Terms/Strategies Flashcards
Explanatory variable
The thing that’s causing something else to change
Response variable
The thing that might be changed by the explanatory variable
Block design
A form of random assignment where a proportion is preserved (for example, randomly assigning people to a group, but keeping the same ratio of males to females as the sample population)
Matched pairs design
An experimental design where participants having the same characteristics get grouped into pairs, then within each pair, 1 participant gets randomly assigned to either the treatment or the control group and the other is automatically assigned to the other group.
Simple random sample
A form of random sampling where everything in the population has an equal chance of being chosen
Random sample
A form of random sampling where everything has at least a chance of being chosen (different from a simple random sample because probabilities of being drawn may not be equal)
Sample study
A study that attempts to make inferences about a larger population by taking a sample of it. Usually randomized
Ex: taking a sample of students in a university to estimate satisfaction levels of all university students there
Observational study
Attempts to find correlations in a sample/population (can’t determine causation). Usually randomized
Divided into 3 types based on time: retrospective (looking back on data), sample survey (looking at current data), and prospective (future data, sort of like a longitudinal study). You’d need more detail than normal to determine whether something was a sample survey or a prospective observational study
Experimental study
A study where researchers give the subjects (for example, people, but could also be other organisms or inanimate objects) an intervention/treatment to determine its effects. Usually randomized, just like any other study
How does conditional probability work?
p(A|B) is the probability of event A occurring, given that event B occurs. The | means “given”
When can we say events are independent?
If knowing one event occurred doesn’t change the probability of the other event, we can say the events are independent
When can we say events are dependent?
If knowing one event occurred changed the probability of the other event, we can say the events are dependent
How can you calculate the probability of independent/dependent events?
Use the general multiplication rule:
P(A and B) = P(A) * P(B|A)
The probability of A and B both happening is equal to the probability of A happening multiplied by the probability of B happening given A happened.
For independent events, the A at the end of P(B|A) functionally doesn’t matter because P(B|A) = P(B)
How do you know when overlap may be a problem?
Let’s say you want to know the chances of Person A and Person B both successfully winning a prize. The chance of each of them winning it is 1/6. What is the chance that one of them gets the prize?
The trick is to recognize when there may be potential overlap. In this case, the condition of one of them winning a prize may be counted twice (overlap). We must consider the chance both of them win the prize, which is 1/6 * 1/6 = 1/36. When calculating the chance of independent events happening, you just multiply the probabilities of them occurring together.
Thus, out of all the possibilities (considering they all add to 1), the chance of both winning is 1/6 + 1/6 - 1/36.
The probabilities stack up like this: NO WIN (25/36) + ONE WIN (10/36) + BOTH WIN (1/36).
If this problem included dependent events, you’d simply multiply different ratios.
Probability of “at least one” success/failure
P(at least 1 success) = 1 − P(all failures)
or
P(at least 1 failure) = 1 − P(all successes)
If you wanted to find the probability of, say, at least two successes/failures, you’d also have to subtract P(1 success/failure), and so on for calculating in the case of more successes/failures
This is because then you’d have the probability of obtaining a result outside of no successes/failures and 1 success/failure, which is 2 successes/failures or more.
