Log Rank Test: Formula, Verified Results, Python, R, SPSS and Excel
Log Rank Test is presented as a complete, dataset-grounded survival analysis guide. It explains test the null hypothesis that two groups share the same survival experience under proportional-hazards-style sensitivity, the exact formula, assumptions, verified calculations, interpretation, software workflows, matched charts, reports, workbook, internal links, and publication checks. The verified example uses an explicitly prepared teaching endpoint from the uploaded 649-row dataset.
Overall curves differ strongly
The log-rank comparison produced χ² = 100.244, p < .001. MS contributed 68 of 100 observed events despite having 226 of 649 records, producing substantial separation from GP.
What does Log Rank Test measure?
an overall comparison of observed and expected events across two survival curves
Log Rank Test focuses on an overall comparison of observed and expected events across two survival curves. The estimand must remain separate from related quantities such as ordinary probability, crude event proportion, mean duration, or an unrelated regression coefficient.
Method target
Log Rank Test is selected to test the null hypothesis that two groups share the same survival experience under proportional-hazards-style sensitivity. The method is applied to ordered follow-up times and event indicators, not to a standalone numeric outcome with censoring ignored. The analysis therefore starts from risk sets and event times.
The worked example defines time as absences plus one and the primary event as G3 below 10. For Log Rank Test, these variables are used only to demonstrate an overall comparison of observed and expected events across two survival curves; they are not presented as naturally observed medical survival times.
What it does not establish
The procedure cannot create causality or a real-world failure process from cross-sectional student records. Its defensible output is the method-specific estimate or test under the stated coding, and the log-rank test distributes weight evenly across event times and is most interpretable when group hazards are approximately proportional.
The log-rank test distributes weight evenly across event times and is most interpretable when group hazards are approximately proportional.
When should Log Rank Test be used?
Decision logic before software
Time outcome?
Confirm a meaningful duration from a common origin.
Event defined?
State event=1 and censor=0 unambiguously.
Method target?
Match Log Rank Test to the estimand.
Assumptions?
Audit censoring, risk sets, ties, and model form.
Reportable?
Retain numerical evidence and limitations.
Appropriate use
Choose this method when the research question is genuinely about an overall comparison of observed and expected events across two survival curves and the required assumptions can be defended. It is preferable to a simple mean or binary comparison because it retains event timing and censoring information relevant to sums unweighted observed-minus-expected event differences across pooled event times.
Log Rank Test is especially useful when its specific estimand is more informative than an ordinary mean comparison or binary event analysis that discards follow-up time.
Inappropriate use
Log Rank Test should be selected from its estimand and weighting or model structure, not from the availability of a command. It is unsuitable for paired observations, inconsistent time origins, or a weight chosen only after inspecting which test is significant. The verified equal-weight statistic is chi-square 100.2444 with p about 1.35×10^-23.
Do not publish Log Rank Test output when the matching charts, PDFs, workbook, and dataset describe different definitions or model specifications.
Log Rank Test dataset and variable construction
The exact 649-row teaching structure
The bundled 649-row dataset is used specifically for equal weighting of observed-minus-expected events across pooled failure times. At every pooled failure time, the GP/MS observed count is compared with its hypergeometric expectation using equal weight and a finite-risk-set variance. The prepared endpoint remains a transparent teaching construction rather than natural clinical, mortality, or equipment-failure follow-up.
| Variable | Role | Coding | Audit note |
|---|---|---|---|
| surv_time | Duration | absences + 1 | Positive values from 1 to 33 |
| surv_event | Primary event | 1 when G3 < 10; 0 otherwise | 100 events and 549 censorings |
| school | Group | GP reference; MS comparison | 423 GP and 226 MS records |
| competing cause | Secondary event | failures > 0 among records without the primary event | 51 competing events |
| predictors | Cox covariates | age, parental education, travel/study time, failures, family relationship, free time, school, gender | Ten-term model |
Log Rank Test assumptions
Conditions required for a defensible result
Independent Groups
Log Rank Test requires independent groups. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
A Common Time Origin
Log Rank Test requires a common time origin. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
Non-Informative Censoring Within Groups
Log Rank Test requires non-informative censoring within groups. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
Correct Event/Status Coding
Log Rank Test requires correct event/status coding. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
Adequate Risk Sets At Weighted Event Times
The assumption review for Log Rank Test converts each condition into a check against the prepared records rather than declaring the method assumption-free. For MS, observed events are 68 compared with an expected count of 26.1877 under the equal-survival null. A warning remains visible whenever the event process, censoring, support, weighting, or model form cannot be justified.
