Week 3

Question 1

Describe a Type I error

Answer 1

Failure to reject the null hypothesis when the hypothesis is indeed false.
FALSE POSITIVE

Question 2

Describe a Type II error

Answer 2

Rejecting the null hypothesis when the null is indeed correct.
FALSE NEGATIVE

Question 3

How do we avoid Type I & II errors when conducting an experiment

Answer 3

By setting the significance level (α alpha) accordingly.
If α is set too high, the chance of a Type I error increases. If α is set too low, the study might not be sensitive enough and the chances of a Type II error increases.

Question 4

At what level is the significance level usually set?

Answer 4

α = 0.05
Meaning there’s a 5% chance of rejecting the null hypothesis if it’s actually true—a Type I error, or a false positive.

Question 5

Define the significance level in statistics

Answer 5

It’s the threshold we set to decide when to reject the null hypothesis

Question 6

Define the power of a test

Answer 6

It’s the probability that a statistical test will correctly reject a false null hypothesis.

Question 7

What factors influence the power

Answer 7

Sample size & Effect size

Question 8

Define the effect size in a test and what does it refer to in ecology?

Answer 8

It is the measure of the magnitude of the experimental effect.
In ecological studies it refers to the strength of a relationship between variables or the size of a difference between groups.

Question 9

What power level percentage is usually targeted in research?

Answer 9

80%

Question 10

Cite 4 different ways to calculate effect size

Answer 10

Cohen’s d
Pearson’s r
Odds ratio
Eta squared (η²)

Question 11

Describe what each of the following tests aim to do and where are they used?
Cohen’s d, Pearson’s r, Odds ratio & Eta squared (η²)

Answer 11

· Cohen’s d: Measures the difference between two means divided by the standard deviation; used in t-tests.
· Pearson’s r: Measures the strength and direction of a linear relationship between two variables; used in correlation studies.
· Odds ratio: Measures the odds of an outcome occurring with an exposure versus without; used in case-control studies.
· Eta squared (η²): Measures the proportion of the total variance that is attributable to an effect; used in ANOVA

Question 12

How do we increase the power of a test?

Answer 12

Power improves with the square root of the sample size.
We can increase the power by increasing the sample size but effect size has a much higher impact on power

Question 13

What do researches must consider when designing an experiment in terms of the power of the statistical test?

Answer 13

We must consider both the anticipated effect size and the feasible sample size when planning studies to ensure they have adequate power to detect meaningful effects. This often involves a trade-off between the practicalities of data collection and the need for statistical robustness.

Question 14

What is a nomogram?

Answer 14

A nomogram is a graphical tool used for the calculation of sample size or power

Question 15

Describe what the mean is in statistics

Answer 15

The sum of all values divided by the number of values. Example: The mean of [1, 2, 3, 4] is (1+2+3+4)/4 = 2.5.

Question 16

Describe what the median is in statistics

Answer 16

The middle value in a list of numbers. Example: The median of [1, 3, 3, 6, 7, 8, 9] is 6.

Question 17

Describe what a mode is

Answer 17

The most frequently occurring value(s) in a dataset. Example: The mode of [1, 2, 2, 3] is 2.

Question 18

What is the standard deviation?

Answer 18

It is the amount of variation in a set of values. Example: SD indicates how much the height of plants varies from the mean height.

Question 19

What is variance?

Answer 19

The average of the squared differences from the Mean. Example: High variance means more spread out data.

Question 20

Describe the terms p-value and give an example

Answer 20

It is the probability of obtaining test results at least as extreme as the results observed, under the assumption that the null hypothesis is correct. Example: A p-value less than 0.05 often suggests significant results in many scientific studies.

Question 21

What is the null hypothesis of an experiment?

Answer 21

The hypothesis that there is no significant difference or effect. Example: H0 can state that there is no difference in growth rates between two plants species under the same conditions.

Question 22

If you set the significance level (α) to 0.01, what happens to the probability of making a Type I error?

Answer 22

The significance level, denoted as α, is the threshold for deciding whether a result is statistically significant. By setting α to 0.01, you are saying that you will only accept results as statistically significant if the probability of them occurring by random chance is less than 1%. This lowers the probability of making a Type I error compared to a higher α level.

Question 23

When rolling a die 100 times, the mean abundance of a butterfly species converges to the expected mean. Which statistical principle does this demonstrate?

Answer 23

The Law of Large Numbers states that as more observations are collected, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes. For dice rolls, as the number of rolls increases, the average result should get closer to the expected mean of 3.5 for a fair six-sided die.

Question 24

After conducting a t-test between two meadow environments, your p-value is 0.03. What does this imply if your α level is set at 0.05?