Keyboard shortcuts

Press ← or → to navigate between chapters

Press S or / to search in the book

Press ? to show this help

Press Esc to hide this help

Analysis reference: every statistical test

One entry per analysis kind: when to use it, the tables it accepts, its options (JSON keys of the spec, with defaults; every key may be left out), what it checks, what the results sheet contains, the method it rests on, and a worked example. The general rules (how missing, excluded and summary values are handled, the assumption-check policy, the sentence format) are in METHODS.md, Results sheets.

Every sheet has: assumption checks (shown first), summary sentences, a methods line, typed sections, and a checklist of what the analysis assumes and cannot tell you. columns are flat column indices (the X column, when there is one, is 0); data sets are named by any of their subcolumns. An empty columns means “the first data sets” (or all, as stated). Multiple-comparison requests have the shape {"method": {"name": "tukey" | "dunnett" (+ "control") | "sidak" | "holm" | "bonferroni" | "dunn" | "benjamini_hochberg"}, "comparisons": {"kind": "all_pairs" | "vs_control" (+ "control") | "selected" (+ "pairs")}}.

The default graph family is what CreateGraph picks for an analysis when family is empty or "auto".

Descriptive statistics (descriptive)

How to get descriptive statistics in Dioptra (mean, SD, SEM, confidence interval of the mean, median, quartiles): select a table, press Analyze (Ctrl-Shift-A) and choose Descriptive statistics.

  • When: describe each data set (n, mean, SD, SEM, CI of the mean, quartiles, range, CV, geometric mean).
  • Tables: column, XY, grouped, variables, nested.
  • Options: columns [] (all), ci_level 0.95, percentiles [] (extra, 0–100).
  • Checks: values used (text and excluded cells counted); independence and normality stated, not tested.
  • Outputs: Descriptive statistics table. Graph: column.
  • Method: descriptive; quartiles by the (n + 1)p rule.
  • Example:
    • Data: PlantGrowth ctrl (n = 10).
    • Result: M = 5.032, SD = 0.5831, 95% CI [4.615, 5.449].
    • Median 5.155, quartiles by Prism’s rule.
    • Checks: every value used.

t test (unpaired, Welch, paired, one-sample) (t_test)

How to run a t test in Dioptra: enter the two groups as data sets of a column table (one row per subject for a paired test), press Analyze (Ctrl-Shift-A) and choose t test, then pick Welch, unpaired, paired, ratio paired or one-sample.

  • When: compare two means (unpaired or paired), a ratio of paired values, or one mean with a hypothetical value.
  • Tables: column, variables, nested.
  • Options: columns (first two data sets), variant "welch" (also "unpaired" = Student, "paired", "ratio_paired", "one_sample"), mu 0, alternative "two_sided" ("greater": the first data set is larger), ci_level 0.95.
  • Checks: values used (pairs dropped for a missing side), sample size, normality of each group / the paired differences / the log ratios, equal variances (informational for Welch), outliers (Grubbs note), effective pairing (correlation of the pairs), independence. Unpaired and one-sample tests also run from mean/SD/N.
  • Outputs: Descriptive, Test (t, df, two-sided P, one-sided P with its direction), Difference (estimate, SE, CI), Effect size (Cohen’s d, Hedges’ g with approximate CIs, R²), Normality, Equal variances, Ratio (ratio paired), Pairing. Brackets: the two groups. Graph: column (unpaired, one-sample), paired preset (paired): bars with a line per subject.
  • Method: ttest.
  • Example:
    • Data: the sleep data, drug1 and drug2 as columns, paired by row.
    • Paired: the mean of the differences was 1.6 (95% CI 0.7 to 2.5), t(9) = 4.06, p = .003, Hedges’ g = 1.17.
    • Welch (as unpaired groups): 1.6 (95% CI -0.2 to 3.4), t(17.8) = 1.86, p = .079.
    • The pairing removes the between-subject scatter: same difference, much narrower CI.