Prespecified Weighting Strategy
Log Rank Test requires prespecified weighting strategy. This condition is evaluated against the prepared duration, event coding, group structure, risk sets, and the method-specific result rather than assumed from the word nonparametric or from successful software execution.
Log Rank Test formula and mechanics
Native browser MathML and a plain-language audit trail
Log Rank Test uses this expression to estimate or test an overall comparison of observed and expected events across two survival curves. Every symbol should be linked to a risk set, event count, survival estimate, covariate, distribution parameter, or weight defined in the surrounding text.
Calculation sequence
- Sort positive durations and verify event/censor coding.
- Construct the exact risk set immediately before each event time.
- Calculate the Log Rank Test contribution defined by the formula.
- Accumulate products, sums, likelihood terms, or weighted contrasts as required.
- Attach uncertainty, diagnostics, and a conclusion that matches the estimand.
Formula interpretation
For Formula interpretation, the Log Rank Test review must connect every symbol to a risk set, event count, likelihood term, or model parameter. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 1 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
The displayed expression uses browser-native MathML and ordinary semantic HTML. Its symbols correspond to the risk sets, event counts, weights, coefficients, or distribution parameters defined in this section; no remote rendering script or equation image is required.
Log Rank Test verified results
Values calculated from the included dataset
| Result item | Verified value |
|---|---|
| Weighted observed component | 68.000 |
| Weighted expected component | 26.188 |
| Variance | 17.440 |
| Standardized z | 10.012 |
| Chi-square | 100.244 |
| p-value | < .001 |
How to interpret Log Rank Test
From statistical output to a restrained conclusion
Primary conclusion
Overall curves differ strongly
For Primary conclusion, the Log Rank Test review must translate the numerical result without overstating causality, equivalence, or natural follow-up. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 2 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
Interpretation order
Log Rank Test in Python
Transparent data preparation and reproducible calculations
This Python section reconstructs an overall comparison of observed and expected events across two survival curves from explicit arrays and auditable intermediate tables. Sums unweighted observed-minus-expected event differences across pooled event times, so the code below exposes the quantities that determine the final result.
import numpy as np
import pandas as pd
from scipy.stats import chi2df = pd.read_csv("dataset.csv")
time = pd.to_numeric(df["absences"]).to_numpy(float) + 1
event = (pd.to_numeric(df["G3"]) < 10).to_numpy(int)
ms = df["school"].eq("MS").to_numpy()
score = variance = 0.0
for tj in np.sort(np.unique(time[event == 1])):
risk = time >= tj
fail = (time == tj) & (event == 1)
n, n_ms = risk.sum(), (risk & ms).sum()
d, d_ms = fail.sum(), (fail & ms).sum()
exp_ms = d * n_ms / n
vj = n_ms * (n - n_ms) * d * (n - d) / (n**2 * (n - 1)) if n > 1 else 0
score += d_ms - exp_ms # equal weight at every event time
variance += vj
chisq = score**2 / variance
print(score, variance, chisq, chi2.sf(chisq, 1))
Python verification checklist
Python is used as a transparent calculation route for Log Rank Test, not as a black-box screenshot generator. The standardized score is about 10.0122 before squaring into the one-degree-of-freedom statistic. Arrays and tables behind each chart are saved, and the implementation is checked by attempting to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity.
Only topic-matching URLs from the uploaded register are embedded. When a Python, R, SPSS, or Excel file is absent, the article states that limitation rather than fabricating a filename or borrowing another post’s asset.
Log Rank Test in R
Independent survival-analysis validation
R provides an independent implementation of the same an overall comparison of observed and expected events across two survival curves. The script states status coding, factor references, and the function or manual calculation needed for this method instead of relying on defaults.
