BIOL 005B Lab Manual (copy)
Q: Why do biologists use statistics?
A: Biologists use statistics to determine whether observed differences or relationships in data are real or due to random chance.
Q: Why are two group means rarely identical?
A: Because natural biological variation causes measurements to differ, even when groups are similar.
Q: What does statistics help determine in biological studies?
A: Whether patterns in data are caused by chance or reflect a real biological difference.
Q: What is continuous data?
A: Numerical data that can take any value within a range.
Q: Give examples of continuous data.
A: Height, weight, temperature, beak length, blood pressure.
Q: What is categorical data?
A: Data divided into distinct groups or categories.
Q: Give examples of categorical data.
A: Male/female, smoker/non-smoker, species type, fur color.
Q: Why is knowing data type important?
A: It helps determine which statistical test is appropriate.
Q: What is variability?
A: The spread of data values in a dataset.
Q: What does low variability mean?
A: Most observations are close to the mean.
Q: What does high variability mean?
A: Observations are spread out over a wider range.
Q: What are two common measures of variability?
A: Standard deviation and variance.
Q: What is variance?
A: A measure of how spread out data points are from the mean.
Q: What does high variance indicate?
A: Data points are more dispersed from the mean.
Q: What does low variance indicate?
A: Data points cluster closely around the mean.
Q: What symbol is commonly used for sample variance?
A: s²
Q: What is standard deviation?
A: A measure of the typical distance of data points from the mean.
Q: What symbol is commonly used for sample standard deviation?
A: s
Q: How is standard deviation related to variance?
A: Standard deviation is the square root of variance.
Q: What percentage of normally distributed data lies within 1 standard deviation of the mean?
A: About 68.3%.
Q: What percentage of normally distributed data lies within 2 standard deviations of the mean?
A: About 95.4%.
Q: Does standard deviation always decrease when sample size increases?
A: No, it can increase or decrease depending on the sample values.
Q: What improves when sample size increases?
A: The accuracy of the sample estimate of the population standard deviation.
Q: What is the mean?
A: The average value of a dataset.
Q: How do you calculate the mean?
A: Add all values and divide by the number of values.
Q: What is the standard error of the mean (SEM)?
A: An estimate of how close the sample mean is to the true population mean.
Q: What does a smaller SEM indicate?
A: The sample mean is likely a more accurate estimate of the population mean.
Q: How does increasing sample size affect SEM?
A: It decreases SEM.
Q: What is the formula for SEM?
A: SEM = standard deviation / √n
Q: What does n represent in the SEM formula?
A: Sample size.
Q: What is inferential statistics?
A: Statistical methods used to draw conclusions about populations from sample data.
Q: What is the null hypothesis?
A: A statement that there is no pattern, effect, or difference in the data.
Q: What symbol is used for the null hypothesis?
A: H₀
Q: What is the alternative hypothesis?
A: A statement that there is a real pattern, effect, or difference in the data.
Q: What symbol is used for the alternative hypothesis?
A: H₁
Q: In a two-group comparison, what does H₀ usually state?
A: The group means are the same.
Q: In a correlation test, what does H₀ usually state?
A: There is no correlation (r = 0).
Q: What is significance level alpha?
A: The threshold probability used to decide statistical significance.
Q: What symbol is used for significance level?
A: α
Q: What significance level is commonly used in biology?
A: 0.05
Q: What does p-value represent?
A: The probability that the observed results occurred by chance if the null hypothesis is true.
Q: If p < 0.05, what decision is made?
A: Reject the null hypothesis.
Q: If p < 0.05, what does that mean?
A: There is a statistically significant pattern or difference.
Q: If p ≥ 0.05, what decision is made?
A: Fail to reject the null hypothesis.
Q: If p ≥ 0.05, what does that mean?
A: There is not enough evidence for a significant pattern or difference.
Q: What test compares the means of two independent groups?
A: Student’s t-test for independent samples.
Q: What types of variables are needed for an independent samples t-test?
A: One categorical variable and one continuous variable.
Q: Give an example of variables for a t-test.
A: Smoker/non-smoker (categorical) and CRP level (continuous).
Q: What statistic is calculated in a t-test?
A: t (observed t-value).
Q: What is tcrit?
A: The critical t-value used for comparison.
Q: If t observed > t critical, what do you conclude?
A: Reject the null hypothesis; the groups are significantly different.
Q: What are degrees of freedom for a two-sample t-test?
A: Total sample size of both groups minus 2.
Q: What does correlation measure?
A: The strength and direction of a relationship between two variables.
Q: What symbol is used for correlation coefficient?
A: r
Q: What values can r range between?
A: -1 to +1
Q: What does r = +1 mean?
A: Perfect positive correlation.
Q: What does r = -1 mean?
A: Perfect negative correlation.
Q: What does r = 0 mean?
A: No correlation.
Q: What does an r-value close to 0 indicate?
A: A weak relationship.
Q: What does a positive correlation mean?
A: As one variable increases, the other tends to increase.
Q: What does a negative correlation mean?
A: As one variable increases, the other tends to decrease.
Q: What is linear regression used for?
A: To model the relationship between two continuous variables.
Q: What type of graph is commonly used for correlation and regression?
A: Scatter plot.
Q: What is the coefficient of determination?
A: R²
Q: How is R² related to r?
A: R² is the square of r.
Q: What does R² measure?
A: The proportion of variation explained by the relationship between variables.
Q: What does R² = 1.00 mean?
A: The regression explains 100% of the variation.
Q: What does R² = 0.00 mean?
A: No association is explained.
Q: Are low R² values always unimportant in biology?
A: No, low R² values can still be statistically significant.
Q: What type of variables are required for correlation and linear regression?
A: Both variables must be continuous.
Q: If studying leaf length and leaf width, what test would be appropriate?
A: Correlation or linear regression.
Q: If comparing plant heights in fertilized vs unfertilized groups, what test is appropriate?
A: Independent samples t-test.
Q: If comparing smoker vs non-smoker inflammation means, what test is appropriate?
A: Independent samples t-test.
Q: If testing whether temperature affects enzyme rate across values, what test is appropriate?
A: Correlation or linear regression.
Q: Why are large sample sizes valuable in biology?
A: They better estimate population parameters and reduce sampling error.
Q: What is sampling error?
A: The difference between a sample statistic and the true population value due to random sampling.
Q: What is a population?
A: The entire group of individuals of interest.
Q: What is a sample?
A: A subset of the population used for measurement.
Q: Why do scientists often use samples instead of populations?
A: Measuring every individual is often impractical or impossible.