T-tests are crucial statistical tools in biology for comparing means between groups or to known values. They help researchers analyze experimental data, from plant heights to blood pressure changes, under specific conditions like normality and independence.

Performing t-tests involves using software, interpreting results, and considering assumptions. Researchers must report findings clearly, including statistics and biological significance, to draw meaningful conclusions about their hypotheses in various biological contexts.

T-tests for Biological Data

Situations for T-tests in Biology

• T-tests compare means between two groups or a sample mean to a known population mean
• Commonly used in biology to analyze experimental data
• One-sample t-tests compare a sample mean to a known population mean to determine if there is a significant difference
  • Compare the mean height of a sample of plants to the known mean height of the plant species
• Paired t-tests (dependent samples) compare means from two related groups, such as measuring a variable before and after treatment on the same subjects
  • Compare blood pressure in patients before and after taking a medication
• Two-sample t-tests (independent samples) compare means from two independent groups
  • Compare the mean weight of mice on two different diets (high-fat vs. low-fat)

Appropriate Conditions for T-tests

• Response variable is continuous and approximately normally distributed
• Sample size is relatively small (typically less than 30)
• Independence of observations within each group
  • Paired t-tests require that the pairs are related or matched
• Homogeneity of variance for two-sample t-tests
  • Variances of the two groups should be approximately equal

Performing T-tests

Using Statistical Software or Calculators

• One-sample t-test: Enter sample data, hypothesized population mean, and significance level (alpha)
  • Output includes t-statistic, degrees of freedom, p-value, and confidence interval
• Paired t-test: Enter paired data for each subject or unit and specify significance level
  • Software calculates differences between pairs and performs t-test on these differences
• Two-sample t-test: Enter data for each group separately and specify whether variances are assumed equal or unequal (Welch's t-test)
  • Output includes t-statistic, degrees of freedom, p-value, and confidence interval for the difference between means

Reporting T-test Results

• Include t-statistic, degrees of freedom, p-value, and confidence interval
• Report means and standard deviations of the groups being compared
• Provide a clear statement of the findings and their biological interpretation
• Consider the biological significance of the results in addition to statistical significance

T-test Assumptions

Independence

• Observations within each group should be independent of each other
• Paired t-tests require that the pairs are related or matched
  • Measurements taken on the same subjects before and after treatment

Normality

• Data should be approximately normally distributed within each group
• Check using histograms, Q-Q plots, or normality tests (Shapiro-Wilk test)
  • For larger sample sizes (n > 30), t-test is robust to moderate violations of normality due to the Central Limit Theorem
• If data is severely non-normal, consider transforming the data or using a non-parametric alternative
  • Wilcoxon signed-rank test or Mann-Whitney U test

Homogeneity of Variance (for two-sample t-tests)

• Variances of the two groups should be approximately equal
• Check using Levene's test or by comparing the variances directly
  • If variances are unequal, use Welch's t-test, which adjusts the degrees of freedom

Outliers

• Check for extreme values that may unduly influence the results
• Investigate the cause of outliers and consider removing them if they are due to measurement error or other factors unrelated to the research question
  • An outlier may be caused by a data entry error or an instrument malfunction

Interpreting T-test Results

P-value and Statistical Significance

• P-value indicates the probability of observing a difference as extreme as the one found in the sample data, assuming the null hypothesis is true
• A small p-value (typically < 0.05) suggests that the observed difference is unlikely to have occurred by chance alone, providing evidence against the null hypothesis
  • A p-value of 0.01 indicates a 1% chance of observing the difference if the null hypothesis is true
• Confidence interval for the mean difference provides a range of plausible values for the true difference in the population
  • If the confidence interval does not contain zero, it suggests a significant difference between the means

Biological Significance and Interpretation

• Consider the biological significance of the findings in addition to the statistical significance
• A statistically significant result may not always be biologically meaningful, depending on the magnitude of the difference and the context of the research question
  • A small difference in plant height may be statistically significant but not biologically relevant
• Use the results of the t-test to draw conclusions about the research question or hypothesis
  • If a two-sample t-test comparing the effects of two treatments on plant growth yields a significant result, conclude that the treatments have different effects on growth
• When reporting the results, include a clear statement of the findings, along with the relevant statistics (means, standard deviations, t-statistic, p-value, and confidence interval) and the biological interpretation of the results