Mann–Whitney test (mann_whitney)

How to run a Mann–Whitney test in Dioptra: enter the two groups as data sets of a column table, press Analyze (Ctrl-Shift-A) and choose Mann–Whitney test.

  • When: two unpaired groups, no assumption of Gaussian distributions.
  • Tables: column, variables.
  • Options: columns (first two), alternative "two_sided", exact null (automatic: exact without ties up to n₁n₂ = 10,000; true forces exact, false asymptotic), ci_level 0.95.
  • Checks: values used, sample size, similar shapes (spread, by Brown–Forsythe), exact or approximate P, independence. Not possible from summary data.
  • Outputs: Descriptive (medians, quartiles), Test (U, U₁, rank sums, z, P), Difference (Hodges–Lehmann shift with Moses CI and achieved level), Effect size (rank-biserial r), Equal variances. Graph: box with a bracket.
  • Method: mannwhitney.
  • Example:
    • Data: sleep drug1 against drug2 as independent groups.
    • The Hodges–Lehmann shift was 1.4 (95% CI -0.1 to 3.6), U = 25.5, p = .069.
    • Medians 1.75 and 0.35; ties, so P is the normal approximation.
    • Check “Exact or approximate P” is a caution.

Wilcoxon signed-rank test (wilcoxon)

How to run a Wilcoxon signed-rank test in Dioptra: enter the paired values as two data sets of a column table, one subject per row, press Analyze (Ctrl-Shift-A) and choose Wilcoxon signed-rank test.

  • When: paired values (two columns) or one column against a hypothetical median, no Gaussian assumption.
  • Tables: column, variables, nested.
  • Options: columns (one: against mu; two: paired), mu 0, alternative "two_sided", ci_level 0.95.
  • Checks: values used, sample size (6 pairs), symmetric differences (skewness), exact or approximate P, independence.
  • Outputs: Descriptive (medians of each column and of the differences), Test (W+, W−, W, zeros dropped, z, P), Pseudo-median (Hodges–Lehmann with CI). Graph: the paired preset (bars with connecting lines) (paired) or box.
  • Method: wilcoxon.
  • Example:
    • Data: sleep, paired by row.
    • The Hodges–Lehmann median of the differences was 1.3 (95% CI 0.8 to 2.8).
    • W+ = 45, W− = 0, p = .008 (normal approximation: the differences have ties).
    • Symmetry check passes.

One-way ANOVA (one_way_anova)

How to run a one-way ANOVA in Dioptra: enter each group as a data set of a column table, press Analyze (Ctrl-Shift-A) and choose One-way ANOVA, and pick the multiple comparisons.

  • When: three or more independent groups, compare means.
  • Tables: column, nested.
  • Options: columns [] (all), post_hoc Tukey all pairs (null for none), welch false, brown_forsythe false.
  • Checks: values used, sample size, normality of the residuals, equal variances (Brown–Forsythe; informational with Welch), outliers, independence. Runs from mean/SD/N (exact), with Bartlett for the variances.
  • Outputs: Descriptive, ANOVA table (SS, df, MS, F, P), tests not assuming equal variances (Welch, Brown–Forsythe), Effect size (η², ω², Cohen’s f), multiple comparisons (Comparison, mean difference, CI, q or t, unadjusted and adjusted P, significant, asterisks), Normality, Equal variances. Tukey for all pairs, Dunnett for a control, Holm–Šidák for selected pairs, Šidák/Bonferroni/Benjamini–Hochberg on request. Brackets: every comparison (up to six; else the significant ones). Graph: column.
  • Method: anova, posthoc.
  • Example:
    • Data: PlantGrowth (ctrl, trt1, trt2; 10 each).
    • F(2, 27) = 4.85, p = .016, η² = .26 (ω² = .20).
    • Tukey: trt1 vs. trt2 differs (mean difference -0.87, 95% CI -1.56 to -0.17, p = .012).
    • The graph carries three brackets: p = .391, p = .198, p = .012.

