Hypothesis testing (ttest, chi2test) in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of a t-test in hypothesis testing?

A t-test checks if the average (mean) of a group is different from a known value or another group's mean. It helps decide if the difference is real or just by chance.

beginner

What does the chi-square test (chi2test) check in data?

The chi-square test checks if two categorical variables are related or independent by comparing observed counts with expected counts.

beginner

In MATLAB, which function is used to perform a one-sample t-test?

The function ttest is used for a one-sample t-test in MATLAB. You give it your data and the mean to compare against.

beginner

What is the null hypothesis in a chi-square test?

The null hypothesis says that the two categorical variables are independent, meaning no association between them.

beginner

What does a p-value tell you in hypothesis testing?

A p-value tells how likely it is to see your data if the null hypothesis is true. A small p-value means the data is unlikely by chance, so you may reject the null.

Which MATLAB function performs a t-test?

A corrcoef

B chi2test

C anova

D ttest

The ttest function is used in MATLAB to perform t-tests.

What does the chi-square test compare?

A Observed and expected frequencies

B Correlation between variables

C Means of two groups

D Variance of a sample

The chi-square test compares observed counts with expected counts to test independence.

If the p-value is less than 0.05, what should you do?

A Increase sample size

B Accept the null hypothesis

C Reject the null hypothesis

D Ignore the result

A p-value below 0.05 usually means rejecting the null hypothesis.

Which test is best for checking if two categorical variables are related?

A t-test

B chi-square test

C linear regression

D ANOVA

The chi-square test is used for relationships between categorical variables.

What is the null hypothesis in a t-test?

A Means are equal

B Means are different

C Variables are independent

D Variables are correlated

The null hypothesis in a t-test states that the means are equal.

Explain how to perform a one-sample t-test in MATLAB and interpret the results.

Think about the data you compare and what the p-value means.

Describe the steps to conduct a chi-square test in MATLAB and what conclusions you can draw.

Focus on comparing counts and what independence means.

Practice

1. What does the MATLAB function ttest primarily test?

easy

A. Whether the data follows a normal distribution

B. Whether two samples have the same variance

C. Whether the mean of a sample differs from a specified value

D. Whether the counts in categories match expected counts

Solution

1. Step 1: Understand the purpose of ttest

   The ttest function in MATLAB tests if the mean of a sample is equal to a given value.

2. Step 2: Compare with other tests

   chi2gof tests counts, not means; variance tests are different; normality tests are separate.

3. Final Answer:

   Whether the mean of a sample differs from a specified value -> Option C

4. Quick Check:

   ttest tests mean difference [OK]

Hint: Remember: ttest checks means, chi2 tests counts [OK]

Common Mistakes:

• Confusing ttest with chi-square test
• Thinking ttest checks variance
• Assuming ttest checks distribution shape

2. Which of the following is the correct syntax to perform a one-sample t-test in MATLAB on data vector X against mean 0?

easy

A. chi2gof(X, 0)

B. ttest(X, 0)

C. ttest(0, X)

D. ttest(X)

Solution

1. Step 1: Recall ttest syntax

   The syntax ttest(X, mu) tests if mean of X equals mu.

2. Step 2: Check options

   chi2gof(X, 0) uses wrong function; ttest(0, X) reverses arguments; ttest(X) misses mean value.

3. Final Answer:

   ttest(X, 0) -> Option B

4. Quick Check:

   Correct syntax is ttest(data, mean) [OK]

Hint: Syntax: ttest(data, mean) for one-sample test [OK]

Common Mistakes:

• Swapping arguments order
• Using chi2gof for mean testing
• Omitting mean parameter

3. What is the output of the following MATLAB code?

X = [5.1, 5.3, 5.0, 5.2, 5.4];
[h, p] = ttest(X, 5.0);
disp(h); disp(p);

medium

A. h = 1, p < 0.05 (reject mean = 5.0)

B. h = 1, p > 0.05 (fail to reject mean = 5.0)

C. h = 0, p < 0.05 (reject mean = 5.0)

D. h = 0, p > 0.05 (fail to reject mean = 5.0)

Solution

1. Step 1: Compute sample statistics

   X mean = (5.1 + 5.3 + 5.0 + 5.2 + 5.4)/5 = 5.2; std ≈ 0.158.

2. Step 2: Interpret ttest output

   t ≈ (5.2 - 5.0) / (0.158 / √5) ≈ 2.83, df=4, p ≈ 0.047 < 0.05, so h=1 (reject null).

3. Final Answer:

   h = 1, p < 0.05 (reject mean = 5.0) -> Option A

4. Quick Check:

   mean=5.2, t≈2.83 > 2.776, p<0.05 [OK]

Hint: Sample mean 5.2 sufficiently differs from 5.0 (t>crit) -> h=1, p<0.05 [OK]

Common Mistakes:

• Assuming data too close to 5.0 for significance (h=0)
• Miscalculating p-value as >0.05
• Confusing h=1 (reject) meaning

4. Identify the error in this MATLAB code snippet for a chi-square goodness-of-fit test:

observed = [20, 30, 50];
expected = [25, 25, 50];
h = chi2gof(observed, 'ExpectedCounts', expected);

medium

A. The 'Expected' parameter is misspelled

B. The vectors observed and expected must be the same length

C. chi2gof cannot be used with expected counts

D. The observed data should be a vector of counts, but chi2gof expects raw data samples

Solution

1. Step 1: Understand chi2gof input requirements

   chi2gof expects raw sample data, not observed counts directly.

2. Step 2: Check usage of 'ExpectedCounts'

   The 'ExpectedCounts' parameter is valid but only used with raw data; providing counts directly leads to incorrect results.

3. Final Answer:

   The observed data should be a vector of counts, but chi2gof expects raw data samples -> Option D

4. Quick Check:

   chi2gof needs raw data, not counts [OK]

Hint: chi2gof needs raw data, not counts vector [OK]

Common Mistakes:

• Passing counts instead of raw data
• Misspelling parameter names
• Assuming chi2gof accepts counts directly

5. You have observed counts obs = [40, 35, 25] and expected proportions expProp = [0.3, 0.4, 0.3]. How do you correctly perform a chi-square goodness-of-fit test in MATLAB to check if observed counts fit expected proportions?

hard

A. Convert expected proportions to expected counts, then use chi2gof with raw data generated from counts

B. Directly use chi2gof(obs, 'Expected', expProp)

C. Use ttest(obs, expProp) to compare counts and proportions

D. Use chi2gof with observed counts and expected counts vectors

Solution

1. Step 1: Calculate expected counts from proportions

   Multiply total observed count by expected proportions: total = 40+35+25=100; expected counts = 100 * expProp = [30, 40, 30].

2. Step 2: Generate raw data samples for chi2gof

   Since chi2gof needs raw data, create a vector with repeated category labels matching observed counts.

3. Step 3: Perform chi-square test

   Use chi2gof with raw data and specify expected counts via 'ExpectedCounts' parameter.

4. Final Answer:

   Convert expected proportions to expected counts, then use chi2gof with raw data generated from counts -> Option A

5. Quick Check:

   chi2gof needs raw data and expected counts [OK]

Hint: Convert proportions to counts, create raw data for chi2gof [OK]

Common Mistakes:

• Passing proportions directly as expected counts
• Using ttest for count data
• Not converting counts to raw data samples