library(survival)
df <- read.csv("dataset.csv", stringsAsFactors=FALSE)
df$time <- as.numeric(df$absences) + 1
df$event <- ifelse(as.numeric(df$G3) < 10, 1, 0)
df$group <- ifelse(df$school == "MS", 1, 0)weighted_two_sample <- function(time, event, group, kind="logrank", rho=0, gamma=0) {
event_times <- sort(unique(time[event == 1]))
U <- 0; V <- 0; Sminus <- 1
for (tt in event_times) {
at_risk <- time >= tt
is_event <- time == tt & event == 1
n1 <- sum(at_risk & group == 1); n0 <- sum(at_risk & group == 0)
d1 <- sum(is_event & group == 1); d0 <- sum(is_event & group == 0)
n <- n1 + n0; d <- d1 + d0
if (kind == "breslow") w <- n
else if (kind == "tarone") w <- sqrt(n)
else if (kind == "fh") w <- Sminus^rho * (1-Sminus)^gamma
else w <- 1
expected1 <- d * n1 / n
U <- U + w * (d1 - expected1)
if (n > 1) V <- V + w^2 * n1*n0*d*(n-d)/(n^2*(n-1))
Sminus <- Sminus * (1 - d/n)
}
c(U=U, variance=V, z=U/sqrt(V), chisq=U^2/V,
p=pchisq(U^2/V, df=1, lower.tail=FALSE))
}
weighted_two_sample(df$time, df$event, df$group, kind="logrank")
R validation checklist
For Log Rank Test, the R section is written to reproduce the same estimand and endpoint as the Python and Excel calculations. Equal event-time weighting is most directly aligned with a proportional-hazards alternative. Reference levels and all nondefault options are displayed so the direction cannot change silently.
Log Rank Test in SPSS
Syntax-first setup and output audit
The SPSS workflow separates native procedures from extensions and preserves the event value in saved syntax. It is reviewed against the same dataset counts and interpretation used by the other software sections.
COMPUTE surv_time = absences + 1.
COMPUTE surv_event = (G3 < 10).
VALUE LABELS surv_event 0 'Censored' 1 'Event'.
EXECUTE.
KM surv_time BY school
/STATUS=surv_event(1)
/PRINT TABLE MEAN
/PLOT SURVIVAL HAZARD
/TEST LOGRANK BRESLOW TARONE.
COXREG surv_time WITH age Medu Fedu studytime failures famrel
/STATUS=surv_event(1)
/METHOD=ENTER age Medu Fedu studytime failures famrel
/PRINT=CI(95) GOODFIT SUMMARY.Log Rank Test in Excel
A visible calculation and reconciliation workbook
The Excel workbook exposes the arithmetic behind χ² = (O₁ − E₁)²/V and reconciles selected rows with the programmatic output. It is an auditable calculation, not a black-box result.
Excel step 1
Create one row per unique event time.
Excel step 2
Calculate pooled and group-specific risk sets.
Excel step 3
Calculate observed and expected group events.
Excel step 4
Apply the method-specific weight before summing U and V.
Excel step 5
Use =CHISQ.DIST.RT(U^2/V,1) for the p-value.
Excel controls
For Excel controls, the Log Rank Test review must make the spreadsheet an auditable calculation rather than a decorative download. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 3 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
Log Rank Test charts and chart-specific interpretation
First chart full-width; remaining charts arranged in pairs
The source register controls every embedded image and download. Filename, extension, software label, and topic stem are reconciled before the URL is assigned to Log Rank Test.
Python chart 1 — Log Rank Test
Python chart 1: shows the prepared 1–33 duration distribution, event/censor pattern, and where the weighted two-sample test obtains most of its information. For this topic, the display should be read with the event definition and the fact that sums unweighted observed-minus-expected event differences across pooled event times.
Python chart 2 — Log Rank Test
Python chart 2: summarizes the principal Log Rank Test output and the numerical components behind the reported conclusion. The log-rank comparison produced χ² = 100.244, p < .001. MS contributed 68 of 100 observed events despite having 226 of 649 records, producing substantial separation from GP.
Python chart 3 — Log Rank Test
Python chart 3: examines the diagnostic path most relevant to the assumptions of this weighted two-sample test. The review priority is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; visible structure is a warning rather than decoration.
Python chart 4 — Log Rank Test
Python chart 4: places uncertainty, residuals, weighted contributions, or fitted discrepancies on a distributional scale. It supports the model or test audit but does not replace the natural-scale result or its confidence interval.
Python chart 5 — Log Rank Test
Python chart 5: collects the key verified metrics used in the article, including sample information and the method-specific estimate. Every displayed value must reconcile with dataset.csv and the downloadable Python output.
R chart 1 — Log Rank Test
R chart 1 independently reproduces the prepared duration, event, and censoring structure for Log Rank Test. Read it with the declared event definition before comparing groups or fitted quantities.
R chart 2 — Log Rank Test
R chart 2 presents the benchmark output using R conventions. Its values should agree with the Python calculation after reference levels, tie handling, weighting, and status coding are aligned.
R chart 3 — Log Rank Test
R chart 3 focuses on the diagnostic evidence for Log Rank Test. Visible departures or sparse-tail behavior should trigger a sensitivity analysis rather than a cosmetic interpretation.
R chart 4 — Log Rank Test
R chart 4 displays uncertainty or residual structure on the scale used by the R workflow. It supports the numerical audit but does not replace the natural-scale estimate and its limitation.