Repeated-measures ANOVA (repeated_measures_anova)

How to run a repeated-measures one-way ANOVA in Dioptra: enter one subject per row and one condition per data set of a column table, press Analyze (Ctrl-Shift-A) and choose Repeated-measures one-way ANOVA.

  • When: each row is one subject measured under every condition (columns).
  • Tables: column.
  • Options: columns [] (all), gg_correction true, post_hoc all pairs.
  • Checks: values used (incomplete rows dropped, counted), sample size, sphericity (Mauchly; pass when corrected), normality of the residuals, independence of subjects.
  • Outputs: Descriptive, ANOVA table (treatment, subjects, residual, total), corrected and uncorrected tests (none, Greenhouse–Geisser, Huynh–Feldt, lower bound, with ε), Sphericity (Mauchly W, χ², df, P), Effect size (partial η²), paired multiple comparisons (paired t tests with Holm–Šidák, or the adjustment asked; CIs for Bonferroni and Šidák), Normality. Graph: the paired preset (bars with connecting lines) with brackets.
  • Method: anova rm_anova, posthoc p_adjust.
  • Example:
    • Data: 6 subjects × Pre, Mid, Post.
    • Greenhouse–Geisser: F(1.53, 7.65) = 61.37, p < .001, partial η² = .92, ε = .77.
    • Every pair differs after Holm–Šidák (largest adjusted p = .007).
    • Sphericity passes (corrected P in use).

Two-way ANOVA (two_way_anova)

How to run a two-way ANOVA in Dioptra: put one factor in the rows and the other in the data sets of a grouped table, replicates in subcolumns, press Analyze (Ctrl-Shift-A) and choose Two-way ANOVA.

  • When: two factors: rows of a grouped table (factor A) and its data sets (factor B), replicates in subcolumns.
  • Tables: grouped.
  • Options: ss_type "iii" (also "i", "ii"), post_hoc null (any request compares the cell means within each row on the pooled residual variance: Tukey for all pairs, else the adjustment named), repeated null ("rows": each row’s subcolumn is one subject measured in every data set; "columns": each subcolumn of a data set is one subject measured in every row).
  • Checks: values used, replicates in every cell, normality of the residuals, equal variances across cells, independence; with a repeated factor: sphericity stated (not tested), balance.
  • Outputs: ANOVA table (Source, SS, df, MS, F, P, partial η²) of the chosen type, Cell means, within-row comparisons, Normality, Equal variances. The interaction sentence comes first. With a repeated factor: the split-plot table (interaction, repeated factor, between factor, subjects, residual). Graph: column (grouped).
  • Method: anova two_way_anova; the split-plot partition is the standard one for one between and one within factor (sequential with unequal groups).
  • Example:
    • Data: 2 rows × 2 data sets × 3 replicates.
    • Interaction F(1, 8) = 8.02, p = .022: the column effect depends on the row.
    • Row factor F(1, 8) = 18.69, p = .003; column factor F(1, 8) = 72.20, p < .001.
    • Tukey within rows: B exceeds A in both rows (p = .004 and p < .001).

Kruskal–Wallis test (kruskal_wallis)

How to run a Kruskal–Wallis test in Dioptra: enter each group as a data set of a column table, press Analyze (Ctrl-Shift-A) and choose Kruskal–Wallis test.

  • When: three or more independent groups, no Gaussian assumption.
  • Tables: column, nested.
  • Options: columns [] (all), dunn true.
  • Checks: values used, chi-square approximation (groups of 5 or more), similar shapes stated, independence.
  • Outputs: Descriptive (medians, quartiles, mean ranks), Test (H, df, P, ε², tie correction), Dunn’s comparisons with Holm adjustment. Graph: box with brackets.
  • Method: anova kruskal_wallis, posthoc dunn_kruskal.
  • Example:
    • Data: PlantGrowth.
    • H(2) = 7.99, p = .018, ε² = .28.
    • Dunn (Holm): trt1 vs. trt2 differs (p = .015).
    • The other two comparisons do not reach adjusted p < .05.

