Measure association strength with reliable likelihood testing today. Review significance, direction, and practical effect size. Compare observed patterns using structured counts and clear outputs.
| Scenario | Cell A | Cell B | Cell C | Cell D | Use Case |
|---|---|---|---|---|---|
| Marketing Response | 45 | 30 | 20 | 55 | Campaign response by segment |
| Medical Screening | 60 | 18 | 27 | 49 | Positive result by group |
| Education Study | 35 | 40 | 22 | 63 | Pass outcome by method |
Expected frequency: E = (row total x column total) / grand total
Log likelihood ratio: G = 2 x sum of [O x ln(O / E)]
Signed LLR: sign x sqrt(G)
Effect size: Phi = sqrt(G / N)
Approximate p value for df = 1: derived from the chi-square distribution.
Zero observed cells contribute zero to the summation because the limit of O ln(O/E) tends to zero as O approaches zero.
The log likelihood ratio compares observed cell frequencies with expected frequencies under independence. It is especially useful for categorical outcomes, A/B testing, text mining, and risk screening. Because the statistic grows when observed counts diverge from expected structure, analysts can quantify whether an apparent association is likely meaningful or simply random variation within a 2x2 table.
The calculator reports the G statistic, which is computed as two times the sum of each observed count multiplied by the natural logarithm of observed over expected count. Larger values indicate stronger evidence against independence. In a one degree of freedom table, values above 3.841 are commonly treated as significant at the 5 percent level.
Expected frequencies matter because they define the benchmark model. Each expected count equals row total multiplied by column total, divided by the grand total. Balanced tables often produce smaller deviations, while highly uneven margins can enlarge or dampen cell contributions. Reviewing expected counts beside observed counts helps users identify where the strongest source of model misfit appears.
A significant test does not automatically mean a large practical effect. That is why this calculator also shows signed log likelihood ratio and phi effect size. Signed LLR adds direction by checking which row has the higher proportion in the first column. Phi summarizes strength relative to sample size, helping analysts compare results across similar studies.
Sample size influences interpretation more than many users expect. With large datasets, even modest differences can generate statistically significant G values. With small datasets, meaningful differences may fail to cross the critical threshold. For that reason, professionals review significance, effect size, odds ratio, and the underlying table together instead of relying on a single decision label.
In operations, healthcare, education, and marketing, the calculator supports evidence checks. Teams can compare treatment groups, response segments, pass rates, screening outcomes, or defect categories. Exportable outputs also help with reporting and peer review. When users pair the test with subject expertise and careful data collection, the resulting decision process becomes more transparent and defensible.
It measures how far observed counts depart from the counts expected under independence in a contingency table.
G is often preferred in likelihood-based workflows, model comparison, and information-theoretic analysis, though both tests usually agree for large samples.
They show the benchmark under independence and reveal which cells create the largest contribution to the test statistic.
Yes. Zero observed cells contribute zero to the summation, provided row and column totals still allow valid expected values.
It adds directional context, helping users see which row has the higher first-column proportion while retaining the likelihood-based magnitude.
No. Review sample size, effect size, odds ratio, expected counts, and domain context before making operational or research decisions.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.