Sample This!
This sampling method selects every k-th individual from a list after a random start. This sampling method selects every k-th individual from a list after a random start.
What is systematic sampling?
This is the name for the range of values, constructed from sample data, that is used to estimate an unknown population parameter.
What is a confidence interval? It provides a plausible range for the true parameter rather than a single point estimate, and is defined by a lower bound, upper bound, and confidence level.
This hypothesis states that there is no effect, no difference, or no relationship in the population.
What is the null hypothesis?
This rule states that the probability of event A OR event B equals P(A) + P(B) − P(A and B).
What is the addition rule (general)? The subtraction of P(A and B) avoids double-counting the overlap. For mutually exclusive events, P(A and B) = 0, so the formula simplifies to P(A) + P(B).
This Greek letter represents the probability of committing a Type I error and is set by the researcher before collecting data.
What is alpha (α)? Common values are 0.05 and 0.01. It is the threshold below which a p-value leads to rejecting H₀.
In this type of sampling, the population is divided into non-overlapping groups and members are randomly selected from each group.
What is stratified random sampling?
This component of a confidence interval accounts for sampling variability and is calculated as the critical value multiplied by the standard error.
What is the margin of error? It determines how wide the interval is. In other words, a larger margin means more uncertainty about where the true parameter lies.
Type I error is committed when this happens?
What is rejecting a true null hypothesis?
This theorem updates the probability of a hypothesis given new evidence, using prior probability and the likelihood of the data.
This occurs when a researcher fails to reject a null hypothesis that is actually false, essentially missing a real effect that exists in the population.
What is a Type II error (false negative)? Its probability is denoted β. It is influenced by sample size, effect size, and alpha level. A study with low power is especially prone to committing this type of error.
In this sampling method, the population is divided into naturally occurring groups, a few groups are randomly selected, and then all members within those chosen groups are surveyed.
What is cluster sampling?
When the sample size increases, this happens to the standard error and consequently to the width of the confidence interval, assuming the confidence level stays the same.
What is the standard error decreases and the interval gets narrower?
The p-value measures this probability.
What is the probability of observing a test statistic as extreme as the one computed?
This is the probability of event A given that event B has already occurred, written P(A|B).
What is conditional probability?
A researcher increases her sample size from 50 to 200 while keeping everything else constant. This is the direct effect on the power of her hypothesis test and why.
What is power increases? Larger samples reduce the standard error, making the sampling distribution tighter and easier to distinguish from the null distribution. Power = 1 − β, so as β shrinks with more data, power rises toward 1.
In this foundational probability sampling method, every individual in the population has an equal and independent chance of being selected.
What is simple random sample?
A researcher reports a 95% confidence interval of (104, 116) for a population mean. A colleague claims this means there is a 95% chance the true mean falls in that range. This claim is wrong for this reason.
What is that the true population mean is a fixed (non-random) value, not a probability? Once the interval is constructed, it either contains the true mean or it doesn't. The 95% refers to the long-run success rate of the procedure across repeated samples.
A researcher tests whether a new drug produces any difference in blood pressure compared to a placebo. This type of test is used because the effect could go in either direction.
What is a two-tailed test?
In a standard deck of 52 cards, the probability of drawing a king given the card is a face card equals this value.
What is 4/12 = 1/3? There are 12 face cards (J, Q, K across 4 suits) and 4 kings among them. P(King | Face card) = 4/12 = 1/3. This is a direct application of conditional probability.
A criminal trial analogy maps perfectly onto hypothesis testing errors — convicting an innocent person corresponds to one error type, and acquitting a guilty person corresponds to the other. Match each outcome to its correct error type.
What is convicting an innocent person = Type I error (false positive, rejecting a true H₀) and acquitting a guilty person = Type II error (false negative, failing to reject a false H₀)? The justice system deliberately sets a high bar for conviction to minimize Type I errors, at the cost of more Type II errors.
This is the key distinction between stratified sampling and cluster sampling in terms of what happens after the population is divided into groups.
What is that in stratified sampling you randomly select individuals from every group, while in cluster sampling you randomly select entire groups and survey all their members? Stratified sampling increases precision; cluster sampling increases convenience and cost efficiency.
If you increase the confidence level from 90% to 99%, this happens to the width of the interval.
What is gets wider?
This hypothesis, denoted H₁ or Hₐ, represents what the researcher is trying to find evidence for and is accepted only when there is sufficient evidence against the null.
What is the alternative hypothesis? It is never directly tested — instead, we evaluate whether the data are inconsistent enough with H₀ to indirectly support H₁. It can be directional (one-tailed) or non-directional (two-tailed) depending on the research question.
A weather forecast says there is a 35% chance of rain. A student uses this rule to quickly determine there is a 65% chance it will not rain.
What is the complement rule? P(A does not occur) = 1 − P(A). It is one of the most useful shortcuts in probability because it is often easier to calculate the probability of an event NOT happening and subtract from 1, especially when the event has many possible outcomes.
Two studies test the same hypothesis with identical sample sizes and alpha levels, but Study A has an effect size of d = 0.20 and Study B has d = 0.80. This is the difference in their statistical power and the reason why.
What is Study B has substantially higher power? A larger effect size means the true population distribution is farther from the null distribution, making it easier to detect the difference. Cohen's d = 0.20 is considered small and requires very large samples to detect reliably, while d = 0.80 is large and detectable even with modest sample sizes.