Friedman test (friedman)

How to run a Friedman test in Dioptra: enter one subject per row and one condition per data set of a column table, press Analyze (Ctrl-Shift-A) and choose Friedman test.

  • When: matched rows (subjects) under three or more conditions, no Gaussian assumption.
  • Tables: column.
  • Options: columns [] (all), dunn true.
  • Checks: values used (incomplete rows dropped), chi-square approximation (10 subjects), independence.
  • Outputs: Descriptive (medians, mean ranks), Test (χ², df, P, Kendall’s W, subjects used and dropped), Dunn’s comparisons (Holm). Graph: the paired preset (bars with connecting lines).
  • Method: anova friedman, posthoc dunn_friedman.
  • Example:
    • Data: 6 subjects × Pre, Mid, Post.
    • χ²(2, N = 6) = 12.00, p = .002, Kendall’s W = 1.00 (every subject ranks the conditions alike).
    • Dunn (Holm): Pre vs. Post differs (p = .002).
    • Chi-square approximation flagged (fewer than 10 subjects).

Chi-square test (chi_square)

How to run a chi-square test in Dioptra: enter the counts in a contingency table, press Analyze (Ctrl-Shift-A) and choose Chi-square test.

  • When: association between the rows and columns of a table of counts; goodness of fit to equal proportions for a parts-of-whole table (or a one-column table).
  • Tables: contingency, parts.
  • Options: yates false (2 × 2 only).
  • Checks: counts are whole numbers (the bad cell is named), expected counts (Cochran’s rule, Fisher offered), independence of subjects.
  • Outputs: Observed counts with totals, Expected counts, Test (Pearson χ², Yates, G, and Fisher’s exact P for 2 × 2), Association (Cramér’s V, φ), Adjusted residuals, and for 2 × 2 the relative risk (Katz CI), odds ratio (Woolf CI) and risk difference (Wald CI). Goodness of fit: observed and expected, χ², df, P. Graph: column.
  • Method: contingency.
  • Example:
    • Data: 2 × 2 counts [[12, 5], [7, 15]] (rows = groups, columns = outcome).
    • Risk 0.706 vs. 0.318: relative risk 2.2 (95% CI 1.1 to 4.4).
    • χ²(1, N = 39) = 5.77, p = .016, Cramér’s V = .38; Fisher p = .025 shown alongside.
    • Expected counts pass (smallest 8.28).

Fisher’s exact test (fisher_exact)

How to run Fisher’s exact test in Dioptra: enter the counts in a contingency table, press Analyze (Ctrl-Shift-A) and choose Fisher’s exact test.

  • When: a 2 × 2 table, especially with small counts; r × c tables by the Fisher–Freeman–Halton test within its work limit.
  • Tables: contingency (2 or more data sets).
  • Options: alternative "two_sided" ("greater": odds ratio > 1; 2 × 2 only).
  • Checks: counts are whole numbers, fixed margins stated, independence.
  • Outputs: Observed counts, Test (two-sided and one-sided P, sample and conditional MLE odds ratios with the exact CI), Effect size (relative risk, odds ratio, risk difference). r × c: exact P, probability of the observed table, number of tables, Cramér’s V; a clear message when the table is too large. Graph: column.
  • Method: contingency fisher_exact_2x2, fisher_exact_rxc.
  • Example:
    • Data: the lady tasting tea, [[3, 1], [1, 3]].
    • Two-sided p = .486.
    • Conditional MLE odds ratio 6.41 (95% CI 0.21 to 626).
    • Relative risk 3.0 (95% CI 0.50 to 18.0).

Correlation (Pearson and Spearman) (correlation)

How to compute a correlation in Dioptra: enter the variables in an XY or Multiple variables table, press Analyze (Ctrl-Shift-A) and choose Correlation.

