did X cause Y?”) and not just correlational.

The big idea, restated

You loaded data, picked a tool that matched the question, ran it, and got a number with a margin of error and a citation. That is the entire workflow. The thousand other functions in MORIE exist because the question can take a thousand other shapes, but the shape of the work doesn’t change.