Population parameters (Greek letters, always referring to the true population value)
| Symbol | Name | Plain English | SPSS label | R output | APA reporting |
|---|---|---|---|---|---|
| μ | mu | Population mean — the true average of the whole population | (not directly reported; appears in "Test Value" for one-sample t) | (implicit in mu = ... argument of t.test) | M = X if you actually know it; otherwise report x̄ |
| σ | sigma | Population standard deviation | rare (used mostly in Z-test macros) | sd argument in pnorm, rnorm | σ = X (italicised Greek) |
| σ² | sigma-squared | Population variance | — | — | σ² = X |
| π | pi | Population proportion | — | — | π (Greek; lowercase) |
| ρ | rho | Population correlation coefficient | — | — | ρ = X |
| β | beta | Population regression slope OR Type II error rate (context-dependent!) | "Beta" (coef), "Power" settings | coefficient estimates; power in pwr package | β = X (regression); 1 − β = power |
| α | alpha | Type I error rate / significance level (chosen in advance; usually 0.05) | "Alpha" in Confidence Interval options | argument in most test functions | α = .05 (no leading zero in APA) |
Sample statistics (Roman letters, computed from your data)
| Symbol | Name | Plain English | SPSS label | R output | APA reporting |
|---|---|---|---|---|---|
| n | n | Sample size (one group) | "N" per group | length(x), n | n = X (italicised, lowercase) |
| N | big-N | Total sample size across all groups | "N" overall | nrow() / sum() | N = X (italicised, uppercase) |
| x̄ | x-bar | Sample mean — your best estimate of μ | "Mean" | mean(x) | M = X (APA uses M; some journals use x̄) |
| s | s | Sample standard deviation — estimate of σ | "Std. Deviation" | sd(x) | SD = X |
| s² | s-squared | Sample variance | "Variance" | var(x) | Report SD not SD² unless specifically asked |
| SE or sx̄ | standard error (of the mean) | How much x̄ varies from sample to sample: s / √n | "Std. Error Mean" | sd(x)/sqrt(length(x)) | SE = X or SEM = X |
| p̂ | p-hat | Sample proportion — estimate of π | "Proportion" | mean(x == 1) | p = X (often; context must distinguish from p-value!) |
| r | r | Pearson correlation (sample estimate of ρ) | "Pearson Correlation" | cor(x, y) | r = .XX (no leading zero when bounded ±1) |
| Q1, Q3 | first / third quartile | 25th and 75th percentiles | "Percentiles 25 / 75" | quantile(x, c(.25, .75)) | Report as median [Q1, Q3] in skewed-data contexts |
| IQR | interquartile range | Q3 − Q1 — robust spread measure | "Interquartile Range" | IQR(x) | IQR = X |
Test statistics
| Symbol | Name | Plain English | SPSS label | R output | APA reporting |
|---|---|---|---|---|---|
| Z | Z or z-score | Distance from mean in standard deviations; follows the standard normal | "Z" in Z-test output | pnorm / qnorm | z = 1.96 (italics, lowercase) |
| t | t or t-statistic | Like Z but accounting for sample-based s instead of σ | "t" | t.test output statistic | t(29) = 2.11 (italicised t, df in parens) |
| χ² | chi-square | Sum of squared, normalized deviations from expected counts | "Chi-Square" | chisq.test output statistic | χ²(1, N = 100) = 0.79 |
| F | F-statistic | Ratio of two variances; used in ANOVA and regression | "F" | anova() output | F(df1, df2) = X |
| df | degrees of freedom | How many values are "free to vary" after constraints | "df" | parameter field in test output | Always report: t(29), F(2, 27) |
| U, W | Mann-Whitney U / Wilcoxon W | Non-parametric test statistics (rank-based) | "Mann-Whitney U" / "Wilcoxon W" | wilcox.test | U = X or W = X |
Probabilities and inference
| Symbol | Name | Plain English | SPSS label | R output | APA reporting |
|---|---|---|---|---|---|
| P(·) | probability | Capital P, a probability in general | "Sig." | p.value | Use p for the p-value specifically |