R chart 5 — Log Rank Test
R chart 5 consolidates the principal metrics used in the R output. Every annotation must reconcile with dataset.csv, the printed result, and the matched downloadable file.
Log Rank Test diagnostics and sensitivity analysis
Evidence required beyond the primary number
Data diagnostics
Before interpreting the primary result, verify the 649-row count, 100 events, 549 censorings, 1–33 duration range, GP/MS composition, tied times, and missing values. The method-specific review then asks analysts to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity.
Method diagnostics
Diagnostics for Log Rank Test target the failure modes of this procedure rather than offering a generic residual checklist. Crossing curves can cause positive and negative event-time contributions to offset in the final score. The specified review is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; any unresolved problem limits the conclusion before publication.
Sensitivity diagnostics
Compare Log Rank Test with log-rank equal weights, Breslow early risk-set weights, Tarone–Ware square-root weights, Fleming–Harrington prespecified early/late weights. Explain whether the substantive conclusion changes and why.
Full Log Rank Test publication audit
Method-specific checkpoints for content, data, formulas, results, and assets
1. Research estimand
Use research estimand to challenge the draft rather than merely document it. Translate the research question into the specific survival, hazard, incidence, or test quantity being estimated. The relevant technical fact is that the estimator sums unweighted observed-minus-expected event differences across pooled event times, which determines what must be checked in the stored output.
The verified equal-weight statistic is chi-square 100.2444 with p about 1.35×10^-23. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the reader should be told that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
2. Time origin
At time origin, the article must move from terminology to evidence. Identify the starting event and verify that all durations use the same origin. Its defining computation sums unweighted observed-minus-expected event differences across pooled event times, and the audit should show where the required quantities appear in the CSV or derived table.
For MS, observed events are 68 compared with an expected count of 26.1877 under the equal-survival null. That checkpoint is considered complete only when the same value appears in code, table, and interpretation. The robustness review should inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the direction statement remains governed by the fact that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
3. Event and status coding
Event and status coding is reviewed separately from statistical significance. Print the status mapping and reconcile each event total with the CSV. For this weighted two-sample test, the core operation sums unweighted observed-minus-expected event differences across pooled event times; the prose, formula, table, and chart must all describe that same operation.
The standardized score is about 10.0122 before squaring into the one-degree-of-freedom statistic. That checkpoint is considered complete only when the same value appears in code, table, and interpretation. The robustness review should inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the direction statement remains governed by the fact that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
4. Censoring definition
Censoring definition defines the checkpoint for this article. Verify that censoring is represented as status information rather than discarded rows. Because the procedure sums unweighted observed-minus-expected event differences across pooled event times, the reviewer must connect the source rows to that mechanism rather than infer correctness from the software label.
Equal event-time weighting is most directly aligned with a proportional-hazards alternative. Any discrepancy across Python, R, SPSS, or Excel must be traced to definitions or defaults. In addition, inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the reader should be told that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
5. Duration scale
The reviewer should pause at duration scale and reproduce the relevant step. Check positivity, units, transformations, and the observed follow-up range. In this analysis the procedure sums unweighted observed-minus-expected event differences across pooled event times; that mechanism sets the boundary for correct interpretation.
Crossing curves can cause positive and negative event-time contributions to offset in the final score. This evidence is read alongside the checkpoint rather than used as a substitute for it. The recommended diagnostic is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, and the final interpretation should remember that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
6. Risk-set or likelihood construction
At risk-set or likelihood construction, the article must move from terminology to evidence. Show which records enter each denominator or censored likelihood term. Its defining computation sums unweighted observed-minus-expected event differences across pooled event times, and the audit should show where the required quantities appear in the CSV or derived table.
The result is unsigned, so the group curves and observed-minus-expected table identify the poorer-survival direction. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, and it will state clearly that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
7. Ties and discretization
Ties and discretization receives an explicit pass, warning, or fail assessment. Check that discretized follow-up does not silently invoke different tie algorithms. This is necessary because the method sums unweighted observed-minus-expected event differences across pooled event times, and a different construction would answer a different survival question.
The verified equal-weight statistic is chi-square 100.2444 with p about 1.35×10^-23. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, and it will state clearly that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
8. Reference coding
A strong account of reference coding names the decision and shows its consequence. Print factor levels and define the numerator and denominator of every contrast. Since the method sums unweighted observed-minus-expected event differences across pooled event times, hidden defaults at this point would propagate into every later value.
