BIOL 005B Lab Manual (copy)

Why do biologists use statistics?

To determine whether observed differences or relationships in data are real or due to random chance.

What causes two group means to rarely be identical?

Natural biological variation causes measurements to differ, even when groups are similar.

What does statistics help determine in biological studies?

Whether patterns in data are caused by chance or reflect a real biological difference.

What is continuous data?

Numerical data that can take any value within a range.

Give examples of continuous data.

Height, weight, temperature, beak length, blood pressure.

What is categorical data?

Data divided into distinct groups or categories.

Give examples of categorical data.

Male/female, smoker/non-smoker, species type, fur color.

Why is knowing data type important?

It helps determine which statistical test is appropriate.

What is variability?

The spread of data values in a dataset.

What does low variability mean?

Most observations are close to the mean.

What does high variability mean?

Observations are spread out over a wider range.

What are two common measures of variability?

Standard deviation and variance.

What is variance?

A measure of how spread out data points are from the mean.

What does high variance indicate?

Data points are more dispersed from the mean.

What does low variance indicate?

Data points cluster closely around the mean.

What symbol is commonly used for sample variance?

s²

What is standard deviation?

A measure of the typical distance of data points from the mean.

What symbol is commonly used for sample standard deviation?

s

How is standard deviation related to variance?

Standard deviation is the square root of variance.

What percentage of normally distributed data lies within 1 standard deviation of the mean?

About 68.3%.

What percentage of normally distributed data lies within 2 standard deviations of the mean?

About 95.4%.

Does standard deviation always decrease when sample size increases?

No, it can increase or decrease depending on the sample values.

What improves when sample size increases?

The accuracy of the sample estimate of the population standard deviation.

What is the mean?

The average value of a dataset.

How do you calculate the mean?

Add all values and divide by the number of values.

What is the standard error of the mean (SEM)?

An estimate of how close the sample mean is to the true population mean.

What does a smaller SEM indicate?

The sample mean is likely a more accurate estimate of the population mean.

How does increasing sample size affect SEM?

It decreases SEM.

What is the formula for SEM?

SEM = standard deviation / √n

What does n represent in the SEM formula?

Sample size.

What is inferential statistics?

Statistical methods used to draw conclusions about populations from sample data.

What is the null hypothesis?

A statement that there is no pattern, effect, or difference in the data.

What symbol is used for the null hypothesis?

H₀

What is the alternative hypothesis?

A statement that there is a real pattern, effect, or difference in the data.

What symbol is used for the alternative hypothesis?

H₁

In a two-group comparison, what does H₀ usually state?

The group means are the same.

In a correlation test, what does H₀ usually state?

There is no correlation (r = 0).

What is significance level alpha?

The threshold probability used to decide statistical significance.

What symbol is used for significance level?

α

What significance level is commonly used in biology?

0.05

What does p-value represent?

The probability that the observed results occurred by chance if the null hypothesis is true.

If p < 0.05, what decision is made?

Reject the null hypothesis.

If p < 0.05, what does that mean?

There is a statistically significant pattern or difference.

If p ≥ 0.05, what decision is made?

Fail to reject the null hypothesis.

If p ≥ 0.05, what does that mean?

There is not enough evidence for a significant pattern or difference.

What test compares the means of two independent groups?

Student’s t-test for independent samples.

What types of variables are needed for an independent samples t-test?

One categorical variable and one continuous variable.

Give an example of variables for a t-test.

Smoker/non-smoker (categorical) and CRP level (continuous).

What statistic is calculated in a t-test?

t (observed t-value).

What is tcrit?

The critical t-value used for comparison.

If t observed > t critical, what do you conclude?

Reject the null hypothesis; the groups are significantly different.

What are degrees of freedom for a two-sample t-test?

Total sample size of both groups minus 2.

What does correlation measure?

The strength and direction of a relationship between two variables.

What symbol is used for correlation coefficient?

r

What values can r range between?

-1 to +1

What does r = +1 mean?

Perfect positive correlation.

What does r = -1 mean?

Perfect negative correlation.

What does r = 0 mean?

No correlation.

What does an r-value close to 0 indicate?

A weak relationship.

What does a positive correlation mean?

As one variable increases, the other tends to increase.

What does a negative correlation mean?

As one variable increases, the other tends to decrease.

What is linear regression used for?

To model the relationship between two continuous variables.

What type of graph is commonly used for correlation and regression?

Scatter plot.

What is the coefficient of determination?

R²

How is R² related to r?

R² is the square of r.

What does R² measure?

The proportion of variation explained by the relationship between variables.

What does R² = 1.00 mean?

The regression explains 100% of the variation.

What does R² = 0.00 mean?

No association is explained.

Are low R² values always unimportant in biology?

No, low R² values can still be statistically significant.

What type of variables are required for correlation and linear regression?

Both variables must be continuous.

If studying leaf length and leaf width, what test would be appropriate?

Correlation or linear regression.

If comparing plant heights in fertilized vs unfertilized groups, what test is appropriate?

Independent samples t-test.

If comparing smoker vs non-smoker inflammation means, what test is appropriate?

Independent samples t-test.

If testing whether temperature affects enzyme rate across values, what test is appropriate?

Correlation or linear regression.

Why are large sample sizes valuable in biology?

They better estimate population parameters and reduce sampling error.

What is sampling error?

The difference between a sample statistic and the true population value due to random sampling.

What is a population?

The entire group of individuals of interest.

What is a sample?

A subset of the population used for measurement.

Why do scientists often use samples instead of populations?

Measuring every individual is often impractical or impossible.