Week 3 Flashcards
Post week reflection
Describe a Type I error
Failure to reject the null hypothesis when the hypothesis is indeed false.
FALSE POSITIVE
Describe a Type II error
Rejecting the null hypothesis when the null is indeed correct.
FALSE NEGATIVE
How do we avoid Type I & II errors when conducting an experiment
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.
At what level is the significance level usually set?
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.
Define the significance level in statistics
It’s the threshold we set to decide when to reject the null hypothesis
Define the power of a test
It’s the probability that a statistical test will correctly reject a false null hypothesis.
What factors influence the power
Sample size & Effect size
Define the effect size in a test and what does it refer to in ecology?
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.
What power level percentage is usually targeted in research?
80%
Cite 4 different ways to calculate effect size
Cohen’s d
Pearson’s r
Odds ratio
Eta squared (η²)
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)
· 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
How do we increase the power of a test?
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
What do researches must consider when designing an experiment in terms of the power of the statistical test?
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.
What is a nomogram?
A nomogram is a graphical tool used for the calculation of sample size or power
Describe what the mean is in statistics
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.
Describe what the median is in statistics
The middle value in a list of numbers. Example: The median of [1, 3, 3, 6, 7, 8, 9] is 6.
Describe what a mode is
The most frequently occurring value(s) in a dataset. Example: The mode of [1, 2, 2, 3] is 2.
What is the standard deviation?
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.
What is variance?
The average of the squared differences from the Mean. Example: High variance means more spread out data.
Describe the terms p-value and give an example
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.
What is the null hypothesis of an experiment?
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.
If you set the significance level (α) to 0.01, what happens to the probability of making a Type I error?
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.
When rolling a die 100 times, the mean abundance of a butterfly species converges to the expected mean. Which statistical principle does this demonstrate?
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.
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?