For 8. Reference coding, the Log Rank Test review must record a method-specific publication checkpoint and the evidence required to pass it. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 4 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
9. Missing-data handling
Use missing-data handling to challenge the draft rather than merely document it. Make missing-value handling visible instead of allowing silent listwise deletion. The relevant technical fact is that the estimator sums unweighted observed-minus-expected event differences across pooled event times, which determines what must be checked in the stored output.
The standardized score is about 10.0122 before squaring into the one-degree-of-freedom statistic. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the directional explanation follows the fact that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
10. Dependence and clustering
Dependence and clustering is reviewed separately from statistical significance. Document the independence assumption and any clustering correction. For this weighted two-sample test, the core operation sums unweighted observed-minus-expected event differences across pooled event times; the prose, formula, table, and chart must all describe that same operation.
Equal event-time weighting is most directly aligned with a proportional-hazards alternative. This is the concrete evidence used for the checkpoint. The sensitivity plan is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the narrative must not forget that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
11. Information and event adequacy
This checkpoint asks whether information and event adequacy has been translated into executable analysis. Recalculate event categories and counts directly from the source columns. The method sums unweighted observed-minus-expected event differences across pooled event times; therefore a generic survival-analysis explanation is not enough for this post.
Crossing curves can cause positive and negative event-time contributions to offset in the final score. That result becomes publishable only after its risk-set, likelihood, or coding trail is reconciled. A useful next check is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity. Directional language must remain consistent with the rule that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
12. Tail support
A strong account of tail support names the decision and shows its consequence. Check whether sparse risk sets support the requested estimate or coefficient complexity. Since the method sums unweighted observed-minus-expected event differences across pooled event times, hidden defaults at this point would propagate into every later value.
The result is unsigned, so the group curves and observed-minus-expected table identify the poorer-survival direction. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the directional explanation follows the fact that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
13. Uncertainty interval
The publication test at uncertainty interval is practical: could another analyst rebuild the same result from dataset.csv? Verify the variance formula and avoid intervals based on a neighboring method. That standard matters because this approach sums unweighted observed-minus-expected event differences across pooled event times.
The verified equal-weight statistic is chi-square 100.2444 with p about 1.35×10^-23. This is the concrete evidence used for the checkpoint. The sensitivity plan is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the narrative must not forget that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
14. Null hypothesis and p-value
At null hypothesis and p-value, the article must move from terminology to evidence. Write the exact null hypothesis and keep practical importance separate from significance. Its defining computation sums unweighted observed-minus-expected event differences across pooled event times, and the audit should show where the required quantities appear in the CSV or derived table.
For MS, observed events are 68 compared with an expected count of 26.1877 under the equal-survival null. This evidence is read alongside the checkpoint rather than used as a substitute for it. The recommended diagnostic is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, and the final interpretation should remember that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
15. Effect magnitude
The reviewer should pause at effect magnitude and reproduce the relevant step. Show the size of the modeled difference rather than reporting significance alone. In this analysis the procedure sums unweighted observed-minus-expected event differences across pooled event times; that mechanism sets the boundary for correct interpretation.
For 15. Effect magnitude, the Log Rank Test review must record a method-specific publication checkpoint and the evidence required to pass it. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 5 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
16. Software defaults
Software defaults is reviewed separately from statistical significance. Save the executable command and all defaults needed for an independent rerun. For this weighted two-sample test, the core operation sums unweighted observed-minus-expected event differences across pooled event times; the prose, formula, table, and chart must all describe that same operation.
For 16. Software defaults, the Log Rank Test review must record a method-specific publication checkpoint and the evidence required to pass it. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 6 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
17. Cross-software reconciliation
Treat cross-software reconciliation as an analytical decision. Record package versions, defaults, factor coding, convergence, and tie settings. Here the method sums unweighted observed-minus-expected event differences across pooled event times; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.
Crossing curves can cause positive and negative event-time contributions to offset in the final score. The article should retain this value in a saved table and connect it to its matching chart. Reviewers should also inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, because the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
18. Chart-to-table audit
Use chart-to-table audit to challenge the draft rather than merely document it. Verify that the figure, caption, data table, and method result describe the same run. The relevant technical fact is that the estimator sums unweighted observed-minus-expected event differences across pooled event times, which determines what must be checked in the stored output.
For 18. Chart-to-table audit, the Log Rank Test review must record a method-specific publication checkpoint and the evidence required to pass it. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 7 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
19. Sensitivity specification
A strong account of sensitivity specification names the decision and shows its consequence. Document whether the conclusion survives a method-specific sensitivity analysis. Since the method sums unweighted observed-minus-expected event differences across pooled event times, hidden defaults at this point would propagate into every later value.
