Statistics comparisons
The pairs students mix up, laid side by side: what each one is, when to use it, and the one-sentence way to keep them straight.
Bar graph vs pie chart: which to useBoth display one categorical variable, but a bar graph compares counts by bar length while a pie chart shows each category as a slice of the whole.Bias vs variability: center vs spreadBias is where a sampling distribution is centered, variability is how wide it is. A bigger sample shrinks the spread; a slanted method keeps its center.Blocking vs stratifying: experiments vs samplingBlocking groups similar units in an experiment; stratifying groups similar individuals in a sample. Same idea, opposite settings, with a worked example.Census vs sample survey: all vs a random sampleA census records data from every individual in a population, while a sample survey measures only a random subset and uses it to estimate the whole.Chi-square homogeneity vs independenceHomogeneity and independence run identical chi-square arithmetic. The sampling design decides which name you use, and it changes the hypotheses.Cluster vs stratified sampling: the differenceStrata are alike inside and you sample within every one. Clusters are a mix inside and you take a few whole ones. The reversal, with a worked example.Confidence level vs confidence intervalThe confidence level is the method's long-run capture rate, like 95%. The confidence interval is the actual range of values it produces from your sample.Confounding vs lurking variable: how they differA confounding variable is tied to both the explanatory and response variables; a lurking variable is one the study left out. What AP tests, and how.Convenience vs voluntary response sampleIn a convenience sample the researcher picks whoever is easy to reach. In a voluntary response sample people pick themselves. Each leans for a different reason.Correlation vs regression: how they differCorrelation gives one number, r, for a linear relationship; regression fits a predictive line. See how they connect with a worked example.Discrete vs continuous variables explainedA discrete variable is counted and takes separate values; a continuous variable is measured across an interval. See a table, quick tests, and an example.Dotplot vs histogram vs stemplot: how to chooseAll three graph one quantitative variable in order. A dotplot marks each value, a stemplot keeps the digits, and a histogram bins values into bars.Expected value vs sample mean: parameter vs dataThe expected value is a parameter from a probability distribution; the sample mean is a statistic from data that estimates it. How each is computed.Experiment vs survey: cause versus descriptionAn experiment imposes treatments and can show cause; a survey records answers to questions and shows association only. When each design fits.Explanatory vs response variable: which is xThe explanatory variable goes on the x-axis, the response on the y-axis. Which is which comes from your question. Swapping them changes the line, not r.Frequency vs relative frequency tablesA frequency is a raw count in a category. A relative frequency divides that count by the total, giving a proportion between 0 and 1.Interpolation vs extrapolation in regressionInterpolation predicts inside the range of x-values used to fit a regression line. Extrapolation predicts outside it and grows less reliable.Law of large numbers vs central limit theoremThe law of large numbers says the average settles toward one value; the central limit theorem says its distribution becomes normal. What each promises.Margin of error vs standard errorThe standard error is how much a statistic varies across samples. The margin of error is a critical value times it, so only the margin carries a level.Observed vs expected counts in chi-squareObserved counts are the data you collected; expected counts are what the null hypothesis predicts. The chi-square statistic compares the two.One-tailed vs two-tailed tests explainedA one-tailed test checks one direction; a two-tailed test checks both. See how the alternative hypothesis, p-value, and decision change, with an example.P-value vs alpha (significance level)Alpha is the significance level you set before testing; the p-value comes from your data. Reject the null when the p-value is at or below alpha.Paired vs two-sample t-test: which to useA paired t-test analyzes matched differences; a two-sample t-test compares two independent groups. See when to use each with a worked example.Placebo vs control group: a kind, not a synonymA placebo group is one kind of control group, not another name for it. The containment, the three common control types, and when a placebo is the wrong choice.Point estimate vs interval estimateA point estimate is one number and says nothing about its own precision. An interval estimate reports a range, so the precision travels with it.Population vs sample: key differencesA population is the whole group you want to study; a sample is the subset you measure. Compare parameters and statistics with a worked example.Power vs Type II error (power = 1 - beta)Power is 1 minus beta, so these are one fact stated from opposite ends. Neither is a number for a test: both need a specific true parameter value.Probability vs sampling distributionA probability distribution describes one random variable; a sampling distribution, a statistic from a sample of size n. For a mean: same center, less spread.Random sampling vs random assignmentRandom sampling decides who enters the study and buys generalization. Random assignment decides who gets which treatment and buys cause and effect.Range vs IQR: which spread to reportThe range is the maximum minus the minimum, so one outlier sets it and it grows with sample size. The IQR spans the middle 50%, so no outlier can touch it.Residual vs error: predicted vs true lineA residual is observed minus predicted, computed from the line you fitted. An error is observed minus the true line, which nobody has, so errors are never seen.Sample proportion vs population proportionp is the fixed, unknown proportion in the population; p-hat is the proportion in one sample, and it changes every time you sample. Five samples worked out.Slope vs correlation coefficient in regressionSlope gives the predicted change in y for each one-unit rise in x and carries units. Correlation r is a unit-free strength score from -1 to 1.Standard deviation vs IQR: which spread to useThe IQR uses only the quartiles, so outliers barely move it; the standard deviation uses every value, so one extreme point inflates it. When to use each.Standard deviation vs variance: the differenceVariance is the sum of squared deviations from the mean over n-1; the standard deviation is its square root, in the data's own units.Systematic vs simple random sampleA systematic sample gives every individual an equal chance without being a simple random sample, because the random start fixes the rest. Enumerated example.Undercoverage vs nonresponse: list or no replyUndercoverage means a person was never on the list, so they could not be selected. Nonresponse means they were selected and never answered.Union vs intersection in probabilityUnion means A or B or both and uses the addition rule. Intersection means A and B together, the joint probability that both events happen.With vs without replacement samplingWith replacement returns each pick, so draws stay independent and probabilities stay constant. Without replacement, probabilities change on every draw.z-interval vs t-interval: when to use eachUse a z-interval for a proportion and a t-interval for a mean, since sigma is unknown. Compare the critical values and standard errors with an example.