Scientific Method, Experimental Design, and Statistical Analysis Notes

Process of Science and Experimental Design

• The process of science is an iterative endeavor that continually builds upon prior research and scientific literature.
• Formulating hypotheses requires developing clear, testable questions that can be evaluated using quantitative methods while minimizing extraneous variables and outside influence.
• Case Study: Ozone Exposure in Cornflowers:
  • Smokey Mountain Cornflower: A well-studied species native to the Eastern United States. Previous literature establishes that exposure to high ozone ($O_3$) levels causes leaf striping or stippling.
  • Rocky Mountain Cornflower: A species observed to display leaf striping/stippling, but lacking prior experimental studies regarding its response to ozone exposure.
  • Experimental Question: Does ozone ($O_3$) exposure cause leaf striping in the Rocky Mountain cornflower?

Experimental Variables and Controls

• Independent Variable: The specific parameter deliberately altered by the experimenter to test its causal effect (e.g., ozone concentration levels).
• Dependent Variable: The variable measured or observed for changes in response to the independent variable (e.g., presence or intensity of leaf striping/stippling, brown leaf stripes).
• Experimental Group: The experimental units subjected to the treatment or altered independent variable (e.g., Rocky Mountain cornflowers exposed to designated ozone levels).
• Control Group: Experimental units maintained under baseline or normal conditions to provide a baseline comparison.
• Positive Control: A group designed to ensure a positive result (e.g., striping present) if the experimental system is functioning properly. Utilizes a well-studied subject such as the Smokey Mountain cornflower.
• Negative Control: A group designed to yield a negative result (e.g., absence of leaf striping) to confirm that no unintended external factor is causing the phenomenon.
• Controlled Variables: Environmental and procedural parameters kept identical across all treatment groups to isolate the independent variable (e.g., soil type, water quantity, ambient temperature, geographical growth origin).
• Confounding Variables (Compounding Variables): Uncontrolled or unnoticed extraneous factors that can systematically influence the dependent variable beyond the experimenter's control.

System Integrity and Equipment Validation

• Control groups serve a critical secondary purpose: validating the good working order of experimental equipment and systems.
• Scenario Example: If equipment is broken or leaking ozone into a negative control enclosure unnoticed, the negative control group will yield an unexpected positive result (leaf striping). This unexpected outcome signals to researchers that experimental hardware is compromised.
• Establishing control groups solidifies baseline expectations before concluding whether data supports or refutes a given hypothesis.

Statistical Concepts and Principles

• Mean: The arithmetic average of a dataset, representing the central point of a normal bell curve distribution.
  • Limitation: The mean does not provide a complete picture of data distribution. Multiple datasets can share identical mean values while possessing vastly different ranges, standard deviations, and $95\%$ confidence intervals.
• Range: The mathematical difference between the maximum and minimum values in a dataset. Highly sensitive to outliers and insufficient on its own for describing data variability.
• Sample Size ($n$) and Replicates:
  • Sample size is denoted by the variable $n$.
  • Replicates represent individual repeated experimental units within a treatment group.
  • Example: An experiment containing $3$ negative control units and $3$ positive control units utilizes a total of $n = 6$ replicates.
  • Increasing sample size ($n$) increases statistical power and generally decreases calculated $p$-values.
• Standard Deviation: A calculated metric representing the degree of variation or dispersion of individual data points relative to the mean.
• Standard Error: Calculated using standard deviation and sample size ($n$). Accounts for variability in relation to the number of experimental replicates; greater dataset dispersion produces a larger standard error.
• $95\%$ Confidence Interval: A calculated range of values within which there is a $95\%$ probability that the true population mean resides.
• $p$-Value and Statistical Significance:
  • The $p$-value measures the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true.
  • A standard threshold for statistical significance is $p \le 0.05$.
  • If $p \le 0.05$ (e.g., $p = 0.00$), the difference between compared experimental groups is statistically significant, leading to the rejection of the null hypothesis.
  • If $p > 0.05$, researchers fail to reject the null hypothesis, concluding that the compared groups are not statistically significantly different from one another.
• Independence of Mean and Variation: The mean and measures of variation (standard deviation/error) operate independently. If every plant in an experiment scores exactly $100$, the mean is $100$, but the variation remains $0$.

Google Sheets Scientific Graphing Protocol

1. Data Transfer:
   • Copy mean values from data tables using keyboard shortcuts (Control + C or Command + C on macOS) and paste them into spreadsheet cells (Control + V or Command + V).
2. Chart Setup:
   • Select treatment data ranges and open the Chart Editor.
   • Under the Setup tab, click Select Data Range (represented by the three-box grid icon).
   • Left-click and drag over target cells to fill data ranges automatically.
3. Formatting Axes and Series:
   • Assign designated experimental treatment conditions (e.g., $0\,O_3$ exposure or $CL_2$ levels) to the X-axis and Series configurations.
4. Inserting Custom Error Bars:
   • Navigate to the Customize tab within Chart Editor.
   • Expand the Series menu and enable the Error Bars checkbox.
   • Set error bar type to Constant or Data Labels.
   • Input standard error values corresponding to each dataset (e.g., assigning a constant standard error of $0.67$ for the $0\,O_3$ baseline group).
5. Troubleshooting Software Errors:
   • If chart bars render with identical colors or fail to separate into discrete treatment series, delete the chart object entirely and re-select data ranges.
   • Ensure browser compatibility (e.g., Chrome or Safari) and check that institutional account permissions are active if accessing embedded sheets or templates.

Course Logistics and Questions & Discussion

• Account Permissions: Accessing pre-lab documents and course files requires logging directly into an official institutional account (AppState account).
• Office Hours Location: Relocated to Reichardt Science North / Rankin Science Hall, Room $303$ (inside the lab or at the large study table situated down the hall to the right of the entrance).
• Lecture Slide Policy: Lecture slides are not posted publicly online to encourage in-class attendance. Concepts are re-explained in makeup files and during office hours.
• Lab Assignment Formatting: Manual questions (e.g., Questions $25\text{--}28$, $29\text{--}32$, and $33$) can be completed by bolding, underlining, or highlighting correct answers and striking through incorrect options.
• Class Duration & Comparisons: Standard lecture sessions run for $75\text{ minutes}$ (ending at $7:20$), while laboratory sessions range from $2\text{ hours}$ up to $3\text{ hours}$ depending on the discipline (e.g., chemistry labs).