The verified equal-weight statistic is chi-square 100.2444 with p about 1.35×10^-23. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, then frame direction according to the principle that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
20. Scientific limitation
A strong account of scientific limitation names the decision and shows its consequence. State what the constructed teaching endpoint cannot establish about a real population. Since the method sums unweighted observed-minus-expected event differences across pooled event times, hidden defaults at this point would propagate into every later value.
For MS, observed events are 68 compared with an expected count of 26.1877 under the equal-survival null. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, while the substantive statement recognizes that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
21. Generalizability boundary
This checkpoint asks whether generalizability boundary has been translated into executable analysis. Keep inference inside the observed design, coding, and follow-up window. The method sums unweighted observed-minus-expected event differences across pooled event times; therefore a generic survival-analysis explanation is not enough for this post.
The standardized score is about 10.0122 before squaring into the one-degree-of-freedom statistic. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, and it will state clearly that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
22. Reproducible record
Reproducible record defines the checkpoint for this article. Audit focus-keyword use, content specificity, and asset ownership before import. Because the procedure sums unweighted observed-minus-expected event differences across pooled event times, the reviewer must connect the source rows to that mechanism rather than infer correctness from the software label.
Equal event-time weighting is most directly aligned with a proportional-hazards alternative. Reproducing that figure from the bundled CSV is required before publication. The diagnostic sequence should inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, while the substantive statement recognizes that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
23. Publication language
The publication test at publication language is practical: could another analyst rebuild the same result from dataset.csv? Preserve the CSV, transformation rules, code, output, metadata, and matched URLs. That standard matters because this approach sums unweighted observed-minus-expected event differences across pooled event times.
Crossing curves can cause positive and negative event-time contributions to offset in the final score. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, then frame direction according to the principle that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
24. SEO and asset consistency
At seo and asset consistency, the article must move from terminology to evidence. Verify that the figure, caption, data table, and method result describe the same run. Its defining computation sums unweighted observed-minus-expected event differences across pooled event times, and the audit should show where the required quantities appear in the CSV or derived table.
For 24. SEO and asset consistency, the Log Rank Test review must record a method-specific publication checkpoint and the evidence required to pass it. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 8 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
25. Event-time weight function
This checkpoint asks whether event-time weight function has been translated into executable analysis. Document the evidence and the consequence of a warning or failure. The method sums unweighted observed-minus-expected event differences across pooled event times; therefore a generic survival-analysis explanation is not enough for this post.
The verified equal-weight statistic is chi-square 100.2444 with p about 1.35×10^-23. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the directional explanation follows the fact that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
26. Crossing survival curves
Before interpreting the principal estimate, resolve crossing survival curves. Define the decision operationally and show how it was checked. The calculation sums unweighted observed-minus-expected event differences across pooled event times, so any mismatch in timing, coding, or risk-set construction can change the target quantity even when the program completes normally.
For MS, observed events are 68 compared with an expected count of 26.1877 under the equal-survival null. This number is retained because it distinguishes the current method from neighboring procedures. The quality-control step is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; the directional explanation follows the fact that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
27. Observed and expected events
Before interpreting the principal estimate, resolve observed and expected events. Print the status mapping and reconcile each event total with the CSV. The calculation sums unweighted observed-minus-expected event differences across pooled event times, so any mismatch in timing, coding, or risk-set construction can change the target quantity even when the program completes normally.
For 27. Observed and expected events, the Log Rank Test review must record a method-specific publication checkpoint and the evidence required to pass it. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 9 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
28. Weighted variance
A strong account of weighted variance names the decision and shows its consequence. Verify the variance formula and avoid intervals based on a neighboring method. Since the method sums unweighted observed-minus-expected event differences across pooled event times, hidden defaults at this point would propagate into every later value.
Equal event-time weighting is most directly aligned with a proportional-hazards alternative. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, then frame direction according to the principle that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
29. Alternative weighting families
A strong account of alternative weighting families names the decision and shows its consequence. Repeat the analysis under a defensible neighboring specification and explain the comparison. Since the method sums unweighted observed-minus-expected event differences across pooled event times, hidden defaults at this point would propagate into every later value.
For 29. Alternative weighting families, the Log Rank Test review must record a method-specific publication checkpoint and the evidence required to pass it. This method sums equally weighted observed-minus-expected events across pooled event times; therefore the editor should inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives. The bundled example supplies the following numerical anchor: The log-rank comparison produced χ² = 100.244, p < .001. Checkpoint 10 passes only when the formula, code output, table, chart caption, and interpretation describe the same event definition and censoring rule.
