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Goodness of fit evaluation in SciPy - Cheat Sheet & Quick Revision

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Recall & Review
beginner
What is the purpose of goodness of fit evaluation in data science?
Goodness of fit evaluation checks how well a statistical model matches observed data. It helps us see if the model explains the data well or if it misses important patterns.
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beginner
Which Python library provides tools for goodness of fit tests like Chi-square and Kolmogorov-Smirnov?
The scipy.stats module offers functions like chisquare() and kstest() to perform goodness of fit tests.
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beginner
What does a low p-value in a goodness of fit test indicate?
A low p-value means the model does not fit the data well. It suggests the observed data is unlikely if the model were true, so we might reject the model.
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intermediate
Explain the Chi-square goodness of fit test in simple terms.
The Chi-square test compares observed counts in categories to expected counts from a model. It measures if differences are too big to be just chance.
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intermediate
What is the Kolmogorov-Smirnov test used for in goodness of fit?
The Kolmogorov-Smirnov test compares the shape of the observed data distribution to a theoretical distribution to see if they match closely.
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Which function in scipy.stats is used for the Chi-square goodness of fit test?
Apearsonr()
Bkstest()
Cttest_ind()
Dchisquare()
What does a high p-value in a goodness of fit test suggest?
ATest is invalid
BModel does not fit data
CModel fits data well
DData is random
Which test compares the cumulative distribution of data to a theoretical distribution?
AKolmogorov-Smirnov test
BChi-square test
CANOVA
DLinear regression
In goodness of fit, what are 'expected counts'?
AObserved data values
BPredicted counts from the model
CRandom numbers
DTest statistics
Which scipy.stats function would you use to test if data fits a normal distribution?
Akstest()
Bchisquare()
Cttest_rel()
Dwilcoxon()
Describe how you would use scipy to check if your data fits a theoretical distribution.
Think about comparing observed data to expected or theoretical distribution.
You got /3 concepts.
    Explain the difference between the Chi-square test and the Kolmogorov-Smirnov test for goodness of fit.
    Focus on what each test measures and the data format.
    You got /3 concepts.

      Practice

      (1/5)
      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