Research And Design Bio

Course Schedule, Admin & Project Timeline

• Biology Faculty Directory Search:

  • Search instructions: Search for biology faculty on the official university website specifically looking for "Professor" in their job title.

• Course Timeline & Monthly Milestones:

  • August – September:

  • Task: Design Experiment.

  • Major deliverables: Group Prospectus, Full Research Proposal.

  • October:

  • Task: Conduct Experiment.

  • Major deliverables: Introduction & Methods sections.

  • November:

  • Task: Data Analysis.

  • Major deliverable: Data collection completed and raw data due.

  • December:

  • Task: Finalizing Research.

  • Major deliverables: Final Paper & Research Presentations.

• Weekly Announcements & Administrative Reminders:

  • Weekly announcements made during the 1st weekly meeting on Mondays.

  • Syllabus Quiz due Friday by $4\,\text{pm}$.

  • Group Prospectus due Wednesday.

  • Wrap up Experimental Design.

  • Topic discussion: "Why Statistics".

  • Curriculum Vitae (CV) Assignment due September $16\text{th}$.

• Research Project Sequence:

  • Step 1: Prospectus.

  • Step 2: Research Proposal.

  • Step 3: Research Article Analysis.

  • Step 4: Start Research.

  • Step 5: Draft Introduction & Methods.

  • Step 6: End Research & Final Presentation.

Research Proposal Writing & Grant Procurement

• Keys to Success in Proposal Writing:

  • Careful Preparation: Ability to communicate clearly and concisely.

  • Targeting Funders: Be careful to target the correct funding agency or organization.

  • Innovation & Creativity: Novel approaches (e.g., studying $O_2$ consumption to restore fish communities).

  • Audience Awareness: Know your audience thoroughly when writing.

• Common Pitfalls in Grant Proposals:

  • Poor communication.

  • Not using time wisely.

  • Fear of rejection.

  • Overambitious plans.

• Definition and Structure of Grants/Proposals:

  • A grant or proposal is a conditional gift.

  • It is a concrete plan of ACTION.

  • Funding entities identify specific problems they want addressed; the broad topics originate with the funding agency.

• Funding Sources & Grant Categories:

  • Federal Governments: Funding is often tied to political agendas.

  • Examples: National Science Foundation (NSF), National Oceanic and Atmospheric Administration (NOAA), Department of Energy (DOE), Department of Defense (DOD).

  • State Governments:

  • Example: California Sea Grant (CA Sea Grant).

  • Private Foundations: Funds are tightly aligned with the specific mission of the foundation.

  • Example: Baily Wildlife Foundation.

  • Corporations / Businesses:

  • Provide funds for public outreach to obtain positive exposure.

  • Provide corporate charity grants ("Get to give").

• The Step-by-Step Grant Writing Process:

  1. Talk to others about your research idea.

  2. Assemble a research team.

  3. Match your research topic to an appropriate funder.

  4. Read the funder's proposal guidelines carefully.

  5. Contact the program manager or sponsor contact.

  6. Build a detailed writing plan.

  7. Write and edit the draft.

  8. Revise! Revise!

  9. Be persistent and resubmit if rejected.

Epistemology of Data, Scientific Investigations & the Scientific Method

• Epistemology & What Can Be Known:

  • In theory, anything can be measured and analyzed.

  • Truth versus belief requires rigorous scientific skepticism.

  • Evaluate whether data sources and criteria are knowledgeable and authoritative.

• Data Definitions & Contextual Evaluation:

  • Data: Measurable information gathered from an experiment; collected information that is analyzed to make informed decisions.

  • Data Evaluation Hierarchy: To avoid falling for false findings, evaluate data along the following strict priority chain:     $\text{Logic} > \text{Honesty} > \text{Context} > \text{Pattern} > \text{P-value}$

  • Logic: Researchers must deeply understand their system to explain and defend research methods. Relying on "My PI or boss said so" is unacceptable—researchers must know why.

  • Honesty: Maintain an honest portrayal of data by conducting Exploratory Data Analysis (EDA) until fully understanding the dataset. Show all messy aspects of data ("muck") and own flaws or limitations. Beware of the "black box" / magic math.

  • Context: Ensure both biological and statistical context make sense. Verify that logical and appropriate statistical analyses were selected.

  • Pattern: Identify consistent patterns and trends in data. Biological patterns are significantly more important than raw P-values.

  • P-value: A mathematical calculation specifying significance within a hypothesis test. A P-value is only meaningful if logic, honesty, context, and patterns are valid first.