30. Direction of separation
This checkpoint asks whether direction of separation has been translated into executable analysis. Establish reference coding before assigning better or worse direction. The method sums unweighted observed-minus-expected event differences across pooled event times; therefore a generic survival-analysis explanation is not enough for this post.
The result is unsigned, so the group curves and observed-minus-expected table identify the poorer-survival direction. This evidence is read alongside the checkpoint rather than used as a substitute for it. The recommended diagnostic is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, and the final interpretation should remember that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
31. Multiple weight searches
At multiple weight searches, the article must move from terminology to evidence. Document the evidence and the consequence of a warning or failure. Its defining computation sums unweighted observed-minus-expected event differences across pooled event times, and the audit should show where the required quantities appear in the CSV or derived table.
The verified equal-weight statistic is chi-square 100.2444 with p about 1.35×10^-23. That result becomes publishable only after its risk-set, likelihood, or coding trail is reconciled. A useful next check is to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity. Directional language must remain consistent with the rule that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
32. Proportional-hazards context
Use proportional-hazards context to challenge the draft rather than merely document it. Define the decision operationally and show how it was checked. The relevant technical fact is that the estimator sums unweighted observed-minus-expected event differences across pooled event times, which determines what must be checked in the stored output.
For MS, observed events are 68 compared with an expected count of 26.1877 under the equal-survival null. The numerical record supports a method-specific audit, but it does not remove design limitations. To test robustness, inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity; when stating direction, note that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
33. Early-versus-late evidence
Treat early-versus-late evidence as an analytical decision. Connect this checkpoint to a saved calculation rather than a generic claim. Here the method sums unweighted observed-minus-expected event differences across pooled event times; a reproducible audit therefore records the relevant inputs, intermediate quantities, and settings before accepting the displayed result.
The standardized score is about 10.0122 before squaring into the one-degree-of-freedom statistic. The result is meaningful only within the constructed endpoint and observed follow-up. The audit should inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, then frame direction according to the principle that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
34. Practical weighting target
Use practical weighting target to challenge the draft rather than merely document it. Document the evidence and the consequence of a warning or failure. The relevant technical fact is that the estimator sums unweighted observed-minus-expected event differences across pooled event times, which determines what must be checked in the stored output.
Equal event-time weighting is most directly aligned with a proportional-hazards alternative. The post links this evidence to the formula and saved output rather than repeating generic advice. A defensible review will inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity, and it will state clearly that the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse.
Final Log Rank Test release decision
This draft is released only when its exact formula, event definition, software settings, numerical result, chart captions, download files, and contextual links agree. The central computational mechanism is that it sums unweighted observed-minus-expected event differences across pooled event times. That statement differentiates the article from the other twenty survival posts and prevents a shared template from substituting for method-specific explanation.
The final robustness record directs the editor to inspect proportional-hazards plausibility, crossing curves, event-time contributions, and weighted-test sensitivity. The directional interpretation remains: the chi-square test has no sign, so the survival curves and O minus E table determine which group fares worse. Because the example is built from absences and G3 in a student-performance dataset, publication must keep the teaching-purpose limitation visible and must not recast the endpoint as clinical survival, mortality, equipment failure, or causal evidence.
Log Rank Test compared with related methods
Choose the method by estimand, not menu proximity
| Related method | Comparison question |
|---|---|
| log-rank equal weights | Log-rank equal weights uses equal event-time weights and is the conventional overall curve comparison under proportional-hazards sensitivity. Compare it with the present method by checking the estimand, censor handling, weight or distribution, uncertainty, and practical interpretation; retain Log Rank Test only when an overall comparison of observed and expected events across two survival curves is the actual target. |
| Breslow early risk-set weights | Breslow early risk-set weights gives greatest influence to early times where pooled risk sets are largest. Compare it with the present method by checking the estimand, censor handling, weight or distribution, uncertainty, and practical interpretation; retain Log Rank Test only when an overall comparison of observed and expected events across two survival curves is the actual target. |
| Tarone–Ware square-root weights | Tarone–ware square-root weights provides intermediate early emphasis by using the square root of the pooled risk set. Compare it with the present method by checking the estimand, censor handling, weight or distribution, uncertainty, and practical interpretation; retain Log Rank Test only when an overall comparison of observed and expected events across two survival curves is the actual target. |
| Fleming–Harrington prespecified early/late weights | Fleming–harrington prespecified early/late weights uses rho and gamma to target a planned part of follow-up. Compare it with the present method by checking the estimand, censor handling, weight or distribution, uncertainty, and practical interpretation; retain Log Rank Test only when an overall comparison of observed and expected events across two survival curves is the actual target. |
How to report Log Rank Test
A complete, restrained result statement
Reporting template
“A Log Rank Test analysis used 649 records from dataset(100).csv. Duration was defined as absences plus one, and the event indicator equaled one when G3 was below 10; 100 events and 549 right-censored observations were available. The log-rank comparison produced χ² = 100.244, p < .001. MS contributed 68 of 100 observed events despite having 226 of 649 records, producing substantial separation from GP. The analysis documented event coding, reference groups, risk sets, ties, assumptions, software settings, diagnostics, matching files, and the educational nature of the prepared survival endpoint.”
