Probability models
21 important questions on Probability models
What is the question that is answered in interferential statistics?
What are two types of probability models to describe distributions of random events?
- All possible outcomes of the random event: individual outcomes are uncertain, but in a large group there is a regular distribution
- A probability for each outcome: proportions of times the outcome would occur in a large number of repetitions
What are the two most important characteristics of the probability distribution?
- Expected value: average outcome of random event
- Variance: measure of the dispersion of the outcomes of the random event
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What is the difference between expected value and variance, in for example calculations on lottery tickets?
- Variance: measure of the spread of the outcomes of random event X
What is a widely used (theoretical) probability distribution for dichotomous (nominal) variables?
What does a bionomial distribution look like?
What are the two possible outcomes for a dichotomous event?
What is the difference between a binomial distribution and a poisson distribution?
- Poisson distribution: the count of independent events is given, there is an unlimited amount of possible outcomes, often used when the trial is very large and the chance of success is low
What are two counterexamples for the fact that counts in these studies need to be independent?
- People need to choose between things, and after the first person has chosen, the second person has one choice less (which can be useful for studying the effect of choices on other people)
To what kind of things can the possion distribution be applied?
What are differences between discrete and continuous probability distributions?
- Discrete: sum of probabilities is 1, continuous: area under the curve is 1
- Discrete: exact probability can be calculated, continuous: probability can be estimated
What are two important values for (continuous) normal distributions?
- variance σˆ2 or standard deviation σ
What are the two types of skews possible for a normal distribution?
- Positive skew: 'tail' is more to the right
What are 68% and 95% confidence intervals?
- 95%: area of 2 st.dev. from the mean
If empirical distributions of data resemble a normal distribution, what do you need to draw conclusions on the population? And what do you use if the empirical distributions do not resemble normal distribution?
- Nonparametric statistics
What do you use the standard normal distribution for?
- Compare where the score of someone lies in two different distributions
How do you compare where the score of someone lies in two different distributions?
How do you calculate the chance that someone has a higher score than a certain individual?
What could be a reason that distributions of certain variables are skewed to the right?
How can you make a normal distribution from a right-skewed distribution in the case that values below 0 are not possible?
What happens with a (normal) distribution when the sample size increases?
- Distribution of sample means becomes more narrow and symmetrical
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