Introduction to Statistical Thinking
Unpredictability / Uncertainty of Events
What is randomness?
Each member in a population has the same chance of being chosen
What is a simple random sampling design?
Type of variable with two or more options like the color of a car or coin flip
What is a categorical variable?
Most frequent observation (mean and median are ways to measure)
What is center?
An arrangement of a set of elements (order matters)
What is a permutation?
P(A∩B) = P(A) * P(B) where A and B are independent
What is the multiplication rule?
Outcomes can be counted like shoe size or dice sums
What is a discrete random variable?
Discrete distribution in which there are only two outcomes
What is a Bernoulli trial?
(Z-score) OR (x-value, mean, SD)
What are the two inputs you can put into pnorm?
What I assume to be true (always in terms of equality)
What is the null hypothesis (Ho)?
Range of values for the population parameter in which you FTR Ho with a certain level of confidence
Answered by collecting data that varies
What is a statistical question?
Each member within natural divisions in a population has the same likelihood of being in a sample
What is a stratified random sampling design?
Type of variable with numerical options like weight or height
What is a quantitative variable?
How data varies around the center (Variance, Standard Deviation, and IQR are ways to measure)
What is spread/variability?
What is a combination?
P(A∪B) = P(A) + P(B) where A and B are disjoint
What is the addition rule?
Outcomes cannot be counted as values can be any value within an interval like weight or tire pressure
What is a continuous random variable?
Fixed # of trials, outcomes are mutually exclusive, trials are independent, and probability of success is constant
What are the assumptions for the binomial distribution?
Shifts the normal distribution to the left or right
What does changing the mean do to a normal distribution?
How far the sample statistic is from the population parameter in units of standard error
What is a test statistic?
Number of standard errors from the point estimate
What is a critical value?
Process by which the treatment is given to the subject by chance
What is random assignment?
Samples composed of entire groups selected at random
What is a cluster sampling design?
Categorical variable with natural ordering / ranking
What is an ordinal variable?
Median and IQR
What are resistant measures to outliers?
All possible outcomes or results
What is the sample space?
P(A∪B) = P(A) + P(B) - P(A∩B)
What is the general addition rule?
Weighted average of outcomes
n*p
What is the expected value for a binomial distribution?
Makes the normal distribution narrower or wider
What does changing the SD do to a normal distribution?
Probability of observing sample data given the null hypothesis is true
What is a p-value?
Sample statistic for a confidence interval
What is a point estimate?
A list of all elements from the population being studied
What is a sampling frame?
Elements are selected based on their proximity to the experimenter
What is a convenience sampling design?
Categorical variable with no natural ordering
What is a nominal variable?
Mean and Standard Deviation
What are not resistant measures to outliers?
The outcome of a trial does not impact the outcome of another trial
What is independence?
P(A|B) = P(A∩B) / P(B)
What is Bayes Rule?
A measure that gives us probabilities of the possible values for a discrete random variable (variables may have two or more outcomes)
What is a probability mass function / discrete distribution?
1 - (P(x>24) + P(x>25))
How would you find the probability of getting less than 24 successes (or at most 23 successes)?
Allows us to approximate the sampling distribution of the sample mean or proportion with a normal distribution
Central Limit Theorem
Rejecting a null hypothesis that is correct
What is a Type I Error?
Critical Value * Standard Error
How do you calculate the margin of error?
An omitted variable that can influence the relationship between the two variables of study
What is a confounding variable?
Participants opt-in to become part of a study
What is a volunteer sampling design?
Categorical variable with only two options
What is a categorical binary variable?
The number of standard deviations a value is from the mean
What is Z-score?
Outcomes of a trial cannot both happen at once
What is mutually exclusive / disjoint?
What is a contingency table?
How far each value deviates from the mean
What is standard deviation?
1-p
What is q?
A measure that gives us probabilities of the possible values for a continuous random variable
What is a probability density function?
Failing to reject a null hypothesis that is not correct
What is a Type II Error?
Z-score of -1.28 or 1.28
What is the critical value for a significance level of 0.1?