| p | p-value | P(data this extreme | H₀ is true). NOT P(H₀ is true). | "Sig." or "Sig. (2-tailed)" | p.value | p = .043 (no leading zero); p < .001 for very small |
| H₀ | H-zero / null hypothesis | The "no effect" claim you start out assuming | stated in test-specific dialog | stated in documentation | H0: μ = 0 (subscript zero) |
| H₁ or Ha | H-one / alternative hypothesis | What you'd believe if you reject H₀ | — | — | H1: μ ≠ 0 |
| CI | confidence interval | A range that, under repeated sampling, contains the true parameter X% of the time | "Confidence Interval" | conf.int | 95% CI [1.2, 3.4] — square brackets, no equals sign |
| 1 − β | power | Probability of correctly rejecting a false H₀ | "Power" | pwr package output | "power = 0.80" or in a sample-size calculation |
Effect sizes
| Symbol | Name | Plain English | SPSS label | R output | APA reporting |
|---|---|---|---|---|---|
| d | Cohen's d | Standardised mean difference: (x̄₁ − x̄₂) / spooled. 0.2 small, 0.5 medium, 0.8 large. | available via dialog "Effect size" | effsize::cohen.d | d = 0.53 |
| V | Cramer's V | χ² effect size, 0-1. Uses χ²/(N·df*) where df* = min(r−1, c−1). | "Cramer's V" | vcd::assocstats | Cramer's V = .17 |
| φ | phi | Same as Cramer's V for 2×2 tables; √(χ²/N) | "Phi" | vcd::assocstats | φ = .21 |
| η² | eta-squared | Proportion of variance explained in ANOVA (like R² for a factor) | "Eta Squared" | effectsize::eta_squared | η² = .14 |
| R² | R-squared | Proportion of variance in Y explained by the regression model | "R Square" | summary(lm)$r.squared | R² = .57 |
Epidemiology measures
| Symbol | Name | Plain English | SPSS label | R output | APA / AMA reporting |
|---|---|---|---|---|---|
| OR | odds ratio | Ratio of odds in exposed to odds in unexposed; 1 = no effect | "Odds Ratio" | epitools::oddsratio | OR = 2.1 (95% CI [1.4, 3.3]) |
| RR | relative risk / risk ratio | Ratio of risk in exposed to risk in unexposed; 1 = no effect | "Risk Ratio" | epitools::riskratio | RR = 1.8 (95% CI [1.2, 2.7]) |
| NNT | number needed to treat | 1 / |risk difference| — how many to treat to prevent one event | derived via crosstabs | Epi::NNT | NNT = 25 |
| PPV / NPV | positive / negative predictive value | P(disease | test+); P(no disease | test−) | diagnostic test dialog | epiR::epi.tests | PPV 0.82, NPV 0.96 |
| LR+, LR− | likelihood ratios | Change in odds of disease given test result; prevalence-independent | "Likelihood Ratio" | epiR::epi.tests | LR+ = 12, LR− = 0.08 |
| sens | sensitivity | P(test+ | disease). Property of the test, not the population. | "Sensitivity" | epiR::epi.tests | Sensitivity 89% |
| spec | specificity | P(test− | no disease) | "Specificity" | epiR::epi.tests | Specificity 97% |
A few translation traps
"p" is overloaded. Lowercase p can mean the p-value OR a sample proportion. Read the surrounding sentence, or the unit: a proportion is 0-1 and always has the same interpretation; a p-value is 0-1 but interpreted as "how surprising is the data under H0."
"M" vs "x̄". APA style uses M and SD in-line (italicised Roman). Most textbooks use x̄ and s. Both mean the same thing; match the convention of your venue.
"Beta" is also overloaded. In regression, β is a coefficient (what you estimate). In power analysis, β is the Type II error rate (what you don't want). SPSS's "Beta" column in regression output means the standardised regression coefficient, not the raw one — that's in the "B" column. Three uses of beta in one screen is entirely normal.
"Sig." in SPSS. SPSS displays "Sig." in output tables — this is the two-tailed p-value by default. Always check whether the test is one- or two-tailed before reporting.
"95% CI" assumes two-tailed. A 95% CI corresponds to α = .05 two-tailed. If your hypothesis is directional, the one-sided 95% upper bound is a different (and typically wider) calculation.