Statistics and Observations in Biological Science

Statistics and Observations in Biological Science

Introduction to the Scientific Method

The scientific method is a systematic approach used in biological research to answer questions and test hypotheses. It ensures that observations and conclusions are based on empirical evidence and logical reasoning.

• Observation: Gathering information about phenomena or events.

• Question: Formulating a question based on observations.

• Hypothesis: Proposing a testable explanation or prediction.

• Experiment: Designing and conducting experiments to test the hypothesis.

• Data Analysis: Analyzing collected data using statistical methods.

• Conclusion: Drawing conclusions based on data analysis; refining the hypothesis if necessary.

Example: "A commitment to tough-minded hypothesis testing and sound experimental design is a hallmark of biological science." (Freeman)

Formulating Scientific Questions

Characteristics of Good Scientific Questions

• Based on observations and/or previous knowledge

• Answerable or measurable

• Lead to experiments

• Generally involve a hypothesis that will be tested

Properly structured questions guide the scientific process and lead to the discovery of truth.

Hypotheses in Biological Experiments

Types of Hypotheses

• Null Hypothesis (H0): Predicts that the treatment will have no effect. It is the default or negative hypothesis (e.g., "There is no difference between groups").

• Alternate Hypothesis (HA): Opposite of the null hypothesis; predicts that the treatment will have an effect (e.g., "There is a difference between groups").

Example: Observation: "Men at BYU seem to be taller than women." Question: Are men at BYU taller than women? Alternate Hypothesis: Men at BYU are taller than women. Null Hypothesis: Men at BYU are not taller than women.

Variables in Experiments

Types of Variables

• Dependent Variable: What the researcher measures; its value depends on the independent variable.

• Independent Variable: What the researcher varies or controls; does not depend on other variables (e.g., time, treatment type).

Parameters and Dimensions

• Parameter: Any measurable characteristic of the system (e.g., concentration, mass, density).

• Dimension: The units of a parameter (e.g., grams, liters, mL, atm, Hz).

Controls in Experiments

Types of Controls

• Positive Control: A treatment known to give a response; expected result if the alternate hypothesis is true.

• Negative Control: Absence of treatment; expected result if the null hypothesis is true.

Practice Example: Experimental Design

Experiment: Mice lacking the α2-adrenergic receptor (ARKO) and normal mice (WT) were compared for cardiac angiotensin II (ANG II) content at 3 and 7 months.

• Null Hypothesis: The ARKO mice and the WT mice will have the same content of heart ANG II.

• Dependent Variable: Cardiac ANG II content.

• Independent Variables: Type of mice (WT and ARKO) and time in months.

• Negative Control: WT mice.

• Positive Control: There is no positive control in this experiment.

Statistical Analysis in Biology

Numerical Descriptors

• Mean: The average value; calculated as the sum of all values divided by the number of values. $\text{Mean} = \frac{\sum x_i}{n}$

• Median: The middle value when data are ordered from lowest to highest.

• Standard Deviation (SD): A measure of the spread or variation in a set of data. $s = \sqrt{\frac{\sum_{i=1}^{n} (y_i - m)^2}{n-1}}$

Example Calculation: For the data set 8, 18, 7, 13, 4:

• Mean = 10

• Median = 8

• Standard Deviation = 5.5

Standard Deviation Interpretation

• A larger standard deviation indicates greater variation in the data.

• A smaller standard deviation indicates less variation.

• Example: Human females have a smaller standard deviation of height than human males.

Standard Error of the Mean (SEM)

The SEM estimates the variability of the sample mean relative to the true population mean.

• Formula: $\text{SEM} = \frac{s}{\sqrt{n}}$

• As a rule of thumb, if the means ± 2 × SEM overlap, the null hypothesis is not rejected.

Testing the Null Hypothesis: Example

Comparing the weights of male and female BYU students:

• n = 46 for men, n = 50 for women

• Men: mean = 163.3, SD = 22.1, SEM = 3.3

• Women: mean = 128.6, SD = 21.1, SEM = 3.0

• Means ± 2 × SEM do not overlap (134.6 vs. 156.7), so the null hypothesis is rejected.

Practice Problems

Group	Mean	Standard Deviation (SD)	Standard Error of the Mean (SEM)
Vehicle	40	14.6	5.5
Drug	30.5	14.1	Additional info: Not calculated in the slide, but would be $\frac{14.1}{\sqrt{7}} \approx 5.3$

Conclusion: The null hypothesis is not rejected because the means are not significantly different.

Statistical Errors

• Type I Error: Rejecting the null hypothesis when it is actually true (false positive). The p-value is the probability of making this error.

• Type II Error: Accepting the null hypothesis when it is actually false (false negative). The probability of making this error is 1 - p.

With p = 0.05, there is still a 5% chance of being wrong in rejecting the null hypothesis.

Summary Table: Key Statistical Terms

Term	Definition	Formula
Mean	Average value	$\frac{\sum x_i}{n}$
Median	Middle value of ordered data	—
Standard Deviation (SD)	Spread of data around the mean	$\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$
Standard Error of the Mean (SEM)	Estimate of how far the sample mean is from the population mean	$\frac{s}{\sqrt{n}}$

Additional info: Statistical tests (e.g., t-tests, ANOVA) are used to determine p-values and assess the significance of results, but the details are beyond the scope of this summary.