• Types of Data Classification:

  • Nominal / Categorical Data: Describes discrete classes, categories, or qualitative attributes without numerical rank (e.g., personality types [introvert, extrovert], favorite colors [red, yellow, green, blue]).

  • Ranked / Ordinal Data: Discrete values or integers reflecting a clear hierarchy or ranking order (e.g., course letter grades [A, B, C, D, F]).

  • Measurement / Quantitative Data: Continuous or discrete numerical measurements associated with treatments.

  • Discrete Data: Numerical values obtained by counting whole units (e.g., counting $3$ ice cream cones; Cone 1 has $2$ scoops).

  • Continuous Data: Measured along a continuous numerical scale with decimal subdivisions (e.g., Cone 3 weighs $79.4\,\text{g}$; Cone 2 ice cream temperature is $8.3^\circ\text{F}$).

• Types of Scientific Investigations:

  1. Observational: Measured variables recorded under naturally occurring conditions without observer intervention. These are descriptive and rarely establish cause-and-effect relationships.

  2. Comparative: Treatments are determined by pre-existing natural conditions across sites or populations.

  3. Perturbation / Response: Measures the system's biological response following a specific disturbance event.

  4. Manipulative: Experimental treatments are directly imposed and manipulated by the researcher.

  5. Deductive Science / Modeling: Generates predictive outcomes using established logical or mathematical equations (e.g., IPCC climate model simulations).

• The Scientific Method Flowchart & Procedure:

  • Observation $\rightarrow$ Formulate Question $\rightarrow$ Conduct Background Research $\rightarrow$ Construct Hypothesis $\rightarrow$ Test via Experimentation.

  • Procedure Evaluation:

  • If Procedure is Not Working: Troubleshoot procedure, carefully checking all setup steps and protocols.

  • If Procedure Works: Collect experimental data. This data serves as background research for future iterations. Formulate new questions and hypotheses.

  • Analysis & Communication:

  • Analyze data and draw conclusions. Whether results align fully, partially, or not at all with the original hypothesis, communicate the findings.

• Data Presentation Guidelines:

  • Tables: Require a descriptive caption above the table (e.g., Table 1.1 Mean, sample size ($n$), standard error ($\text{SE}$), and range of serum cholesterol levels ($\text{mg/100\,mL}$) of male and female turtles).

  • Figures: Graphs, diagrams, scatter plots, and conceptual models require captions below the figure explaining all axis labels, trend lines, and symbols.

Experimental Design & Variables

• Core Experimental Variables:

  • Independent Variable: The manipulated factor or treatment condition controlled by the experimenter (plotted on the X-axis).

  • Dependent Variable (Response Variable): The measured outcome variable that responds to changes in the independent variable (plotted on the Y-axis).

  • Control / Constant Variables: All extraneous factors held constant across all experimental treatments to prevent confounding effects on the dependent variable.

• Distinction Between Control Treatment and Constant Variables:

  • Control Treatment: The experimental benchmark where the independent variable is absent or kept at a baseline level.

  • Constant Variables: Environmental or procedural conditions kept uniform across both control and experimental treatments.

• Experimental Units & Pseudoreplication:

  • Experimental Unit: The smallest independent research subject to which a treatment is applied.

  • Pseudoreplication: Treating non-independent measurements as independent replicates (e.g., taking $3$ leaf samples from a single plant means the plant is the experimental unit ($n=1$), not the $3$ leaves).

  • Replication Target: Recommended replicate size across treatments is $40\text{--}50$ independent units.

• Formulating Biological & Statistical Hypotheses:

  • Biological Hypothesis Requirements: Must explicitly identify the dependent response variable, the statistic under investigation, the independent variable, and the research subject. Never use "if-then" phrasing.

  • Null Hypothesis ($H_0$): States that the independent variable has no effect on the dependent variable.

  • Alternative Hypothesis ($H_a$): States that the independent variable significantly affects the dependent variable.

  • Purpose of a Research Prospectus: To outline experimental design, methodologies, and analytical strategies before conducting research.

Descriptive Statistics: Central Tendency & Dispersion

• Fundamental Definitions in Biostatistics:

  • Statistics: The scientific study of numerical data ("data" is plural; "datum" is singular).

  • Purpose: Removes investigator bias and quantifies probability. Statistics cannot strictly "prove" hypotheses; it evaluates probabilities.

  • Biostatistics: Application of statistical methods to solve biological questions while accounting for natural biological variation.

