Explore Library
AI FundamentalsProbability, Statistics, and Linear Algebra for AI

51 items

1

A/B Testing: Power, p-values, and CUPED

Flashcard
2

Simpson's Paradox: Aggregating Stratified Rates

Code Quiz
3

Simpson's Paradox and Confounding

Quiz
4

A/B Testing: Power, P-values, CUPED

Slides / Video
5

Confounding and Simpson's Paradox

Flashcard
6

Two-Proportion Z-Test for A/B Test

Code Quiz
7

Peeking at A/B Test Results

Quiz
8

Confidence Interval From Sample Mean

Code Quiz
9

Interpreting a 95% Confidence Interval

Quiz
10

Simpson's Paradox and Confounders

Slides / Video
11

Confidence Intervals & the Sampling Distribution

Flashcard
12

Hypothesis Testing in A/B Experiments

Flashcard
13

Distributions, Sampling & Confidence Intervals

Slides / Video
14

Hypothesis Testing & A/B Design

Slides / Video
15

Interpreting the p-value Wrong

Code Quiz
16

Interpreting P-values Correctly

Quiz
17

Buggy Standard Deviation Function

Code Quiz
18

Mean vs Median in Skewed Data

Quiz
19

P-value Significance Check Bug

Code Quiz
20

Understanding P-values and Correlation

Quiz
21

Population Variance Bug

Code Quiz
22

Mean vs Median in Skewed Data

Quiz
23

Hypothesis Testing, P-values & Causation

Slides / Video
24

P-values and Correlation vs Causation

Flashcard
25

Hypothesis Testing, p-values & Intervals

Slides / Video
26

P-values & Confidence Intervals

Flashcard
27

Extracting an Eigenvector from np.linalg.eig

Code Quiz
28

Data as Vectors and Matrices

Slides / Video
29

Gradients and Partial Derivatives

Slides / Video
30

Singular Value Decomposition Basics

Slides / Video
31

Matrix Transpose and Inverse

Slides / Video
32

Linear Independence, Span, and Basis

Slides / Video
33

Vector Norms and Distance Metrics

Slides / Video
34

Dot Product and Vector Similarity

Slides / Video
35

Matrix Multiplication in AI

Slides / Video
36

Matrices and Matrix Operations

Slides / Video
37

Vectors and Vector Operations

Slides / Video
38

Confidence Intervals

Slides / Video
39

Hypothesis Testing and p-values

Slides / Video
40

Sampling and the Central Limit Theorem

Slides / Video
41

Descriptive Statistics: Center and Spread

Slides / Video
42

Maximum Likelihood Estimation

Slides / Video
43

Joint, Marginal, Conditional Distributions

Slides / Video
44

Covariance and Correlation

Slides / Video
45

Expectation, Variance, Standard Deviation

Slides / Video
46

Bayes' Theorem in AI

Slides / Video
47

Conditional Probability and Independence

Slides / Video
48

Gaussian, Bernoulli, Binomial Distributions

Slides / Video
49

Discrete vs Continuous Distributions

Slides / Video
50

Random Variables and Distributions

Slides / Video
51

Eigenvalues and Eigenvectors Basics

Slides / Video
Code Quiz

Two-Proportion Z-Test for A/B Test

Spot the standard-error mistake in a two-proportion z-test used for A/B experiment analysis.

Codepython
from scipy import stats
import numpy as np

def ab_test(conv_a, n_a, conv_b, n_b):
    # conv_* = number of conversions, n_* = number of visitors
    p_a = conv_a / n_a
    p_b = conv_b / n_b
    p_pool = (conv_a + conv_b) / (n_a + n_b)

    se = np.sqrt(p_a * (1 - p_a) / n_a + p_b * (1 - p_b) / n_b)
    z = (p_b - p_a) / se
    p_value = 2 * (1 - stats.norm.cdf(abs(z)))
    return z, p_value

# Example: A had 120/2400, B had 150/2450
print(ab_test(120, 2400, 150, 2450))

The function is meant to run a significance test on whether B's conversion rate differs from A's. What is the bug?