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Housekeeping🧹

Important Dates:

Programming Practice #5 due today
Section Check-In #6 due tomorrow (@ 11:59PM)

Resub cycle also closes

HW5: Mapping due next Friday, 8/14 @ 11:59PM
Project Code & Report due Sunday, 8/16 @ 11:59PM
Final Exam is on Friday, 8/21 during lecture

Practice exams early next week!

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Section Plan

🃏🎴

In today’s section, we’ll go over

Stats 101
Hypothesis testing, p-values, p-hacking
Machine learning

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Statistics 101

Examples of Summary Statistics

Number of values in our dataset
Mean

The “average” value

Median

The value in the middle of our dataset

Standard deviation

How spread out our values are

Min, max, mode, range, etc.

Distributions

How our values are distributed

Uniform
Normal

Start by asking students: "If I gave you 100 test scores and asked you to describe them in one number, what would you pick?" That naturally motivates the mean. Then show the dataset 2, 4, 4, 5, 7, 8, 10 and walk through each stat by hand.

For mean vs. median, give them an intuition pump: "Imagine 9 people in a room earning $30k/year, and one billionaire walks in. The mean salary shoots up, but the median barely moves ,which one better describes the 'typical' person?" This is why median is preferred for income data.

For standard deviation, tell them: "Two classes both average 70 on a test. Class A has scores from 68–72. Class B has scores from 20–100. The mean hides that story — std deviation tells it."

Distributions — what to say

Uniform: "Rolling a fair die — every number 1–6 has the same chance." Normal: "Heights, test scores, measurement errors — nature loves the bell curve. Most people are near average, fewer are extreme." Skewed: "Income, house prices, social media followers — a few extreme values on one side drag the mean away from where most data actually sits."

A good closing point: "The shape of your distribution tells you which summary stats to trust. If it's skewed, the mean is misleading — use the median."

Sonnet 4.6

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Hypothesis Tests

Null Hypothesis is the hypothesis that supports the pre-existing expectations or probability

Alternative Hypothesis is the hypothesis that something is different, one that if true, would allow us to reject the null hypothesis

Our p-value is the chance that this situation would happen in a world bound by the null hypothesis

If our p-value is lower than a given significance level (usually 0.05), it is significant enough to reject the null hypothesis

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P-hacking and HARKing

P-hacking: due to the randomness in the experiment, can keep running experiments until we get a decent p-value
HARKing: making hypotheses AFTER experimentation

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ML pipeline for regression tasks

# Separate data

features = data.loc[:, data.columns != 'target']

labels = data['target']

# Create and train model

model = DecisionTreeRegressor()

model.fit(features, labels)

# Predict on some data

predictions = model.predict(features)

# Assess accuracy

mean_squared_error(labels, predictions)

For tasks whose labels are numeric (e.g. House price prediction)
Models: DecisionTreeRegressor(), LinearRegression()

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ML pipeline for classification tasks

# Separate data

features = data.loc[:, data.columns != 'target']

labels = data['target']

# Create and train model

model = DecisionTreeClassifier()

model.fit(features, labels)

# Predict on some data

predictions = model.predict(features)

# Assess accuracy

accuracy_score(labels, predictions)

For tasks whose labels are categorical (e.g. cat vs. dog)
Models: DecisionTreeClassifier()

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Train-test split

The goal of machine learning is not to memorize the labels of the data we already have, but to learn a model that generalizes to future, unseen data.

We need to hold out data our model will never see during training, then test it on that data set (test set)

from sklearn.model_selection import train_test_split

# Breaks data into 80% train and 20% test

X_train, X_test, y_train, y_test =

train_test_split(X, y, test_size=0.2)

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Underfitting vs. overfitting

Models won’t always perform well on test data.

Suppose we’re training a classification model…

Underfitting occurs when the model is too simple to capture the relationships in the data it’s trained on

68% accuracy on training set, 65% accuracy on test set

Overfitting occurs when the model does too good of a job fitting to the specific data it’s trained on (too complex)

98% accuracy on training set, 55% accuracy on test set

We want our models to be somewhere in between the two!

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Practice Problems!

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Project Check In

Discussion Questions:

Briefly describe your project or portfolio to your group members. If you’re doing a project, what data and questions are you working with? If you’re doing a portfolio, what work are you revising?
What is the current status of your project or portfolio?
What was the feedback you got from the TA, and how do you plan to incorporate it into your upcoming work?
What is your game plan for the next week?
Do you have lingering questions?

After discussing, group members should ask follow-up questions or offer insights!

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