13. Case Studies I

Updated

October 5, 2026

This session is only intended for the in-person session and brings together everything from Sessions 1–11 in three worked case studies, then adds two practical Python tools: outlier detection and handling missing values with np.nan.

Overview

This session brings together the statistical methods from Sessions 1–11 in three worked case studies. Each scenario requires you to select the appropriate test, justify the choice, check assumptions, and interpret the results (including effect sizes and practical significance).

Scenario 1: Acid Catalyst Optimization

Background: You are optimizing a reaction that requires an acid. You expect that switching from hydrochloric acid (HCl) to acetic acid will give a better reaction yield. You collect the following data with replicates in lists.

Data (reaction yield, %):

No acid:          [2.1, 4.9, 2.9, 4.0, 4.4, 5.9, 5.6, 4.2, 5.9, 3.0]
Hydrochloric acid: [79.3, 76.0, 84.9, 78.0, 82.6, 77.9, 81.0, 77.4, 83.5, 79.2]
Acetic acid:       [88.2, 86.2, 95.8, 95.7, 79.1, 92.0, 83.4, 83.4, 93.8, 84.8]

Tasks:

  • Identify your negative and positive control experiments from the data above.
  • Formulate a null hypothesis.
  • Evaluate the data using appropriate statistical methods.
  • Justify your choices.
  • Describe follow-up experiments.

Scenario 2: Fluorescent Probe Characterization

Background: You have synthesized four small molecules (S1–S4) with different chemical groups at one position. You want to evaluate the fluorescence response for this family of molecules.

Data (fluorescence intensity):

No small molecule: [1033, 997, 898, 957, 996]
S1: [9856, 9389, 9884, 10020, 9673]
S2: [16124, 15821, 14955, 15251, 15240]
S3: [24448, 24260, 26876, 25435, 22777]
S4: [19498, 18113, 20209, 20305, 21459]
Commercial fluorophore: [14946, 16995, 21231, 20041, 19364]

Tasks:

  • Identify your negative and positive control experiments from the data above.
  • Formulate a null hypothesis.
  • Evaluate the data using appropriate statistical methods.
  • Justify your choices.
  • Describe follow-up experiments.

Scenario 3: Enzyme Activity Comparison

Background: You expect that enzyme B has improved turnover numbers compared to enzyme A.

Data (turnover number, s⁻¹):

No enzyme: [107, 205, 49, 64, 54, 186, 83, 77, 68, 57]
Enzyme A: [857000, 821700, 770000, 752800, 787300, 782400, 704300, 738400, 708200, 354700]
Enzyme B: [2710800, 1774300, 2311700, 1051500, 2432300, 1883400, 1832700, 1536600, 1018900, 842000]

Tasks:

  • Identify your negative and positive control experiments from the data above.
  • Formulate a null hypothesis.
  • Evaluate the data using appropriate statistical methods.
  • Justify your choices.
  • Describe follow-up experiments.