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t test
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Why does a t test use the t distribution and ANOVA the F distribution?
How the t, F and chi-square reference distributions are derived from the way each test statistic is built, and what to do when no formula exists.
Read the answer →Skewed data with zeros: is log(x + 1) OK, and what else works?
Why log(x + c) gives results that hinge on an arbitrary constant, and better options for skewed data with zeros: log-link GLMs, two-part models and asinh.
Read the answer →Kolmogorov-Smirnov, t test or Mann-Whitney: which detects a change from a baseline?
What each two-sample test detects, why Kolmogorov-Smirnov misses changes in spread with small samples, and how to compare against a baseline.
Read the answer →Significant ANOVA but no significant pairwise comparisons: how can that happen?
Why a one-way ANOVA F test can reject while every pairwise or Tukey comparison does not (and the reverse), and how far apart their p values can get.
Read the answer →t tests vs the F test in regression: what is the difference?
Why regression output gives a t test for each coefficient and one overall F test, when the two agree exactly, and why they can point in opposite directions.
Read the answer →Why can a CI for Cohen's d include zero when the t test is significant?
Why an effect size interval for Cohen's d can cross zero while the mean difference interval does not, and which d and interval agree with the test.
Read the answer →Why does the Welch t statistic only approximately follow a t distribution?
Why a sum of two weighted chi-square variances breaks the exact t distribution, and how the Satterthwaite fractional df approximate it.
Read the answer →What does r mean when it is reported next to a t test, and how do you turn it into d?
Why papers report an r with a t test, how it is computed from t, what r squared means, how to convert r to Cohen's d, and how to report it in APA style.
Read the answer →t test or Mann-Whitney in small samples: how do you choose?
Why a normality pre-check is a weak way to pick a t test or a rank test with small n, what a power simulation shows, and where permutation tests fit.
Read the answer →Paired vs independent t test: which should you use?
How to tell whether your data are paired, why pairing can turn a hopeless comparison into a clear one, and what goes wrong when you pick the wrong test.
Read the answer →How are alpha and beta (Type I and Type II error rates) related?
Why lowering alpha raises beta, why the trade-off is not linear or a fixed ratio, and what a Bonferroni correction does to power.
Read the answer →How do you compare a short ordinal rating scale between two groups?
t test, Mann-Whitney or chi-square for a 1-4 rating item: what each one tests, how they compare in a simulation, and how to report the result.
Read the answer →t test vs ANOVA with two groups: are the assumptions really different?
Why a pooled t test and a one-way ANOVA on two groups give the same p value, and why their normality assumptions are the same thing stated two ways.
Read the answer →How do you interpret Cohen's d, and are 0.2, 0.5 and 0.8 a real standard?
What Cohen's d says about group overlap, where the 0.2/0.5/0.8 cutoffs come from, why fields differ, and how to report d in APA style.
Read the answer →Does a t test need a minimum sample size?
Why no fixed minimum n makes a t test valid, what small samples really cost (power and robustness), and how to justify your sample size.
Read the answer →Welch vs Student t test: should you just always use Welch?
Why Welch's t test is the safer default for two independent groups, what it costs when variances are equal, and where Mann-Whitney fits.
Read the answer →One-tailed vs two-tailed tests: why not just test the direction the data point to?
Why a two-tailed test is the default, why choosing the tail after seeing the data doubles your false-positive rate, and when a one-tailed test is legitimate.
Read the answer →Log-transforming data: when it helps, and what it changes
Logs turn multiplicative, right-skewed data into additive, roughly symmetric data. Here is when that helps and how results translate back.
Read the answer →What do p values and t values actually mean?
A t value is an effect measured in standard errors; the p value turns it into a tail probability under the null. What both mean, in plain language.
Read the answer →What are degrees of freedom in statistics, really?
Degrees of freedom count how much of your data is left for estimating variability once other quantities are estimated. The idea in plain language.
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