  • When: association between two variables, or a matrix of several.
  • Tables: XY (X with each data set by default), variables (numeric variables), column (data sets paired by row).
  • Options: columns [] (all), method "pearson" (also "spearman", "kendall"), ci_level 0.95.
  • Checks: values used (pairwise deletion counted), sample size, normality of each variable (Pearson), linear or monotonic relationship stated, outliers, independence.
  • Outputs: Correlation table (pair, n, r, CI, r², P, Holm-adjusted P for several pairs), the matrix for more than two variables, Normality. Graph: scatter of the pair, or correlation_matrix.
  • Method: correlation.
  • Example:
    • Data: X = 1…10, Y = 2.1, 3.9, …, 19.7.
    • r(8) = .999 (95% CI .998 to 1.000), p < .001, n = 10.
    • Spearman on request: ρ with the Bonett–Wright CI.
    • Linearity is stated, not tested: look at the scatter plot.

Linear regression (linear_regression)

How to run a simple linear regression in Dioptra: enter X and Y in an XY table, press Analyze (Ctrl-Shift-A) and choose Simple linear regression.

  • When: a straight line through XY data, each data set separately.
  • Tables: XY (replicates are separate points; mean/SD/N rows give their means).
  • Options: datasets [] (all), through_origin false, bands "none" (also "confidence", "prediction", "both", for graphs), ci_level 0.95, residuals false (adds a residuals table).
  • Checks: linearity (runs test), replicates test, normality of the residuals, equal scatter (|residual| against X), influential points (standardized residual, Cook’s distance), X without error stated, independence (Durbin–Watson shown).
  • Outputs: Best-fit values (slope, intercepts with SE, CI, t, P), Goodness of fit (n, R², Sy.x, SS, F, P, Durbin–Watson), Runs test, Replicates test, Normality, Residuals. Graph: scatter with the line and its band (linear and log X).
  • Method: regression simple_linear_regression.
  • Example:
    • Data: X = 1…10, Y = 2.1, 3.9, …, 19.7.
    • Slope 1.99 (95% CI 1.94 to 2.05), Y-intercept 0.060 (95% CI -0.280 to 0.400).
    • R² = .999, F(1, 8) = 7052.15, p < .001.
    • Runs test passes.

Nonlinear regression and curve fitting (dose-response, EC50) (nonlinear_regression)

How to fit a curve in Dioptra, such as a dose-response curve for an EC50: enter X and Y in an XY table, press Analyze (Ctrl-Shift-A) and choose Nonlinear regression (curve fit), and pick an equation.

  • When: fit a model (dose-response, exponential, enzyme kinetics, binding, growth, or a formula) to XY data.
  • Tables: XY.
  • Options: datasets [] (all, each fitted separately), equation {"name": "four_parameter_logistic"} (snake_case names such as one_phase_decay, michaelis_menten, log_inhibitor_variable_slope, Prism names and the aliases 4PL, 3PL, 5PL, line, MM; or {"name": "...", "formula": "Y = A*exp(-K*X) + C"}), weighting "none" (also "relative_y2" = 1/Y², "poisson_y" = 1/Y, "inverse_sd2" = 1/SD² of the replicates), robust false, constraints [] ({"kind": "fixed" | "min" | "max", "param", "value"}, {"kind": "shared", "param"} for a global fit), initial {} (by parameter name), compare_with null (a second equation), profile_ci false, rout_q null (ROUT outlier removal at Q percent), ci_level 0.95, bands "confidence" (for graphs).
  • Checks: values used, convergence (hit constraint, ambiguous, not converged), runs test, replicates test, normality of the residuals, outliers (ROUT when asked, otherwise stated), X as log(concentration) for the log equations, scatter of Y stated, independence.
  • Outputs: Best-fit values (value, SE, CI, profile CI when asked, status, dependency), Derived values (EC50 from LogEC50, half-life, Span…), Goodness of fit (n, df, R², adjusted R², SS, Sy.x, AICc), Convergence, Runs test, Replicates test, Outliers (ROUT), Model comparison (extra-sum-of-squares F test and AICc with probabilities and the preferred model), Normality. Graph: scatter with each curve and its band (linear and log X).
  • Method: nonlinear, equations.
  • Example:
    • Data: 4PL dose-response, 11 log concentrations in duplicate.
    • LogEC50 = -6.45 (95% CI -6.54 to -6.35), so EC50 = 3.58E-7 (95% CI 2.88E-7 to 4.45E-7).
    • HillSlope = 0.75 (95% CI 0.63 to 0.87); R² = .995.
    • Against the fixed-slope model: F(1, 18) = 14.52, p = .001; AICc prefers the variable slope (99.2%).