• Populations, Samples, and Randomness:

  • Population: The complete set of all individuals or entities that exist or could exist.

  • Sample: A representative subset drawn from a population used to estimate population parameters.

  • Randomness: A strict mathematical condition where every individual in the population has an equal, non-zero probability of selection.

• Location (Central Tendency) & Dispersion (Precision):

  • Location / Central Tendency: Represents accuracy and typical values within a dataset.

  • Sample Mean ($\bar{x}$):       $\bar{x} = \frac{\sum_{i=1}^n x_i}{n}$       Not robust to extreme outliers.

  • Population Mean ($\mu$): The true mean of the entire population.

  • Median: The middle score when values are arranged in order. Highly robust and resistant to extreme values/outliers.

  • Mode: The most frequently occurring value in a dataset.

  • Dispersion: Represents precision and the degree of scatter around central tendency metrics.

  • Range: Difference between maximum and minimum values ($X_{\text{max}} - X_{\text{min}}$).

  • Sample Variance ($s^2$): Average of squared deviations from the sample mean divided by degrees of freedom ($df = n - 1$):       $s^2 = \frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n - 1}$

  • Population Variance ($\sigma^2$):       $\sigma^2 = \frac{\sum_{i=1}^n (x_i - \mu)^2}{n}$

  • Sample Standard Deviation ($s$): Square root of sample variance, describing dataset spread:       $s = \sqrt{s^2} = \sqrt{\frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n - 1}}$

  • Population Standard Deviation ($\sigma$):       $\sigma = \sqrt{\sigma^2} = \sqrt{\frac{\sum_{i=1}^n (x_i - \mu)^2}{n}}$

• Worked Example of Standard Deviation Calculation:

  • Given dataset A: $3, 5, 7$

  • Calculate mean:       $\mu = \frac{3 + 5 + 7}{3} = 5$

  • Calculate standard deviation:       $\sigma = \sqrt{\frac{(3-5)^2 + (5-5)^2 + (7-5)^2}{3}} = \sqrt{\frac{4 + 0 + 4}{3}} = \sqrt{\frac{8}{3}} \approx 1.63$

  • Given dataset B: $4, 5, 6$

  • Mean $\mu = 5$, standard deviation $\sigma = 0.82$.

  • Conclusion: Dataset A has a larger $\sigma$ ($1.63$ vs $0.82$), producing a wider, flatter curve reflecting greater spread.

Normal Distributions, Standard Scores (Z-Scores) & Worked Examples

• Characteristics of Normal Curves:

  • Perfectly symmetrical bell curve where mean = median = mode.

  • Exactly $50\%$ of values fall above the mean, and $50\%$ fall below.

  • Mean $\mu$ dictates curve location; standard deviation $\sigma$ dictates curve spread/width.

  • Empirical Rule Boundaries:

  • Within $\pm 1\sigma$: $68.27\%$ of population area.

  • Within $\pm 2\sigma$: $95.45\%$ of population area.

  • Within $\pm 3\sigma$: $99.73\%$ of population area.

• Standardized Normal Distribution ($Z$) & Score Formula:

  

  • Standardizing converts any normal distribution into a standard normal curve with mean $\mu = 0$ and standard deviation $\sigma = 1$.

  • Standard score ($Z$) equation:     $Z = \frac{x_i - \mu}{\sigma}$

  • Positive $Z$-scores denote values above the mean; negative $Z$-scores denote values below the mean.

• Detailed Worked Examples:

  • Exam Grade Example:

  • Given $\mu = 0.75$ ($75\%$) and $\sigma = 0.11$ ($11\%$). Student score $x_i = 0.92$ ($92\%$).

  • $Z = \frac{0.92 - 0.75}{0.11} = 1.55$

  • Proportion scoring same or better ($Z \ge 1.64$): $P = 0.0505$ ($5.05\%$).

  • Proportion scoring worse: $1 - 0.0505 = 0.9495$ ($94.95\%$).

  • Scores exactly $1\sigma$ above and below mean:

    • Above: $x_i = 0.75 + 1(0.11) = 0.86$ ($86\%$).

    • Below: $x_i = 0.75 - 1(0.11) = 0.64$ ($64\%$).

    • Proportion within $\pm 1\sigma$ range ($0.64\text{--}0.86$): $1 - 2(0.1587) = 0.6826$ ($68.26\%$).

