BIOL 208 - Lab 0: Statistics in Biology PDF

# Lab 0: Part 3: Statistics in Biology ## Overview - This lab focuses on the interpretation of statistical test results, rather than the calculations themselves. - It covers both descriptive statistics (e.g., mean, confidence intervals) and more advanced statistical tests. ## Objectives - Ident...

# Lab 0: Part 3: Statistics in Biology ## Overview - This lab focuses on the interpretation of statistical test results, rather than the calculations themselves. - It covers both descriptive statistics (e.g., mean, confidence intervals) and more advanced statistical tests. ## Objectives - Identify why statistics are used in biology. - Distinguish between measures of central tendency (mean, median, mode) and range (standard deviation, variance). - Calculate mean, standard deviation, and 95% confidence interval. - Apply the appropriate statistical test to a given data set. - Distinguish between continuous and discrete data sets. - Describe what a p-value means. - Interpret p-values to assess statistical significance. ## Statistics in Biology ### Why do I need to learn statistics for a biology course? - Our brains are good at finding patterns, even when they don't actually exist - Statistics provide tools to rule out the possibility of finding "false" patterns. - Ecologists collect data with a high degree of variability. - Descriptive statistics are essential for communicating the spread or range of your data. ### Measures of central tendency and spread - Measures of central tendency describe where most of the values in a dataset tend to lie: - Mean (average) - Median - Mode - Measures of spread describe the upper and lower limits of the data: - Range - Standard Deviation - Variance **Mean (x):** - The most widely used measure of central tendency. - Calculated by the formula: Σx₁ / n - Σx₁ = the sum of all individual observations - n = the total number of observations - Can be calculated using Excel's "Descriptive Statistics" toolpak or the formula "=AVERAGE(...)". **Variance (s²):** - The most statistically useful measure of spread. - Calculated as the average of the square of the deviations of the measurements from the mean: Σ(xᵢ - x)² / (n - 1) **Standard deviation (s):** - Square root of the variance. - Calculated in Excel using the formula "=STDEV(...)" or "=STDEV.S(...)". ### Normal Distribution - Most observations are clustered around the average, creating a bell-shaped curve. - 68.3% of observations lie within one standard deviation of the mean. - 95.4% of observations lie within two standard deviations of the mean. - 99.7% of observations lie within three standard deviations of the mean. ### Samples, Populations, and Confidence Intervals - It's usually impossible to measure the entire population, so we use samples to make estimates. - Confidence Intervals are used to create an interval around the sample mean that is likely to contain the true population mean, taking into account sample size and variability. **Confidence Intervals are:** - A range around a sample estimate that is likely to contain the true population value. - Their size depends on: - The size (n) and variability (s²) of your sample. - The statistically defined confidence level (usually 95%). - A less variable sample implies a smaller confidence interval, as the sample mean is likely closer to the true population mean. - A more variable sample implies a larger confidence interval, as the sample mean could be further from the true population mean. **Standard Error of the Mean (Sx):** - Used to calculate confidence intervals. - Formula: Sx = s / √n or Sx = √(s² / n). **Confidence Interval Formula:** - x + (t * Sx) - x = sample mean. - t = value obtained from a statistical t-table (based on degrees of freedom and desired confidence level). - Sx = Standard Error of the Mean. ### Significance and Interpreting p-values - Statistical tests help determine the significance of trends observed in a sample data. - **P-value:** The probability of getting a result at least as extreme as your own, given that the null hypothesis is true. - **Null Hypothesis:** States that there is no difference between groups or no relationship between variables. - If the p-value is less than the alpha value (p<0.05), we reject the null hypothesis and conclude that the result is statistically significant. - If the p-value is greater than or equal to the alpha value (p≥0.05), we fail to reject the null hypothesis and conclude that the result is not statistically significant. ### Types of Data - **Measurement Data (Continuous Data):** - Can fall anywhere on a continuous number line (e.g., 12.5 cm, 152.75 kg, 20.8 °C). - Includes means/averages calculated from count/enumeration data. - **Count/Enumeration Data (Discrete Data):** - Represents counted values that can only be whole numbers (e.g., 0, 1, 2, 3, 4). ### Summary - Understand the importance of statistics in biology for analyzing data and making informed conclusions. - Differentiate between measures of central tendency and range. - Calculate mean, standard deviation, and confidence intervals. - Identify the appropriate statistical test based on the type of data and research question. - Interpret p-values to assess statistical significance.