Statistics Essentials
84 flashcards by MentisLibrary
Descriptive statistics, sampling, confidence intervals, hypothesis testing, and regression, with the correct interpretation spelled out for each. Learn what a p-value actually means and what it does not.
- What is the difference between a population and a sample?
- A population is every member of the group of interest, a sample is the subset you actually measure
- What is the difference between a parameter and a statistic?
- A parameter describes a population, a statistic describes a sample
- What is the difference between categorical and quantitative data?
- Categorical data places items in groups, quantitative data measures amounts
- What are the four levels of measurement?
- Nominal (labels), ordinal (ordered), interval (equal gaps, no true zero), ratio (true zero)
- What is the mean and when is it a poor summary?
- The arithmetic average. It is a poor summary when the data is skewed or has outliers
- What is the median and why is it robust?
- The middle value when sorted. It is robust because moving an extreme value does not move it
- What is the mode?
- The most frequently occurring value
- How do the mean and median compare in a skewed distribution?
- The mean is pulled toward the long tail, so it exceeds the median in a right-skewed distribution
- What are the range and the interquartile range?
- Range is max minus min, IQR is $Q_3 - Q_1$, the spread of the middle half
- What is variance and what is standard deviation?
- Variance is the average squared deviation from the mean, standard deviation is its square root
- Why does the sample standard deviation divide by $n-1$?
- Because using the sample mean uses up one degree of freedom, and dividing by $n$ would underestimate the spread
- What is a z-score?
- The number of standard deviations a value sits from the mean
- What is the empirical rule?
- For a roughly normal distribution, about $68\%$ of data falls within one standard deviation, $95\%$ within two, and $99.7\%$ within three
- What is the 1.5 IQR rule for outliers?
- A value is an outlier if it falls below $Q_1 - 1.5\,\text{IQR}$ or above $Q_3 + 1.5\,\text{IQR}$
- What does a boxplot show?
- The five-number summary: minimum, $Q_1$, median, $Q_3$, and maximum, with outliers plotted separately
- What is a percentile?
- The value below which a given percentage of observations fall
- What is a simple random sample?
- A sample in which every group of the given size has an equal chance of being chosen
- What is stratified sampling?
- Dividing the population into homogeneous strata, then randomly sampling within each
- What is cluster sampling?
- Splitting the population into clusters, randomly choosing whole clusters, and measuring everyone inside them
- What is systematic sampling?
- Choosing every $k$th item after a random start
- What is nonresponse bias?
- Bias arising because the people who do not respond differ systematically from those who do
- What is response bias?
- Bias created by the way a question is asked or by respondents answering untruthfully
- What is the difference between an observational study and an experiment?
- An experiment imposes a treatment on subjects, an observational study only records what already happens
- What is a confounding variable?
- A variable associated with both the explanatory variable and the response, blurring their relationship
- Why does random assignment matter in an experiment?
- It makes the treatment groups comparable on average, so differences in outcome can be attributed to the treatment
- What are blinding and double blinding?
- Blinding hides the treatment from the subject, double blinding also hides it from those measuring the outcome
- What is a sampling distribution?
- The distribution of a statistic across all possible samples of a given size
- What is the Central Limit Theorem?
- For a large enough sample, the sampling distribution of the sample mean is approximately normal regardless of the population's shape
- What is the standard error of the mean?
- The standard deviation of the sampling distribution of $\bar{x}$
- What is a confidence interval?
- A range of plausible values for a parameter, built with a method that captures the truth a stated percentage of the time