Goodness of fit evaluation in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function used for goodness of fit test from scipy.stats.

SciPy

from scipy.stats import [1]

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

Attest_ind

Bpearsonr

Cchisquare

Dlinregress

Attempts:

3 left

💡 Hint

Common Mistakes

Importing a test for means like ttest_ind instead of chisquare.

Confusing correlation tests with goodness of fit tests.

The chisquare function from scipy.stats is used to perform the chi-square goodness of fit test.

2fill in blank

medium

Complete the code to perform a chi-square goodness of fit test on observed data.

SciPy

observed = [20, 30, 50]
expected = [25, 25, 50]
stat, p_value = chisquare(f_obs=[1], f_exp=expected)

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

Aobserved

Bexpected

C[25, 25, 50]

D[20, 30, 50]

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping observed and expected data in the function call.

Passing the expected list to f_obs.

The f_obs parameter requires the observed frequencies, so we pass the observed list.

3fill in blank

hard

Fix the error in the code to correctly calculate the chi-square test statistic and p-value.

SciPy

from scipy.stats import chisquare
observed = [15, 25, 60]
expected = [20, 20, 60]
stat, p_value = chisquare(f_obs=observed, f_exp=[1])

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

Aobserved

Bexpected

C[15, 25, 60]

D[20, 25, 60]

Attempts:

3 left

💡 Hint

Common Mistakes

Passing observed data as expected frequencies.

Using incorrect lists for expected frequencies.

The f_exp parameter must be the expected frequencies, so expected is correct.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each category to its observed frequency only if the frequency is greater than 20.

SciPy

categories = ['A', 'B', 'C', 'D']
observed = [10, 25, 30, 15]
result = {categories[i]: [1] for i in range(len(categories)) if [2]

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

Aobserved[i]

Bcategories[i]

Cobserved[i] > 20

Dcategories[i] > 20

Attempts:

3 left

💡 Hint

Common Mistakes

Using category names as values instead of frequencies.

Filtering by category names instead of frequencies.

The dictionary maps category names to observed frequencies, but only includes those where the frequency is greater than 20.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase category names to observed frequencies only if the frequency is less than or equal to 25.

SciPy

categories = ['a', 'b', 'c', 'd']
observed = [10, 25, 30, 15]
result = { [1]: [2] for i in range(len(categories)) if [3] }

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

Acategories[i].upper()

Bobserved[i]

Cobserved[i] <= 25

Dcategories[i]

Attempts:

3 left

💡 Hint

Common Mistakes

Not converting category names to uppercase.

Using wrong comparison operators in the condition.

Mixing up keys and values in the dictionary comprehension.

The dictionary comprehension maps uppercase category names to observed frequencies, including only those frequencies less than or equal to 25.

Practice

1. What does the chi-square goodness of fit test in scipy.stats.chisquare primarily evaluate?

easy

A. The mean difference between two samples

B. How well observed data matches expected frequencies

C. The correlation between two variables

D. The variance within a single dataset

Solution

1. Step 1: Understand the purpose of chi-square test

   The chi-square goodness of fit test compares observed data frequencies to expected frequencies to check if they match.

2. Step 2: Identify what scipy.stats.chisquare does

   This function calculates the chi-square statistic and p-value to evaluate the fit between observed and expected counts.

3. Final Answer:

   How well observed data matches expected frequencies -> Option B

4. Quick Check:

   Goodness of fit = observed vs expected match [OK]

Hint: Chi-square tests observed vs expected frequencies [OK]

Common Mistakes:

• Confusing goodness of fit with correlation
• Thinking it measures mean differences
• Mixing variance analysis with goodness of fit

2. Which of the following is the correct way to import the chi-square goodness of fit test function from scipy?

easy

A. import scipy.chisquare

B. from scipy import chisquare

C. from scipy.stats import chisquare

D. import scipy.stats.chisquare as cs

Solution

1. Step 1: Recall the module structure of scipy

   The chi-square test function is inside the stats submodule of scipy.

2. Step 2: Identify correct import syntax

   The correct import is from scipy.stats import chisquare to directly access the function.

3. Final Answer:

   from scipy.stats import chisquare -> Option C

4. Quick Check:

   Correct import = from scipy.stats import chisquare [OK]

Hint: Import from scipy.stats for statistical tests [OK]

Common Mistakes:

• Trying to import chisquare directly from scipy
• Using incorrect module paths
• Using alias without import

3. What will be the output of the following code?

from scipy.stats import chisquare
observed = [20, 30, 50]
expected = [25, 25, 50]
result = chisquare(f_obs=observed, f_exp=expected)
print(round(result.statistic, 2), round(result.pvalue, 3))

medium

A. 2.0 0.368

B. 3.0 0.223

C. 0.5 0.778

D. 1.0 0.607

Solution

1. Step 1: Calculate chi-square statistic manually

   Chi-square = sum((observed - expected)^2 / expected) = ((20-25)^2/25) + ((30-25)^2/25) + ((50-50)^2/50) = (25/25)+(25/25)+0 = 1+1+0 = 2.0

2. Step 2: Interpret p-value from scipy output

   Using scipy.stats.chisquare with these values gives a p-value around 0.368, indicating moderate fit.

3. Final Answer:

   2.0 0.368 -> Option A

4. Quick Check:

   Chi-square stat = 2.0, p-value ≈ 0.368 [OK]

Hint: Calculate chi-square stat then check p-value [OK]

Common Mistakes:

• Forgetting to square differences
• Dividing by wrong expected values
• Mixing up statistic and p-value

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

from scipy.stats import chisquare
observed = [15, 25, 35]
expected = [20, 20]
result = chisquare(f_obs=observed, f_exp=expected)
print(result)

medium

A. Observed and expected arrays have different lengths

B. chisquare function is not imported correctly

C. Expected frequencies must be integers

D. Missing p-value extraction from result

Solution

1. Step 1: Check input array lengths

   The observed array has 3 elements, but expected has only 2 elements, which is invalid for chi-square test.

2. Step 2: Understand scipy requirement

   Both observed and expected arrays must be the same length to compare frequencies correctly.

3. Final Answer:

   Observed and expected arrays have different lengths -> Option A

4. Quick Check:

   Array length mismatch causes error [OK]

Hint: Observed and expected must be same length [OK]

Common Mistakes:

• Ignoring length mismatch
• Assuming expected must be integers
• Thinking import or print is the error

5. You have observed counts of [40, 35, 25] for three categories. You expect them to be equally likely. Using scipy.stats.chisquare, what is the p-value indicating if the observed data fits the equal distribution? (Hint: expected counts are equal for all categories.)

hard

A. 0.789

B. 0.223

C. 0.456

D. 0.174

Solution

1. Step 1: Calculate expected counts for equal distribution

   Total counts = 40+35+25 = 100. Expected counts = [100/3, 100/3, 100/3] ≈ [33.33, 33.33, 33.33].

2. Step 2: Perform chi-square test with scipy

   Using chisquare(f_obs=[40,35,25], f_exp=[33.33,33.33,33.33]) gives a chi-square statistic ≈ 3.5 and p-value ≈ 0.174.

3. Final Answer:

   0.174 -> Option D

4. Quick Check:

   Unequal counts vs equal expected gives p-value ≈ 0.174 [OK]

Hint: Equal expected counts = total/number categories [OK]

Common Mistakes:

• Using observed counts as expected
• Not dividing total counts equally
• Misinterpreting p-value significance