Normality tests (Shapiro–Wilk, D’Agostino) (normality)

How to test for normality in Dioptra: select a table, press Analyze (Ctrl-Shift-A) and choose Normality tests.

  • When: look at the distribution of each data set.
  • Tables: column, XY, grouped, variables, nested.
  • Options: columns [] (all), tests ["shapiro_wilk", "dagostino_pearson"] (also "anderson_darling", "kolmogorov_smirnov" = Lilliefors).
  • Checks: values used (tests that cannot run are named), power of the tests (n < 8 or n > 500), what the tests mean.
  • Outputs: Normality tests (data set, test, n, statistic, P, passed), Descriptive (mean, SD, skewness, excess kurtosis). Graph: qq.
  • Method: normality.
  • Example:
    • Data: PlantGrowth.
    • ctrl: Shapiro–Wilk W = 0.96, p = .747; D’Agostino–Pearson K² = 0.23, p = .890.
    • All three groups are consistent with a Gaussian distribution.
    • That is absence of evidence, not proof.

Identify outliers (Grubbs, ROUT) (outliers)

How to find outliers in Dioptra: select a table, press Analyze (Ctrl-Shift-A) and choose Identify outliers.

  • When: look for values that may be errors, one data set at a time.
  • Tables: column, XY, grouped, variables, nested.
  • Options: columns [] (all), method {"method": "rout", "q": 1} (Q in percent) or {"method": "grubbs", "alpha": 0.05}.
  • Checks: values used, normality of the values without the flagged ones, decision to exclude (flagged values are never removed).
  • Outputs: Flagged values (data set, row, cell, value), Before and after (n, flagged, mean and SD with and without), Grubbs’ steps, Normality. Graph: strip.
  • Method: outliers.
  • Example:
    • Data: 10.1, 9.8, 10.3, 10.0, 9.9, 10.2, 25, 10.1.
    • ROUT (Q = 1%) flags 25 (row 7); so does Grubbs at α = 0.05.
    • Without it M = 10.1, SD = 0.172 (with it M = 11.9, SD = 5.29).
    • The value stays in the table until you exclude it.

Kaplan–Meier survival analysis (survival)

How to draw Kaplan–Meier survival curves and compare them in Dioptra: enter times as X and events (1) or censoring (0) per group in a survival table, press Analyze (Ctrl-Shift-A) and choose Survival curves (Kaplan–Meier).

  • When: time to an event with censoring, one or more groups.
  • Tables: survival (X = time; each data set 1 = event, 0 = censored).
  • Options: compare "log_rank" (also "gehan_breslow_wilcoxon", which leads the sentence; both are always shown), ci_level 0.95.
  • Checks: values used, event codes (the bad cell is named), number of events, proportional hazards (stated, not tested), uninformative censoring, independence.
  • Outputs: a Kaplan–Meier table per group (time, at risk, events, censored, percent survival, SE, CI), Median survival with the Brookmeyer–Crowley CI, Curve comparison (log-rank, Gehan–Breslow–Wilcoxon, trend for three or more groups), Observed and expected events, Hazard ratio both ways (Mantel–Haenszel and log-rank methods). Graph: kaplan_meier (step curves, censor ticks, CI bands, numbers at risk).
  • Method: survival.
  • Example:
    • Data: Gehan’s leukaemia trial, 6-MP (21 patients, 9 relapses) and placebo (21, 21).
    • Median survival 23 weeks with 6-MP (95% CI 13 to undefined), 8 with placebo (95% CI 4 to 11).
    • Log-rank χ²(1) = 16.79, p < .001.
    • Hazard ratio (6-MP / placebo, Mantel–Haenszel) 0.19 (95% CI 0.09 to 0.43).

