Biostats Final Cheat Sheet

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∩ means intersection: the set composed of all elements that belong to both A and B

word form: "and"

∪ means union: the set of all elements that are in A or B or both

word form: "or"

Probability axioms:

0 ≤ P ≤ 1

When calculating Probability for independent events, use the MULTIPLICATION RULE

P(A ∩ B) = P(A) * P(B)

IS ONLY VALID IF THE TWO EVENTS ARE INDEPENDENT!

We can assume independence if the sample size is ≤ %5 of the population size

When calculating probability for events that are not specified as independent, use ADDITION RULE

P (A ∪ B) = P(A) + P(B) − P(A∩B)

If P (A ∪ B) = Ø (is disjoint), then use P (A ∪ B)= P(A) + P(B) as the formulas as P(A∩B) = 0

Interpreting Probability:

Step 1: Define the experiment

Step 2: "As the experiment is repeated to infinity, drawing with replacement/ replacing each sample, the proportion of values within the interval will converge to the probability."

Normal Curve requirements:

bell-shaped

symmetric around the mean μ

The value of σ indicates the spread of the distribution

Standardization:

Given X̅ ~ N ( μ, σ / √​​​​​​​n ), Z ~ N ( (X̅- μ) / (σ / √​​​​​​​n) )

Then, use standard normal table to find the probability of Z (If Z > some number, use the negative of your calculated Z score on the table!)

Definition of Power:

P (conclude H1| H1 is true)

The probability of correctly rejecting the null hypothesis when it is false

Requirements for high power:

Obtain a random sample

X̅ ~ N ( μ, σ / √​​​​​​​n )

Hypothesis Conclusions (We will use α = 0.05 as our level of significance)

If p-value < 0.05, reject Ho in favor of H1

If p-value > 0.05, conclude Ho

Risk = (number in category) / (total number in group)

Relative Risk: The ratio of risks for two different categories; (risk in category 1) / (risk in category 2)

Odds = (number in category) / (number not in category)

Odds Ratio: Ratio of two odds; (Odds #1) / (Odds #2)

Notes to complete:

Probability Axioms

Hypothesis Conclusions

Double check the interpretation of probability is correct

Remember: The probability of μ falling within a Confidence interval can only be 0 or 1, the 95% just means that the method used to determine the confidence interval had a 95% chance of producing an interval containing μ

Go through STATS Exam 3 Review in the notes on your phone to see if there's anything to add

Make sure you have either Exam cheat sheet 1 or Exam cheat sheet 2 with you as well

Write this all out maybe add a couple examples, like the Shere Hite example in those notes on your phone and the Risk/Odds example in the exam you made

The Exam will be from 3pm-5pm in your regular room in the Main Hall!