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.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.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.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.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.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.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.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.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.