  • Lesser Dodos Blood Glucose Problem Set ($\mu = 65\,\text{mg/dL}, \sigma = 25\,\text{mg/dL}$):

  • Question 4.3: Proportion with glucose $\ge 85\,\text{mg/dL}$:       $Z = \frac{85 - 65}{25} = 0.80 \rightarrow P(Z \ge 0.80) = 0.2119 \quad (21.2\%)$

  • Question 4.4: Proportion with glucose $< 45\,\text{mg/dL}$:       $Z = \frac{45 - 65}{25} = -0.80 \rightarrow P(Z \le -0.80) = 0.2119 \quad (21.2\%)$

  • Question 4.5: Proportion between $45$ and $85\,\text{mg/dL}$:       $1 - 0.2119 - 0.2119 = 0.5762 \quad (57.62\%)$

  • Question 4.6: For sample $n = 20$, probability sample mean $\bar{X} > 70\,\text{mg/dL}$:       $\text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{25}{\sqrt{20}} = 5.59\,\text{mg/dL}$       $Z = \frac{70 - 65}{5.59} = 0.89 \rightarrow P(Z \ge 0.89) = 0.1867 \quad (18.67\%)$

  • Question 4.7: Concentration exceeded by upper $5\%$ of population:       $Z_{0.05} = 1.645 \rightarrow X = 65 + 1.645(25) = 106.13\,\text{mg/dL}$

  • Question 4.8: Treatment limits for outside middle $70\%$ (tail area = $15\%$ each side, $Z = 1.035$):       $\text{Lower Limit} = 65 - 1.035(25) = 39.13\,\text{mg/dL}$       $\text{Upper Limit} = 65 + 1.035(25) = 90.88\,\text{mg/dL}$

  • Professor Grade Allocation Problem Set ($\mu = 923, \sigma = 101$):

  • Grade A (Top $10\%$, $Z = 1.282$): Cutoff $X = 923 + 1.282(101) = 1052.48$ points ($\ge 1052.28$).

  • Grade B (Next $20\%$, top $30\%$, $Z = 0.525$): Range $976.03\text{--}1052.28$ points ($X = 923 + 0.525(101) = 976.03$).

  • Grade C (Next $50\%$, top $80\%$, bottom $20\%$, $Z = -0.84$): Range $838.16\text{--}976.03$ points ($X = 923 - 0.84(101) = 838.16$).

  • Grade D (Next $15\%$, bottom $5\%$, $Z = -1.645$): Range $756.35\text{--}838.16$ points ($X = 923 - 1.645(101) = 756.35$).

  • Grade F (Lowest $5\%$): Score $< 756.35$ points.

Parametric Assumptions, Error Types & Data Transformations

• NnnhnnnnnnnnnnNhnhnnnnnnnnnnnnnnnNThree Core Parametric Assumptions:

  1. Normality: Data in each treatment group are normally distributed.

  2. Independence: Experimental units are independent; pseudoreplication is avoided.

  3. Homogeneity of Variance (Homoscedasticity): Variances across treatment groups are equal. Tested using tests of homogeneity such as the Simple Variance F-test:      $F = \frac{s_{\text{larger}}^2}{s_{\text{smaller}}^2}$

  • $H_0: s_1^2 = s_2^2$ (Variances do not differ; homoscedastic).

  • $H_a: s_1^2 \neq s_2^2$ (Variances differ significantly; heteroscedastic).

• Options When Data Violate Parametric Assumptions:

  • Scenario 1: Run parametric test regardless $\rightarrow$ Output is unreliable; high risk of erroneous conclusions.

  • J Scenario 2?9

  • Scenario 3: Non-Parametric Test $\rightarrow$ Use distribution-free test methods.

  • Scenario 4: Dual Analysis $\rightarrow$ Run both parametric and non-parametric tests on untransformed data and compare stability.

• Parametric vs. Non-Parametric Tests & Statistical Decision Matrix:

  • Parametric Tests: Highly robust/sensitive; higher statistical power; increased risk of Type I Error (False Positive).

  • Non-Parametric Tests: Less robust/sensitive; rank-based; increased risk of Type II Error (False Negative).

• Common Data Transformation Methods:

  • Logarithmic Transformation ($\log(x)$ or $\log(x + c)$):

  • Applied to right-skewed data, heteroscedastic variances, and zero-inflated counts.

  • Cannot compute $\log(0)$; add a small constant $c$ to all data points before transforming.

  • Square Root Transformation ($\sqrt{x}$):tftyyty has * b. C l

  • Applied to count data to achieve normality and correct left skewness.