ROC curve (roc)

How to draw a ROC curve in Dioptra: enter controls and patients as two data sets of a column table, press Analyze (Ctrl-Shift-A) and choose ROC curve.

  • When: how well a measurement separates patients from controls; choose a cut-off.
  • Tables: column (controls first, then patients), variables (a score variable and a category variable with positive_label).
  • Options: columns (first two), positive_label null, ci_level 0.95.
  • Checks: direction (AUC < 0.5 means the columns are the wrong way round), sample size, representative samples stated, independence.
  • Outputs: Area under the curve (DeLong and Hanley–McNeil SEs and CIs), test of AUC = 0.5, Cut-offs (sensitivity and specificity with Wilson CIs, LR+, LR−, Youden J), Best cut-offs (Youden, closest to (0, 1)). Graph: roc.
  • Method: roc.
  • Example:
    • Data: 10 controls (1.2 … 2.0) and 10 patients (3.4 … 5.2).
    • AUC = .90 (95% CI .77 to 1.00, DeLong), p < .001 against chance.
    • Youden cut-off ≥ 3.3: sensitivity 80.0%, specificity 90.0%.
    • Direction check passes.

Bland–Altman analysis (bland_altman)

How to run a Bland–Altman analysis in Dioptra: enter the two methods as two data sets of a column table, one subject per row, press Analyze (Ctrl-Shift-A) and choose Bland–Altman.

  • When: agreement between two methods measured on the same subjects.
  • Tables: column, variables (two data sets paired by row).
  • Options: columns (first two), method "difference" (also "ratio", "percent_difference"), ci_level 0.95.
  • Checks: values used (unpaired rows dropped), sample size (30 pairs), normality of the differences, proportional bias, acceptable agreement stated, independence.
  • Outputs: Bias and limits of agreement (bias, SD, lower and upper limits, each with CI), Proportional bias (slope of the difference on the mean), Normality. Graph: bland_altman (differences), scatter with bias and limit lines (ratio, percent).
  • Method: agreement bland_altman.
  • Example:
    • Data: the ROC example’s two columns read as methods A and B.
    • Bias (A − B) -1.6 (95% CI -2.3 to -0.9).
    • Limits of agreement -3.4 (95% CI -4.6 to -2.2) to 0.20 (95% CI -0.96 to 1.36).
    • No proportional bias (p = .458).

Principal component analysis (PCA) (pca)

How to run a principal component analysis in Dioptra: enter the variables in a Multiple variables table, press Analyze (Ctrl-Shift-A) and choose Principal component analysis.

  • When: summarise several correlated numeric variables by a few components.
  • Tables: variables.
  • Options: columns [] (all numeric), standardize true (correlation matrix), components null (chosen by Horn’s parallel analysis).
  • Checks: values used (incomplete rows dropped), rows per variable (5 or more), comparable scales when not standardized, linear relationships stated, independence.
  • Outputs: Eigenvalues (% of variance, cumulative %, parallel-analysis 95th percentile, retained), Loadings, Eigenvectors, Scores. Graph: scatter (scores on PC1 and PC2); column gives the scree plot.
  • Method: multivariate.
  • Example:
    • Data: three variables on 10 cases, two of them strongly correlated with each other and negatively with the third.
    • The first component explains 97.1% of the variance.
    • Parallel analysis and Kaiser’s rule both retain one component.