Hypothesis testing (ttest, chi2test) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to perform a t-test on sample data.

MATLAB

data = [5.1, 4.9, 5.0, 5.2, 5.3];
[h, p] = [1](data, 5);

Drag options to blanks, or click blank then click option'

Achi2test

Bttest

Canova1

Dttest2

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'chi2test' which is for categorical data, not means.

Using 'ttest2' which is for two-sample tests.

The ttest function performs a one-sample t-test comparing the mean of data to the value 5.

2fill in blank

medium

Complete the code to perform a chi-square test on observed and expected counts.

MATLAB

observed = [20, 30, 50];
expected = [25, 25, 50];
[h, p] = chi2gof(1:length(observed), 'Ctrs', 1:length(observed), 'Frequency', [1], 'Expected', expected);

Drag options to blanks, or click blank then click option'

Aobserved

Bexpected

Ch

Dp

Attempts:

3 left

💡 Hint

Common Mistakes

Passing expected counts as 'Frequency' instead of observed counts.

Confusing the parameters and their order.

The 'Frequency' parameter requires the observed counts to compare against expected counts in the chi-square goodness-of-fit test.

3fill in blank

hard

Fix the error in the code to perform a two-sample t-test between two groups.

MATLAB

group1 = [5.1, 5.3, 5.2];
group2 = [4.9, 5.0, 5.1];
[h, p] = [1](group1, group2);

Drag options to blanks, or click blank then click option'

Attest

Banova1

Cchi2test

Dttest2

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ttest' which is for one sample or paired tests.

Using 'chi2test' which is not for means.

The ttest2 function performs a two-sample t-test comparing the means of two independent groups.

4fill in blank

hard

Fill both blanks to create a structure with counts and perform a chi-square test.

MATLAB

counts = [10, 15, 25];
expected = [15, 15, 20];
[h, p] = chi2gof([1], 'Frequency', [2], 'Expected', expected);

Drag options to blanks, or click blank then click option'

A1:length(counts)

Bcounts

Cexpected

Dcounts + expected

Attempts:

3 left

💡 Hint

Common Mistakes

Passing counts as the first argument instead of categories.

Passing expected counts as 'Frequency'.

The first argument is the data points (categories), here 1 to length of counts. The 'Frequency' parameter is the observed counts.

5fill in blank

hard

Fill all three blanks to perform a paired t-test and display the p-value.

MATLAB

before = [5.1, 5.3, 5.2, 5.4];
after = [5.0, 5.1, 5.3, 5.5];
[h, p] = [1]([2], [3]);
disp(p);

Drag options to blanks, or click blank then click option'

Attest

Bbefore

Cafter

Dttest2

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ttest2' which is for independent samples, not paired.

Swapping the order of 'before' and 'after'.

The ttest function with two inputs performs a paired t-test comparing before and after samples.

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