Include
Avoid calling hazard a probability, treating censoring as missingness, or converting a nonsignificant result into proof of equality. The final sentence should answer the stated estimand and no broader question.
Avoid
A complete report states the prepared time origin, event and censor codes, sample and event counts, group or predictor reference, exact method, formula, estimate or statistic, uncertainty, and the relevant diagnostics. It then gives this result: The log-rank comparison produced χ² = 100.244, p < .001. MS contributed 68 of 100 observed events despite having 226 of 649 records, producing substantial separation from GP.
Log Rank Test downloads
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Log Rank Test frequently asked questions
Method-specific answers for draft review
What does Log Rank Test measure?
Log Rank Test is used for the estimand defined in this article. It sums equally weighted observed-minus-expected events across pooled event times. The interpretation remains conditional on the stated time origin, event code, censoring rule, group or predictor coding, and any distributional or proportionality assumptions.
When should Log Rank Test be used?
Use Log Rank Test when the research objective requires equal weighting of observed-minus-expected events across pooled failure times and the assumptions listed in the article are defensible. The method is inappropriate when a different event type, time emphasis, adjustment strategy, or hazard shape is the scientific target.
What data are used in this Log Rank Test example?
At every pooled failure time, the GP/MS observed count is compared with its hypergeometric expectation using equal weight and a finite-risk-set variance. All values come from the uploaded 649-row file and the disclosed absences-plus-one/G3 event construction.
What is the main Log Rank Test result?
The result is summarized by this verified anchor: The log-rank comparison produced χ² = 100.244, p < .001. It should be read together with the method-specific assumptions, uncertainty, and the teaching-endpoint limitation rather than as a stand-alone causal conclusion.
How does censoring affect Log Rank Test?
Censored records contribute to risk sets or likelihood survival terms until their observed duration. Their handling matters because sums equally weighted observed-minus-expected events across pooled event times; treating censoring as an event or deleting censored rows would change the estimate and usually bias the analysis.
How are ties handled in Log Rank Test?
The prepared durations are integer-valued, so tied times are common. The article states the exact pooled-event rule, weight, or Efron/Breslow approximation used for Log Rank Test, and software results should be reconciled only after those defaults match.
Can Log Rank Test be completed in Python?
Yes. The Python section reconstructs the data fields and exposes the intermediate quantities required for Log Rank Test. It prints the benchmark result and supports the diagnostic task to inspect observed and expected events, variance, curve crossing, proportional-hazards context, and weighted alternatives.
Can Log Rank Test be completed in R?
Yes. The R section uses a method-appropriate survival or competing-risk routine, declares factor references and tie or weighting settings, and provides an independent check of the benchmark result for Log Rank Test.
Can Log Rank Test be completed in SPSS?
SPSS is used only where a native procedure matches Log Rank Test. When no exact native command exists, the post describes SPSS as a data-management, charting, or integration route and does not rename a different test or model.
How does Excel support Log Rank Test?
Excel supports Log Rank Test by displaying observed and expected events, equal-weight score, variance, chi-square, and p-value in visible cells. The matching workbook must reproduce selected Python and R benchmark values and retain the exact event, censoring, group, tie, and interval definitions.
What is the largest reporting mistake for Log Rank Test?
The largest Log Rank Test reporting error is using log-rank as a universal difference test when curves cross or the scientific target is early or late separation. The article also keeps the teaching-endpoint limitation visible so the worked result is not presented as causal or naturally observed survival evidence.
Which internal guides support Log Rank Test?
Start with Breslow Test because it provides the nearest check on equal weighting of observed-minus-expected events across pooled failure times. Use Tarone Ware Test, Fleming Harrington Test, Kaplan Meier Survival Curve to compare weighting, probability scale, model assumptions, or software implementation; each link has a specific methodological role rather than serving as generic navigation.